BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yoshinori Gongyo (The University of Tokyo) DTSTART:20200423T160000Z DTEND:20200423T170000Z DTSTAMP:20260422T225725Z UID:ZAG/1 DESCRIPTION:Title: On a generalized Batyrev's cone conjecture\nby Yoshinori Gongyo (The Unive rsity of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/ZAG/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Hacon (The University of Utah) DTSTART:20200428T160000Z DTEND:20200428T170000Z DTSTAMP:20260422T225725Z UID:ZAG/2 DESCRIPTION:Title: Rece nt progress in the MMP for 3-folds and 4-folds in char p>0\nby Christo pher Hacon (The University of Utah) as part of ZAG (Zoom Algebraic Geometr y) seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ZAG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnaud Beauville (Université de Nice) DTSTART:20200430T150000Z DTEND:20200430T160000Z DTSTAMP:20260422T225725Z UID:ZAG/3 DESCRIPTION:Title: Vect or bundles on Fano threefolds and K3 surfaces\nby Arnaud Beauville (Un iversité de Nice) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbs tract: TBA\n LOCATION:https://researchseminars.org/talk/ZAG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences\, Fudan Univ ersity) DTSTART:20200505T150000Z DTEND:20200505T160000Z DTSTAMP:20260422T225725Z UID:ZAG/4 DESCRIPTION:Title: Mini mal log discrepancies of 3-dimensional non-canonical singularities\nby Chen Jiang (Shanghai Center for Mathematical Sciences\, Fudan University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nCanonical and terminal singularities\, introduced by Reid\, appear naturally in min imal model program and play important roles in the birational classificati on of higher dimensional algebraic varieties. Such singularities are well- understood in dimension 3\, while the property of non-canonical singularit ies is still mysterious. We investigate the difference between canonical a nd non-canonical singularities via minimal log discrepancies (MLD). We sho w that there is a gap between MLD of 3-dimensional non-canonical singulari ties and that of 3-dimensional canonical singularities\, which is predicte d by a conjecture of Shokurov. This result on local singularities has appl ications to global geometry of Calabi–Yau 3-folds. We show that the set of all non-canonical klt Calabi–Yau 3-folds are bounded modulo flops\, a nd the global indices of all klt Calabi–Yau 3-folds are bounded from abo ve.\n LOCATION:https://researchseminars.org/talk/ZAG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Grushevsky (Stony Brook University) DTSTART:20200507T180000Z DTEND:20200507T190000Z DTSTAMP:20260422T225725Z UID:ZAG/5 DESCRIPTION:Title: Geom etry of moduli of cubic threefolds\nby Samuel Grushevsky (Stony Brook University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nThe moduli space of cubic threefolds can be thought of as a GIT quotient of the projective space of all cubic polynomials\, studied via the period map to a ball quotient\, or via the intermediate Jacobians. We describe t he relations between various compactifications of the moduli space of cubi c threefolds that arise in these ways\, and compute their cohomology. Base d on joint works with S. Casalaina-Martin\, K. Hulek\, R. Laza.\n LOCATION:https://researchseminars.org/talk/ZAG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kristin De Vleming (University of California\, San Diego) DTSTART:20200512T160000Z DTEND:20200512T170000Z DTSTAMP:20260422T225725Z UID:ZAG/6 DESCRIPTION:Title: Wall crossing for K-moduli spaces of plane curves\nby Kristin De Vleming ( University of California\, San Diego) as part of ZAG (Zoom Algebraic Geome try) seminar\n\n\nAbstract\nThis talk will focus on compactifications of t he moduli space of smooth plane curves of degree d at least 4. We will re gard a plane curve as a log Fano pair (P2\, aC)\, where a is a rational nu mber\, and study the compactifications arising from K stability for these pairs and log Fano pairs in general. We establish a wall crossing framewo rk to study these spaces as a varies and show that\, when a is small\, the moduli space coming from K stability is isomorphic to the GIT moduli spac e. We describe all wall crossings for degree 4\, 5\, and 6 plane curves a nd discuss the picture for general Q-Gorenstein smoothable log Fano pairs. This is joint work with Kenneth Ascher and Yuchen Liu.\n LOCATION:https://researchseminars.org/talk/ZAG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:John Christian Ottem (University of Oslo) DTSTART:20200514T153000Z DTEND:20200514T163000Z DTSTAMP:20260422T225725Z UID:ZAG/7 DESCRIPTION:Title: Trop ical degenerations and stable rationality\nby John Christian Ottem (Un iversity of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbst ract: TBA\n LOCATION:https://researchseminars.org/talk/ZAG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Mircea Mustață (University of Michigan) DTSTART:20200519T170000Z DTEND:20200519T180000Z DTSTAMP:20260422T225725Z UID:ZAG/11 DESCRIPTION:Title: Min imal exponent and Hodge filtrations\nby Mircea Mustață (University o f Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nI will discuss an invariant of singularities\, Saito's minimal exponent\ , and its connections with various other invariants of singularities. The minimal exponent is a refinement of the log canonical threshold that can b e used to also measure rational hypersurface singularities. This is based on joint work with Mihnea Popa.\n LOCATION:https://researchseminars.org/talk/ZAG/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Zsolt Patakfalvi (École polytechnique fédérale de Lausanne) DTSTART:20200526T170000Z DTEND:20200526T180000Z DTSTAMP:20260422T225725Z UID:ZAG/12 DESCRIPTION:Title: On the Beauville-Bogomolov decomposition in positive characteristic\nby Z solt Patakfalvi (École polytechnique fédérale de Lausanne) as part of Z AG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: I will pres ent a joint with Maciej Zdanowicz towards a positive characteristic versio n of the Beauville-Bogomolov decomposition. Over the complex numbers this decomposition was shown using differential geometry methods in the 70's an d in the 80's. It concerns varieties with trivial canonical bundle\, which we call K-trivial here. The main statement over the complex number is tha t smooth projective K-trivial varieties admit an etale cover which splits as a product of three types of varieties: abelian\, Calabi-Yau and symplec tic. I will present a similar statement in positive characteristic for (we akly) ordinary K-trivial varieties\, the proof of which uses purely positi ve characteristic methods.\n LOCATION:https://researchseminars.org/talk/ZAG/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Roulleau (University of Aix-Marseille) DTSTART:20200521T110000Z DTEND:20200521T120000Z DTSTAMP:20260422T225725Z UID:ZAG/13 DESCRIPTION:Title: On the geometric models of K3 surfaces with finite automorphism group and Pic ard number larger than two\nby Xavier Roulleau (University of Aix-Mars eille) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nVin berg and Nikulin classified K3 surfaces which have finite automorphism gro up and Picard number 4 and 3\,5\,..\,19 respectively. That classification is lattice theoretic\, according to the Neron-Severi group of these surfac es\; there are 118 such lattices. In this talk I will discuss on the geome tric construction of these surfaces (by double coverings or complete inter sections) and describe their (finite) set of (-2)-curves\, which gives the ample cone. Most of the moduli spaces of these K3 surfaces are unirationa l. A part of this talk is based on a joint work with Michela Artebani and Claudia Correa Diesler.\n LOCATION:https://researchseminars.org/talk/ZAG/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Kuznetsova (Higher School of Economics) DTSTART:20200528T140000Z DTEND:20200528T150000Z DTSTAMP:20260422T225725Z UID:ZAG/18 DESCRIPTION:Title: Sex tic double solids\nby Alexandra Kuznetsova (Higher School of Economics ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract : One of the first examples of unirational non-rational threefold was prov ided by Artin and Mumford and it was a double cover of P^3 branched in a n odal quartic surface\, so called quartic double solid.\nThen Endrass studi ed this class of varieties and showed that the example by Artin and Mumfor d gives a unique family of non-rational nodal quartic double solids. I am going to tell about the next interesting class of threefolds --- nodal sex tic double solids. I will describe 4 families of them such that any non-ra tional variety of this type lies in one of those families and explain the proof.\n LOCATION:https://researchseminars.org/talk/ZAG/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Schreieder (Leibniz University) DTSTART:20200602T110000Z DTEND:20200602T120000Z DTSTAMP:20260422T225725Z UID:ZAG/19 DESCRIPTION:Title: Equ ality in the Bogomolov-Miyaoka-Yau inequality in the non-general type case \nby Stefan Schreieder (Leibniz University) as part of ZAG (Zoom Algeb raic Geometry) seminar\n\n\nAbstract\nWe classify all good minimal models of dimension n and with vanishing Chern number $c_1^{n-2}c_2(X)=0$\, which corresponds to equality in the Bogomolov-Miyaoka—Yau inequality in the non-general type case. Here the most interesting case is that of Kodaira d imension n-1\, where any minimal model is known to be good. Our result sol ves completely a problem a Kollar. In dimension three\, our approach toget her with previous work of Grassi and Kollar also leads to a complete solut ion of a conjecture of Kollar\, asserting that on a minimal threefold\, c_ 1c_2 is either zero or universally bounded away from zero. Joint work with Feng Hao.\n LOCATION:https://researchseminars.org/talk/ZAG/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Caucher Birkar (University of Cambridge) DTSTART:20200604T130000Z DTEND:20200604T140000Z DTSTAMP:20260422T225725Z UID:ZAG/20 DESCRIPTION:Title: Geo metry of polarised varieties\nby Caucher Birkar (University of Cambrid ge) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will talk about projective varieties polarised by ample divisors (or more gene rally nef and big divisors) in particular from a birational geometry point of view\, and present some recent results in this direction.\n LOCATION:https://researchseminars.org/talk/ZAG/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Prokhorov (Moscow State University) DTSTART:20200609T153000Z DTEND:20200609T163000Z DTSTAMP:20260422T225725Z UID:ZAG/21 DESCRIPTION:Title: Gen eral elephants for 3-fold extremal contractions\nby Yuri Prokhorov (Mo scow State University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nI will discuss effective results on the classification of ext remal contractions in the 3-dimensional MMP. In particular\, I will presen t some recent result based on joint work with Shigefumi Mori on the existe nce of general elephants.\n LOCATION:https://researchseminars.org/talk/ZAG/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilya Zharkov (Kansas State University) DTSTART:20200611T140000Z DTEND:20200611T150000Z DTSTAMP:20260422T225725Z UID:ZAG/22 DESCRIPTION:Title: Top ological SYZ fibrations with discriminant in codimension 2\nby Ilya Zh arkov (Kansas State University) as part of ZAG (Zoom Algebraic Geometry) s eminar\n\n\nAbstract\nTo date only for K3 surfaces (trivial) and the quint ic threefold (due to M. Gross) the discriminant can be made to be in codim ension two. I will outline the source of the problem and how to resolve it in much more general situations using phase and over-tropical pairs-of-pa nts. Joint project with Helge Ruddat.\n LOCATION:https://researchseminars.org/talk/ZAG/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolaos Tziolas (University of Cyprus) DTSTART:20200616T153000Z DTEND:20200616T163000Z DTSTAMP:20260422T225725Z UID:ZAG/23 DESCRIPTION:Title: Vec tor fields on canonically polarized surfaces\nby Nikolaos Tziolas (Uni versity of Cyprus) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA bstract\nIn this talk I will present some results about the geometry of c anonically polarized surfaces defined over a field of positive characteris tic which have a nontrivial global vector field\, equivalently non reduced automorphism scheme\, and the implications that the existence of such sur faces has in the moduli problem of canonically polarized surfaces.\n LOCATION:https://researchseminars.org/talk/ZAG/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Claire Voisin (Collège de France) DTSTART:20200618T140000Z DTEND:20200618T150000Z DTSTAMP:20260422T225725Z UID:ZAG/24 DESCRIPTION:Title: Tri angle varieties and surface decomposition of hyper-Kahler manifolds\nb y Claire Voisin (Collège de France) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nIn recent years\, new constructions of complete families of polarized hyper-Kahler manifolds have been found starting fro m Fano geometry. These hyper-Kahler manifolds also appear as general defor mations of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will int roduce the notion of surface decomposition for a variety X with a nontrivi al Hodge structure on degree 2 cohomology. I will show that this notion is restrictive topologically\, as it implies Beauville-Fujiki type relations . I will also show the existence of such a surface decomposition for the general hyper-Kahler manifolds mentioned above. This has interesting co nsequences on Beauville's conjecture on the Chow ring of hyper-Kahler mani folds.\n LOCATION:https://researchseminars.org/talk/ZAG/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Polishchuk (University of Oregon) DTSTART:20200623T170000Z DTEND:20200623T180000Z DTSTAMP:20260422T225725Z UID:ZAG/25 DESCRIPTION:Title: Hyp erelliptic limits of quadrics through canonical curves and the super-Schot tky locus\nby Alexander Polishchuk (University of Oregon) as part of Z AG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will describe joint works with Eric Rains and with Giovanni Felder and David Kazhdan. The firs t part will be about a classical topic of quadrics through canonically emb edded curves. We study limiting quadrics as canonical curves approach a hy perelliptic limit. There is a surprizingly simple description of all such limits. I will also discuss the connection to ribbon curves (which are thi ckenings of rational normal curves) and to the blow up of the moduli space of curves at the hyperelliptic locus. In the second part I will talk abou t the super-period map for supercurves and the calculation of its infinite simal variation. This variation is given by a natural Massey product that can be defined for any curve with a theta-characteristic. Combining this w ith the result of part 1 we get some information about the super-Schottky locus.\n LOCATION:https://researchseminars.org/talk/ZAG/25/ END:VEVENT BEGIN:VEVENT SUMMARY:David Mumford (Harvard University and Brown University) DTSTART:20200625T150000Z DTEND:20200625T160000Z DTSTAMP:20260422T225725Z UID:ZAG/26 DESCRIPTION:Title: A m oduli space in the differential geometry world\nby David Mumford (Harv ard University and Brown University) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nThe space of simple closed smooth plane curves is an infinite dimensional manifold and supports a great diversity of Riem annian metrics. They have very diverse curvature properties and even inclu de universal Teichmuller space. I want to talk in particular about a recen t example: modeling 2D waves in water (aka gravity waves) that some believ e explains so-called rogue waves.\nAfter the talk\, we plan to have Q&A se ssion at 16:00 GMT. If you have a question for Prof. Mumford\, let Ivan Ch eltsov know in advance (by e-mail).\n LOCATION:https://researchseminars.org/talk/ZAG/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Izzet Coskun (University of Illinois at Chicago) DTSTART:20200630T150000Z DTEND:20200630T160000Z DTSTAMP:20260422T225725Z UID:ZAG/27 DESCRIPTION:Title: The stabilization of the cohomology of moduli spaces of sheaves on surfaces\nby Izzet Coskun (University of Illinois at Chicago) as part of ZAG (Zo om Algebraic Geometry) seminar\n\n\nAbstract\nThe Betti numbers of the Hil bert scheme of points on a smooth\, irreducible projective surface have be en computed by Gottsche. These numbers stabilize as the number of points t ends to infinity. In contrast\, the Betti numbers of moduli spaces of semi stable sheaves on a surface are not known in general. In joint work with M atthew Woolf\, we conjecture these also stabilize and that the stable numb ers do not depend on the rank. We verify the conjecture for large classes of surfaces. I will discuss our conjecture and provide the evidence for it .\n LOCATION:https://researchseminars.org/talk/ZAG/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Susanna Zimmermann (Université Angers) DTSTART:20200702T100000Z DTEND:20200702T110000Z DTSTAMP:20260422T225725Z UID:ZAG/28 DESCRIPTION:Title: Fin ite quotients of Cremona groups\nby Susanna Zimmermann (Université An gers) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe Cremona group is the group of birational self-maps of the projective space \, and it is very very big. While in dimension 2 over algebraically closed fields there are no finite quotients of this group\, there are many such quotients over non-closed fields and in higher dimension. I will discuss w hy this is and how these quotients come up.\n LOCATION:https://researchseminars.org/talk/ZAG/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Zhuang (MIT) DTSTART:20200707T170000Z DTEND:20200707T180000Z DTSTAMP:20260422T225725Z UID:ZAG/29 DESCRIPTION:Title: K-s tability of Fano varieties via admissible flags\nby Ziquan Zhuang (MIT ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI'll pre sent a general approach to prove the K-stability of explicit Fano varietie s. Among the applications\, we confirm the existence of K\\"ahler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two\, calculate th e stability thresholds of some Fano varieties and provide a counterexample to the Higher Rank Finite Generation conjecture. Based on joint work with Hamid Ahmadinezhad.\n LOCATION:https://researchseminars.org/talk/ZAG/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Harold Blum (University of Utah) DTSTART:20200709T150000Z DTEND:20200709T160000Z DTSTAMP:20260422T225725Z UID:ZAG/30 DESCRIPTION:Title: On properness of K-moduli spaces and destabilizations of Fano varieties\n by Harold Blum (University of Utah) as part of ZAG (Zoom Algebraic Geometr y) seminar\n\n\nAbstract\nK-stability is an algebraic notion that detects when a smooth Fano variety admits a Kahler-Einstein metric. Recently\, the re has been significant progress on constructing moduli spaces of K-polyst able Fano varieties using algebraic methods. One of the remaining open pro blems is to show that these moduli spaces are proper. In this talk\, I wil l discuss work with Daniel Halpern-Leistner\, Yuchen Liu\, and Chenyang Xu \, in which we reduce the properness of such K-moduli spaces to the existe nce of certain optimal destabilization of Fano varieties.\n LOCATION:https://researchseminars.org/talk/ZAG/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Hélène Esnault (Freie Universität Berlin) DTSTART:20200714T140000Z DTEND:20200714T150000Z DTSTAMP:20260422T225725Z UID:ZAG/31 DESCRIPTION:Title: Den sity of arithmetic representations\nby Hélène Esnault (Freie Univers ität Berlin) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra ct\nThe lecture surveys recent work with Moritz Kerz. The motivation is t he conjecture that the Hard-Lefschetz (HL) property holds on smooth proje ctive varieties defined over algebraically closed char. $p>0$ fields for cohomology with values in semi-simple $\\ell$-adic local systems $V$. We know it is true if $V$ comes from geometry (Deligne\, Beilinson-Bernstein- Deligne-Gabber) by Deligne’s theory of weights. In absence of weights\, we proved it if $V$ has rank $1$ and reduced the whole HL conjecture to a density conjecture on arithmetic semi-simple $\\ell$-adic systems on $P^1$ minus $3$ closed points\, which we can prove in rank $2$.\n LOCATION:https://researchseminars.org/talk/ZAG/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Schuett (Leibniz Universität Hannover) DTSTART:20200716T153000Z DTEND:20200716T163000Z DTSTAMP:20260422T225725Z UID:ZAG/32 DESCRIPTION:Title: Rat ional curves on Enriques surfaces\, but only few\nby Matthias Schuett (Leibniz Universität Hannover) as part of ZAG (Zoom Algebraic Geometry) s eminar\n\n\nAbstract\nRational curves play a fundamental role for the stru cture of an Enriques surface. I will first review the general theory befor e focussing on the case of low degree rational curves. To this end\, I wil l discuss joint work with S. Rams (Krakow) which develops an explicit shar p bound on the number of rational curves of given degree relative to the d egree of the surface. The proof builds on a general argument in parallel t o the case of K3 surfaces which allows us to extend bounds of Miyaoka and Degtyarev.\n LOCATION:https://researchseminars.org/talk/ZAG/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Jihun Park (POSTECH) DTSTART:20200721T110000Z DTEND:20200721T120000Z DTSTAMP:20260422T225725Z UID:ZAG/33 DESCRIPTION:Title: Cay ley octads\, plane quartic curves\, Del Pezzo surfaces of degree 2 and dou ble Veronese cones\nby Jihun Park (POSTECH) as part of ZAG (Zoom Algeb raic Geometry) seminar\n\n\nAbstract\nA net of quadrics in the 3-dimension al projective space whose singular members are parametrized by a smooth pl ane quartic curve has exactly eight distinct base points\, called a regula r Cayley octad. It is a classical result that there is a one-to-one corr espondence between isomorphism classes of regular Cayley octads and isomor phism classes of smooth plane quartic curves equipped with even theta-char acteristics. We can also easily observe a one-to-one correspondence betwe en isomorphism classes of smooth plane quartic curves and isomorphism clas ses of smooth Del Pezzo surfaces of degree 2. In this talk\, we set up a o ne-to-one correspondence between isomorphism classes of smooth plane quart ic curves and isomorphism classes of double Veronese cones with 28-singula r points. Also\, we explain how the 36 even theta characteristics of a giv en smooth quartic curve appear in the corresponding double Veronese cone. This is a joint work with Hamid Ahmadinezhad\, Ivan Cheltsov and Constanti n Shramov.\n LOCATION:https://researchseminars.org/talk/ZAG/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruadhai Dervan (University of Cambridge) DTSTART:20200723T150000Z DTEND:20200723T160000Z DTSTAMP:20260422T225725Z UID:ZAG/34 DESCRIPTION:Title: Sta bility of fibrations\nby Ruadhai Dervan (University of Cambridge) as p art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe notion of K-stability of a polarised variety has been heavily studied in recent year s\, due to its link both with moduli theory (one should be able to form mo duli spaces of K-stable varieties) and to Kahler geometry (K-stability sho uld be equivalent to the existence of a constant scalar curvature Kahler m etric on the variety). This story has been particularly successful for Fan o varieties. I will describe a notion of stability for polarised fibration s\, which generalises K-stability of polarised varieties when the base of the fibration is a point\, and slope stability of a vector bundle when the variety is the projectivisation of a vector bundle. I will speculate that one should be able to form moduli spaces of stable fibrations\, much as o ne can form moduli spaces of slope stable vector bundles over a fixed base . The main result\, however\, will be a description of the link with certa in canonical metrics on fibrations. This is joint work with Lars Sektnan.\ n LOCATION:https://researchseminars.org/talk/ZAG/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Pierre Demailly (Université Grenoble Alpes) DTSTART:20200728T153000Z DTEND:20200728T163000Z DTSTAMP:20260422T225725Z UID:ZAG/35 DESCRIPTION:Title: Her mitian-Yang-Mills approach to the conjecture of Griffiths on the positivit y of ample vector bundles\nby Jean-Pierre Demailly (Université Grenob le Alpes) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\n Given a vector bundle of arbitrary rank with ample determinant line bundle on a projective manifold\, we propose a new elliptic system of differenti al equations of Hermitian-Yang-Mills type for the curvature tensor. The sy stem is designed so that solutions provide Hermitian metrics with positive curvature in the sense of Griffiths - and even in the stronger dual Nakan o sense. As a consequence\, if an existence result could be obtained for e very ample vector bundle\, the Griffiths conjecture on the equivalence be tween ampleness and positivity of vector bundles would be settled. We also discuss a new concept of volume for vector bundles.\n LOCATION:https://researchseminars.org/talk/ZAG/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziwen Zhu (University of Utah) DTSTART:20200730T150000Z DTEND:20200730T163000Z DTSTAMP:20260422T225725Z UID:ZAG/36 DESCRIPTION:Title: Equ ivariant K-stability under finite group action\nby Ziwen Zhu (Universi ty of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nEquivariant K-stability is defined via equivariant test configurations. By definition it is weaker than the usual K-stability and for varieties wi th large symmetry\, it is often easier to check equivariant K-stability. F or reductive group action\, it is conjectured that equivariant K-polystabi lity implies K-polystability. In this talk\, I will discuss recent results about equivariant K-stability and present a proof of the conjecture for f inite group action. The talk is based on joint work with Yuchen Liu.\n LOCATION:https://researchseminars.org/talk/ZAG/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Hamid Ahmadinezhad (Loughborough University) DTSTART:20200804T140000Z DTEND:20200804T150000Z DTSTAMP:20260422T225725Z UID:ZAG/37 DESCRIPTION:Title: Bir ational geometry of Fano 3-fold hypersurfaces of higher index\nby Hami d Ahmadinezhad (Loughborough University) as part of ZAG (Zoom Algebraic Ge ometry) seminar\n\n\nAbstract\nI will speak about an approach to birationa l classification of Fano 3-folds\, post MMP. As a part of this general gui deline\, I will highlight some recent results about birational geometry of Fano hypersurfaces of higher index. The latter is a joint work with Ivan Cheltsov and Jihun Park.\n LOCATION:https://researchseminars.org/talk/ZAG/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Marina Logares (Universidad Complutense de Madrid) DTSTART:20200806T150000Z DTEND:20200806T160000Z DTSTAMP:20260422T225725Z UID:ZAG/38 DESCRIPTION:Title: Poi sson and symplectic geometry of the moduli spaces of Higgs bundles\nby Marina Logares (Universidad Complutense de Madrid) as part of ZAG (Zoom A lgebraic Geometry) seminar\n\n\nAbstract\nI will talk about some natural P oisson and symplectic properties of the moduli spaces of Higgs bundles whe n some extra structure\, such as a framing\, is added. This is an overview of various past and ongoing work with I. Biswas\, J. Martens\, A. Peón-N ieto and S. Szabó. I will not assume any previous knowledge on the subjec t.\n LOCATION:https://researchseminars.org/talk/ZAG/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Lazarsfeld (Stony Brook University) DTSTART:20200811T170000Z DTEND:20200811T180000Z DTSTAMP:20260422T225725Z UID:ZAG/39 DESCRIPTION:Title: Cay ley-Bacharach theorems and multiplier ideals\nby Robert Lazarsfeld (St ony Brook University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n \nAbstract\nCayley-Bacharach theorems originate in the classical statement if two plane curves of degrees c and d meet in cd points\, then any cur ve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. Following work of Griffiths and Harri s in the 1970s\, one now sees this as a special case of a general result a bout zero-loci of sections of a vector bundle. I will explain how bringing multiplier ideals into the picture leads (for free) to a variant that all ows for excess vanishing. This is joint work with Lawrence Ein.\n LOCATION:https://researchseminars.org/talk/ZAG/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuchen Liu (Yale University) DTSTART:20200813T150000Z DTEND:20200813T160000Z DTSTAMP:20260422T225725Z UID:ZAG/40 DESCRIPTION:Title: On K-stability of cubic hypersurfaces\nby Yuchen Liu (Yale University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nK-stability of Fano varieties is an algebro-geometric stability condition characterizi ng the existence of K\\"ahler-Einstein metrics. Recent progress on K-stabi lity suggests that it provides a good moduli theory for Fano varieties. In this talk\, I will explain how K-moduli spaces can help us prove K-stabil ity of smooth cubic hypersurfaces in dimension at most 4\, using a local-t o-global volume comparison result. Part of this talk is based on joint wor k with Chenyang Xu.\n LOCATION:https://researchseminars.org/talk/ZAG/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Corti (Imperial College London) DTSTART:20200818T170000Z DTEND:20200818T180000Z DTSTAMP:20260422T225725Z UID:ZAG/41 DESCRIPTION:Title: Smo othing Gorenstein toric affine 3-folds\nby Alessio Corti (Imperial Co llege London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra ct\nI will state a conjecture on the smoothing components of the deformati on space\, and discuss one or more of the following topics: possible strat egies for proving it\, applications to the Fanosearch program\, global and higher dimensional analogs. The talk is based on a recent collaboration w ith Andrea Petracci and Matej Filip.\n LOCATION:https://researchseminars.org/talk/ZAG/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Pagani (University of Liverpool) DTSTART:20200820T150000Z DTEND:20200820T160000Z DTSTAMP:20260422T225725Z UID:ZAG/42 DESCRIPTION:Title: Cla ssifying fine compactified universal Jacobians\nby Nicola Pagani (Univ ersity of Liverpool) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nWe introduce the notion of a fine compactified Jacobian of a no dal curve\, as an arbitrary compact open subspace of the moduli space of r ank-1 torsion-free simple sheaves. We show that fine compactified Jacobian s correspond to a certain combinatorial datum\, which is obtained by only keeping track\, for all sheaves\, of (1) the locus where it fails to be lo cally free\, and (2) its multidegree. This notion generalizes to flat fami lies of curves\, and so does its combinatorial counterpart. When the famil y is the universal family over the moduli space of curves\, we have the fo llowing results: (a) in the absence of marked points\, we can fully classi fy these combinatorial data and deduce that the only fine compactified uni versal Jacobians are the classical ones (which were constructed by Pandhar ipande and Simpson in the nineties) and (b) in the presence of marked poin ts there are exotic (and new) examples that cannot be obtained as compacti fied universal Jacobians associated to a polarization. This is a joint wor k in progress with Jesse Kass.\n LOCATION:https://researchseminars.org/talk/ZAG/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Boehning (University of Warwick) DTSTART:20200825T170000Z DTEND:20200825T180000Z DTSTAMP:20260422T225725Z UID:ZAG/43 DESCRIPTION:Title: Rig id\, not infinitesimally rigid surfaces of general type with ample canonic al bundle\nby Christian Boehning (University of Warwick) as part of ZA G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn the talk I will repo rt on work in progress\, joint with Roberto Pignatelli and Hans-Christian von Bothmer\, that concerns the construction of surfaces of general type w ith ample canonical bundle and Kuranishi space (and possibly also Gieseker moduli space) a non-reduced point. The main tools are configurations of l ines and their incidence schemes as well as the theory of abelian covers d ue to Pardini and others.\n LOCATION:https://researchseminars.org/talk/ZAG/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Berman (Chalmers University of Technology) DTSTART:20200827T100000Z DTEND:20200827T110000Z DTSTAMP:20260422T225725Z UID:ZAG/44 DESCRIPTION:Title: Kah ler-Einstein metrics\, Archimedean Zeta functions and phase transitions\nby Robert Berman (Chalmers University of Technology) as part of ZAG (Zo om Algebraic Geometry) seminar\n\n\nAbstract\nWhile the existence of a uni que Kahler-Einstein metrics on a canonically polarized manifold X was esta blished already in the seventies there are very few explicit formulas avai lable (even in the case of complex curves!). In this talk I will give a no n-technical introduction to a probabilistic approach to Kahler-Einstein me trics\, which\, in particular\, yields canonical approximations of the Kah ler-Einstein metric on X. The approximating metrics in question are expres sed as explicit period integrals and the conjectural extension to the case of a Fano variety leads to some intriguing connections with Zeta function s and the theory of phase transitions in statistical mechanics.\n LOCATION:https://researchseminars.org/talk/ZAG/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Jarod Alper (University of Washington) DTSTART:20200903T170000Z DTEND:20200903T180000Z DTSTAMP:20260422T225725Z UID:ZAG/46 DESCRIPTION:Title: Adv ances in moduli theory\nby Jarod Alper (University of Washington) as p art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe will survey how recent advances in moduli theory allow for a new technique to constru ct projective moduli spaces of objects with potentially non-finite automor phism groups such as sheaves\, complexes or Fano varieties. We will prim arily explore this technique through the lens of the moduli space of vecto r bundles over a smooth curve where the definitions and concepts are most readily internalized. Time permitting\, we will discuss applications to B ridgeland stability and perhaps how this construction technique\, which wo rks now only in characteristic zero\, can be generalized to positive chara cteristic.\n LOCATION:https://researchseminars.org/talk/ZAG/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Höring (Université Côte d'Azur) DTSTART:20200908T100000Z DTEND:20200908T110000Z DTSTAMP:20260422T225725Z UID:ZAG/47 DESCRIPTION:Title: Fan o manifolds such that the tangent bundle is (not) big\nby Andreas Hör ing (Université Côte d'Azur) as part of ZAG (Zoom Algebraic Geometry) se minar\n\n\nAbstract\nLet X be a Fano manifold. While the properties of the anticanonical divisor -KX and its multiples have been studied by many aut hors\, the positivity of the tangent bundle TX is much more elusive. We gi ve a complete characterisation of the pseudoeffectivity of TX for del Pezz o surfaces\, hypersurfaces in the projective space and del Pezzo threefold s. This is joint work with Jie Liu and Feng Shao.\n LOCATION:https://researchseminars.org/talk/ZAG/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Joaquín Moraga (Princeton University) DTSTART:20200910T150000Z DTEND:20200910T160000Z DTSTAMP:20260422T225725Z UID:ZAG/48 DESCRIPTION:Title: Top ology and geometry of Kawamata log terminal singularities\nby Joaquín Moraga (Princeton University) as part of ZAG (Zoom Algebraic Geometry) se minar\n\n\nAbstract\nIn this talk\, we will discuss the topology of Kawama ta log terminal singularities. We show that from the perspective of the fu ndamental group klt singularities are close to quotient singularities. For instance\, the regional fundamental group of a klt singularity of dimensi on n contains a normal abelian subgroup of rank at most n and index at mos t c(n). Then\, we proceed to study geometric implications of the topology of klt singularities. We give a characterization theorem in the case that the abelian part of the fundamental group is large of full rank.\n LOCATION:https://researchseminars.org/talk/ZAG/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Julie Rana (Lawrence University) DTSTART:20200915T150000Z DTEND:20200915T160000Z DTSTAMP:20260422T225725Z UID:ZAG/49 DESCRIPTION:Title: Sin gularities and divisors in the moduli space of surfaces\nby Julie Rana (Lawrence University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nThe KSBA moduli space of stable surfaces (surfaces with slc s ingularities and ample canonical class) is a natural compactification of G ieseker's moduli space of surfaces of general type. In contrast with the m oduli space of curves\, very little is known about the birational geometry of KSBA moduli spaces\; indeed\, there are very few examples of divisors in KSBA moduli spaces. I will give an example of a divisor in the moduli s pace of quintic surfaces corresponding to surfaces with cyclic quotient si ngularities. I also discuss joint work with Giancarlo Urz\\'ua where we gi ve bounds that help to narrow the search.\n LOCATION:https://researchseminars.org/talk/ZAG/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Varilly-Alvarado (Rice University) DTSTART:20200527T150000Z DTEND:20200527T160000Z DTSTAMP:20260422T225725Z UID:ZAG/50 DESCRIPTION:Title: Rat ional curves on K3 surfaces\nby Anthony Varilly-Alvarado (Rice Univers ity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ZAG/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Louis Colliot-Thelene (Université Paris-Sud) DTSTART:20200922T140000Z DTEND:20200922T150000Z DTSTAMP:20260422T225725Z UID:ZAG/51 DESCRIPTION:Title: Zer o-cycles on del Pezzo surfaces\nby Jean-Louis Colliot-Thelene (Univers ité Paris-Sud) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst ract\nLet k be an arbitary field of characteristic zero and X be a smooth\ , projective\, geometrically rational surface. Birational classification o f such surfaces (over k) is due to Enriques\, Manin\, Iskovskikh\, Mori. W e are interested in zero-cycles on such surfaces. In 1974\, Daniel Coray s howed that on a smooth cubic surface X with a closed point of degree prim e to 3 there exists a closed point of degree 1\, 4 or 10. Whether 4 and 10 may be omitted is still an open question. We first show how a combination of generisation\, specialisation\, Bertini theorems and "large" fields a voids considerations of special cases in Coray's argument. For smooth cubi c surfaces X with a rational point\, we show that any zero-cycle of degree at least 10 is rationally equivalent to an effective cycle. We establish analogues of these results for del Pezzo surfaces X of degree 2 and of deg ree 1. This completes the proof that for any geometrically rational surfac e X with a rational point\, there exists an integer N which depends only on the geometry of the surface\, such that any zero-cycle of degree at le ast N is rationally equivalent to an effective zero-cycle. For smooth cubi c surfaces X without a rational point\, we relate the question whether the re exists a degree 3 point which is not on a line to the question whether rational points are dense on a del Pezzo surface of degree 1.\n LOCATION:https://researchseminars.org/talk/ZAG/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Alan Thompson (Loughborough University) DTSTART:20200924T150000Z DTEND:20200924T160000Z DTSTAMP:20260422T225725Z UID:ZAG/52 DESCRIPTION:Title: Mir ror symmetry for fibrations and degenerations\nby Alan Thompson (Lough borough University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nIn a 2004 paper\, Tyurin briefly hinted at a novel relationship between Calabi-Yau mirror symmetry and the Fano-LG correspondence. More sp ecifically\, if one can degenerate a Calabi-Yau manifold to a pair of (qua si-)Fanos\, then one expects to be able to express the mirror Calabi-Yau i n terms of the corresponding Landau-Ginzburg models. Some details of this correspondence were worked out by C. F. Doran\, A. Harder\, and I in a 201 7 paper\, but much remains mysterious. In this talk I will describe recent attempts to better understand this picture\, and how it hints at a broade r mirror symmetric correspondence between degeneration and fibration struc tures. As an example of this correspondence\, I will discuss the question of finding mirrors to certain exact sequences which describe the Hodge the ory of degenerations. The material in this talk is joint work in progress with C. F. Doran.\n LOCATION:https://researchseminars.org/talk/ZAG/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Zarhin (Penn State University) DTSTART:20200929T140000Z DTEND:20200929T150000Z DTSTAMP:20260422T225725Z UID:ZAG/53 DESCRIPTION:Title: Jor dan properties of automorphism groups of algebraic varieties and complex m anifolds\nby Yuri Zarhin (Penn State University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA classical theorem of Jordan a sserts that each finite subgroup of the complex general linear group GL(n) is "almost commutative": it contains a commutative normal subgroup with index bounded by an universal constant that depends only on n. We discuss an analogue of this property for the groups of birational (and biregular) automorphisms of complex algebraic varieties and the groups of bimeromorp hic automorphisms of compact complex manifolds.\n LOCATION:https://researchseminars.org/talk/ZAG/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Burt Totaro (UCLA) DTSTART:20201001T160000Z DTEND:20201001T170000Z DTSTAMP:20260422T225725Z UID:ZAG/54 DESCRIPTION:Title: The Hilbert scheme of points on affine space\nby Burt Totaro (UCLA) as pa rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will discuss the Hilbert scheme of d points in affine n-space\, with some examples. Thi s space has many irreducible components for n at least 3 and has been poor ly understood. For n greater than d\, we determine the homotopy type of th e Hilbert scheme in a range of dimensions. Many questions remain. (Joint w ith Marc Hoyois\, Joachim Jelisiejew\, Denis Nardin\, Maria Yakerson.)\n LOCATION:https://researchseminars.org/talk/ZAG/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Junliang Shen (MIT) DTSTART:20201006T160000Z DTEND:20201006T170000Z DTSTAMP:20260422T225725Z UID:ZAG/55 DESCRIPTION:Title: Coh omology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture< /a>\nby Junliang Shen (MIT) as part of ZAG (Zoom Algebraic Geometry) semin ar\n\n\nAbstract\nWe describe the cohomological structure of the moduli sp ace of stable SL_n Higgs bundles on a curve following the topological mirr or symmetry conjecture of Hausel-Thaddeus. For the approach\, we establish a connection between:\n(a) the moduli space of twisted Higgs bundles by a n effective divisor of degree greater than 2g-2\, and\n(b) the moduli spac e of K_C-Higgs bundles\,\nusing vanishing cycle functors. This allows us t o apply Ngo's support theorem\, which has a simpler form in the case (a) ( by Ngo\, Chaudouard-Laumon\, de Cataldo)\, to the case of (b) which concer ns hyper-Kähler geometries. In particular\, this gives a new proof of the Hausel-Thaddeus conjecture proven previously by Gröchenig-Wyss-Ziegler v ia p-adic integrations. Based on joint work with Davesh Maulik.\n LOCATION:https://researchseminars.org/talk/ZAG/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Timothy Logvinenko (Cardiff University) DTSTART:20201008T153000Z DTEND:20201008T163000Z DTSTAMP:20260422T225725Z UID:ZAG/56 DESCRIPTION:Title: Ske in-triangulated representations of generalised braids\nby Timothy Logv inenko (Cardiff University) as part of ZAG (Zoom Algebraic Geometry) semin ar\n\n\nAbstract\nOrdinary braid group Br_n is a well-known algebraic stru cture which encodes configurations of n non-touching strands (“braids” ) up to continious transformations (“isotopies”). A classical result o f Khovanov and Thomas states that there is a natural categorical action of Br_n on the derived category of the cotangent bundle of the variety of co mplete flags in C^n.\nIn this talk\, I will introduce a new structure: the category GBr_n of generalised braids. These are the braids whose strands are allowed to touch in a certain way. They have multiple endpoint configu rations and can be non-invertible\, thus forming a category rather than a group. In the context of triangulated categories\, it is natural to impose certain relations which result in the notion of a skein-triangulated repr esentation of GBr_n.\nA decade-old conjecture states that there a skein-tr iangulated action of GBr_n on the cotangent bundles of the varieties of fu ll and partial flags in C^n. We prove this conjecture for n = 3. We also s how that any categorical action of Br_n can be lifted to a skein-triangula ted action of GBr_n\, which behaves like a categorical nil Hecke algebra. This is a joint work with Rina Anno and Lorenzo De Biase.\n LOCATION:https://researchseminars.org/talk/ZAG/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana-Maria Castravet (Université de Versailles St-Quentin-en-Yveli nes) DTSTART:20201013T140000Z DTEND:20201013T150000Z DTSTAMP:20260422T225725Z UID:ZAG/57 DESCRIPTION:Title: Blo wn-up toric surfaces with non-polyhedral effective cone\nby Ana-Maria Castravet (Université de Versailles St-Quentin-en-Yvelines) as part of ZA G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will report on recent joint work with Antonio Laface\, Jenia Tevelev and Luca Ugaglia.\nWe cons truct examples of projective toric surfaces whose blow-up at a general poi nt has a\nnon-polyhedral pseudoeffective cone\, both in characteristic 0 a nd in prime characteristic.\nAs a consequence\, we prove that the pseudo-e ffective cone of the Grothendieck-Knudsen moduli space of stable\, n-point ed\, rational stable curves\, is not polyhedral if\nn>=10 in characterist ic 0 and in positive characteristic for an infinite set of primes of posit ive density.\nIn particular\, these moduli spaces are not Mori dream space s even in positive characteristic.\n LOCATION:https://researchseminars.org/talk/ZAG/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandra Di Rocco (KTH) DTSTART:20201015T140000Z DTEND:20201015T150000Z DTSTAMP:20260422T225725Z UID:ZAG/58 DESCRIPTION:Title: Alg ebraic Geometry of Data\nby Sandra Di Rocco (KTH) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIt is often convenient to visu alise algebraic varieties (and hence systems of polynomial equations) by sampling. The key challenge is to have the right distribution and density in order to recover the shape\, i.e the topology of the variety. Bottlenec ks are pairs of points on the variety joined by a line which is normal to the variety at both points. These points play a special role in determinin g the appropriate density of a point-sample. Under suitable genericity ass umptions the number of bottlenecks of an affine variety is finite and we c all it the bottleneck degree. We show that it is determined by (classical) invariants of the variety\, i.e. polar classes. The talk is based on join t work with D. Eklund and M. Weinstein.\n LOCATION:https://researchseminars.org/talk/ZAG/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Gergely Berczi (Aarhus University) DTSTART:20201020T150000Z DTEND:20201020T160000Z DTSTAMP:20260422T225725Z UID:ZAG/59 DESCRIPTION:Title: Non -reductive group actions and hyperbolicity\nby Gergely Berczi (Aarhus University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nNon-reductive reparametrisation group actions play central role in hyper bolicity questions. Using recently developed intersection theory on non-re ductive geometric invariant theory-type quotients and following the strate gy of Demailly\, Siu et al\, last year we completed a proof of the Green-G riffiths-Lang and Kobayashi hyperbolicity conjectures for generic hypersur faces of polynomial degree. We explain elements of the proof. Joint work w ith F. Kirwan.\n LOCATION:https://researchseminars.org/talk/ZAG/59/ END:VEVENT BEGIN:VEVENT SUMMARY:David Mumford (Harvard University and Brown University) DTSTART:20200625T160000Z DTEND:20200625T170000Z DTSTAMP:20260422T225725Z UID:ZAG/60 DESCRIPTION:Title: Q&A with legendary geometers: David Mumford\nby David Mumford (Harvard Un iversity and Brown University) as part of ZAG (Zoom Algebraic Geometry) se minar\n\n\nAbstract\nQ&A with David Mumford (please\, no algebraic geometr y questions). If you want to ask a question you should e-mail it in advanc e to i.cheltsov@ed.ac.uk\n LOCATION:https://researchseminars.org/talk/ZAG/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Liedtke (Technical University of Munich) DTSTART:20200917T150000Z DTEND:20200917T160000Z DTSTAMP:20260422T225725Z UID:ZAG/61 DESCRIPTION:Title: Rat ional curves on K3 surfaces\nby Christian Liedtke (Technical Universit y of Munich) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nWe prove that every complex projective K3 surface contains infinitely r ational curves\, which confirms a folklore conjecture on K3 surfaces. This was previously known for elliptic K3 surfaces (Bogomolov-Tschinkel)\, for very general K3 surfaces (Chen)\, as well as for K3 surfaces of odd Picar d rank (Bogomolov-Hassett-Tschinkel\, Li-Liedtke). We finish this conjectu re by introducing two new techniques: “regeneration” (a sort of conver se to degeneration) and the “marked point trick” (a technique for cont rolled degenerations)\, which allows to treat the missing cases. This is j oint work with Xi Chen and Frank Gounelas.\n LOCATION:https://researchseminars.org/talk/ZAG/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Borisov (Binghamton University) DTSTART:20201022T150000Z DTEND:20201022T160000Z DTSTAMP:20260422T225725Z UID:ZAG/62 DESCRIPTION:Title: Pro jective geometry approach to Jacobian Conjecture\nby Alexander Borisov (Binghamton University) as part of ZAG (Zoom Algebraic Geometry) seminar\ n\n\nAbstract\nacobian Conjecture is one of the oldest unsolved problems i n Algebraic Geometry\, going back to a 1939 paper by Keller. It is infamou s for the large number of incorrect proofs that have been proposed over th e years. In fact\, it is quite possible that the conjecture is false\, esp ecially in higher dimensions. For the past 10-15 years I have been making slow but steady progress in understanding this enigma in dimension two\, u sing classical methods of algebraic geometry of projective surfaces and so me inspiration from the Minimal Model Program. I will explain my approach and where it has led me\, and will also discuss some related conjectures.\ n LOCATION:https://researchseminars.org/talk/ZAG/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Greb (University of Duisburg-Essen) DTSTART:20201027T160000Z DTEND:20201027T170000Z DTSTAMP:20260422T225725Z UID:ZAG/63 DESCRIPTION:Title: Pro jective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor\nby Daniel Greb (University of Duisburg-Essen) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will dis cuss a criterion for the projectivisation of a reflexive sheaf on a klt sp ace to be induced by a projective representation of the fundamental group of the smooth locus. This criterion is then applied to give a characterisa tion of finite quotients of projective spaces and Abelian varieties by Q-C hern class (in)equalities and a suitable stability condition. This stabili ty condition is formulated in terms of a naturally defined extension of th e tangent sheaf by the structure sheaf. I will further examine cases in wh ich this stability condition is satisfied\, comparing it to K-semistabilit y and related notions. This is joint work with Stefan Kebekus and Thomas P eternell.\n LOCATION:https://researchseminars.org/talk/ZAG/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Junyan Cao (Université Côte d'Azur) DTSTART:20201029T140000Z DTEND:20201029T150000Z DTSTAMP:20260422T225725Z UID:ZAG/64 DESCRIPTION:Title: On the Ohsawa-Takegoshi extension theorem\nby Junyan Cao (Université Cô te d'Azur) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\ nAbstract: Since it was established\, the Ohsawa-Takegoshi extension theor em turned out to be a fundamental tool in complex geometry. We establish a new extension result for twisted canonical forms defined on a hypersurfac e with simple normal crossings of a projective manifold with a control on its L^2 norme. It is a joint work with Mihai Paun.\n LOCATION:https://researchseminars.org/talk/ZAG/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Bianca Viray (University of Washington) DTSTART:20201103T170000Z DTEND:20201103T180000Z DTSTAMP:20260422T225725Z UID:ZAG/65 DESCRIPTION:Title: On quadratic points on intersections of two quadrics\nby Bianca Viray (Un iversity of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\n \n\nAbstract\nSpringer's theorem and the Amer-Brumer theorem together impl y that intersections of two quadrics have a rational point if and only if they have a 0-cycle of degree 1. In this talk\, we consider whether this statement can be strengthened in the case when there is no rational point\ , namely when 1) the least degree of a 0-cycle can be 2\, and 2) when this occurs\, whether there is an effective 0-cycle of degree 2. We report on results in this direction\, paying particular attention to the case of lo cal and global fields. This is joint work with Brendan Creutz.\n LOCATION:https://researchseminars.org/talk/ZAG/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiano Spotti (Aarhus University) DTSTART:20201105T130000Z DTEND:20201105T140000Z DTSTAMP:20260422T225725Z UID:ZAG/66 DESCRIPTION:Title: Geo metric aspects of Kaehler-Einstein metrics on klt pairs\nby Cristiano Spotti (Aarhus University) as part of ZAG (Zoom Algebraic Geometry) semina r\n\n\nAbstract\nIn this talk I will discuss about the existence and geome tric properties (e.g.\, tangent cones asymptotics\, metric degenerations\, etc...) of conical Kähler-Einstein metrics on klt pairs.\n LOCATION:https://researchseminars.org/talk/ZAG/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksandr Pukhlikov (University of Liverpool) DTSTART:20201110T150000Z DTEND:20201110T160000Z DTSTAMP:20260422T225725Z UID:ZAG/67 DESCRIPTION:Title: Rat ionally connected rational double covers of primitive Fano varieties\n by Aleksandr Pukhlikov (University of Liverpool) as part of ZAG (Zoom Alge braic Geometry) seminar\n\n\nAbstract\nWe show that for a Zariski general hypersurface $V$ of degree $M+1$ in ${\\mathbb P}^{M+1}$ for $M\\geqslant 5$ there are no Galois rational covers $X\\dashrightarrow V$ with an abeli an Galois group\, where $X$ is a rationally connected variety. In particul ar\, there are no rational maps $X\\dashrightarrow V$ of degree 2 with $X$ rationally connected. This fact is true for many other families of primit ive Fano varieties as well and motivates a conjecture on absolute rigidity of primitive Fano varieties.\n LOCATION:https://researchseminars.org/talk/ZAG/67/ END:VEVENT BEGIN:VEVENT SUMMARY:‪Jürgen Hausen‬ (University of Tübingen) DTSTART:20201112T160000Z DTEND:20201112T170000Z DTSTAMP:20260422T225725Z UID:ZAG/68 DESCRIPTION:Title: Aut omorphisms of k*-surfaces\nby ‪Jürgen Hausen‬ (University of Tüb ingen) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAft er recalling the necessary background on k*-surfaces\, we give a complete description of the automorhpism group of a non-toric rational normal proje ctive k*-surface in terms of isotropy group orders and self intersection n umbers of suitable invariant curves. We also discuss the basic ingredients and ideas of the proof.\n LOCATION:https://researchseminars.org/talk/ZAG/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Michela Artebani (Universidad de Concepcion) DTSTART:20201117T150000Z DTEND:20201117T160000Z DTSTAMP:20260422T225725Z UID:ZAG/69 DESCRIPTION:Title: Cox rings of K3 surfaces\nby Michela Artebani (Universidad de Concepcion) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nGiven a n ormal complex projective variety X with finitely generated divisor class g roup\, its Cox ring R(X) is the Cl(X)-graded algebra whose homogeneous pie ces are Riemann-Roch spaces of divisors of X. This object is particularly interesting when it is finitely generated\, since in such case X can be ob tained as a GIT quotient of an open subset of Spec R(X) by the action of a quasi-torus [1]. Finding a presentation or even a minimal generating set for R(X) is in general a difficult problem\, already in the case of surfac es. In this talk\, after an introduction to the subject\, we will concentr ate on complex projective K3 surfaces\, which are known to have finitely g enerated Cox ring exactly when their automorphism group is finite [2]. We show that the Cox ring can be generated by homogeneous elements whose degr ees are either classes of (-2)-curves\, sums of at most three elements in the Hilbert basis of the nef cone\, or classes of divisors of the form 2(E +E')\, where E\,E' are elliptic curves with E.E'=2. As an application\, we compute Cox rings of Mori dream K3 surfaces of Picard number 3 and 4. Thi s is joint work with C. Correa Deisler\, A. Laface and X. Roulleau [3\,4]. \n\nReferences.\n[1] I. Arzhantsev\, U. Derenthal\, J. Hausen\, and A. Laf ace\, Cox rings\, Cambridge Studies in Advanced Mathematics\, vol. 144\, C ambridge University Press\, Cambridge\, 2015.\n[2] M. Artebani\, J. Hausen \, and A. Laface\, On Cox rings of K3 surfaces\, Compos. Math. 146 (2010)\ , no. 4\, 964–998. arXiv:0901.0369\n[3] M. Artebani\, C. Correa Deisler\ , and A. Laface\, Cox rings of K3 surfaces of Picard number three\, J. Alg ebra 565C (2021)\, 598–626. arXiv:1909.01267\n[4] M. Artebani\, C. Corre a Deisler\, and X. Roulleau\, Mori dream K3 surfaces of Picard number four : projective models and Cox rings. arXiv:2011.00475.\n LOCATION:https://researchseminars.org/talk/ZAG/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Yukari Ito (Kavli IPMU) DTSTART:20201119T100000Z DTEND:20201119T110000Z DTSTAMP:20260422T225725Z UID:ZAG/70 DESCRIPTION:Title: The McKay correspondence\nby Yukari Ito (Kavli IPMU) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe original McKay corresponde nce was observed by John McKay as a correspondence between a finite subgro up G of SL(2\,C) and simple Lie algebra in representation theory and devel oped as a correspondence between the group G and the minimal resolution of the quotient singularity C^2/G in algebraic geometry. In this talk\, I wi ll introduce the McKay correspondence in dimension three and show recent p rogress and open problems.\n LOCATION:https://researchseminars.org/talk/ZAG/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Kazushi Ueda (University of Tokyo) DTSTART:20201124T100000Z DTEND:20201124T110000Z DTSTAMP:20260422T225725Z UID:ZAG/71 DESCRIPTION:Title: Non commutative del Pezzo surfaces\nby Kazushi Ueda (University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: We introduce the notion of noncommutative del Pezzo surfaces\, and show th at a collection of 12-d general vector bundles of certain ranks and degree s on an elliptic curve produces a noncommutative del Pezzo surface of degr ee d. We also define the moduli stack of marked noncommutative del Pezzo s urfaces\, and show that it contains the configuration space of 9-d points in general position on the projective plane as a locally closed substack. This is a joint work in progress with Tarig Abdelgadir and Shinnosuke Okaw a.\n LOCATION:https://researchseminars.org/talk/ZAG/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuji Odaka (Kyoto University) DTSTART:20201126T100000Z DTEND:20201126T110000Z DTSTAMP:20260422T225725Z UID:ZAG/72 DESCRIPTION:Title: On compactifying moduli and degenerations of K-trivial varieties\nby Yuji Odaka (Kyoto University) as part of ZAG (Zoom Algebraic Geometry) seminar \n\n\nAbstract\nSome background review: the KSBA moduli of varieties of am ple canonical classes is interpreted via K-stability resp.\, KE metrics (O ’10\, resp.\, Berman-Guenancia’13). A recent trend since 2012 is to es tablish its Fano analogue\, and study their K-stability itself\, which sti ll continues to be developed by more and more contributors wonderfully. Lu ckily\, in both cases\, K-polystable / KE varieties (should) form projecti ve (compact) moduli schemes.\nHowever\, nevertheless of general K-moduli e xpectation\, such existence of projective moduli of K-polystable/cscK (pol arized) varieties is NOT true “at the boundary”\, even for classical K -trivial / Calabi-Yau cases. Indeed\, as a general theory\, no “canonica l” algebro-geometric compactification theory of moduli of polarized CY v ars seems established. E.g. An idea pursued and fairly developed is to att ach ample extra divisors on the CY vars (to pass to “K:ample”-like sit uations) and take their “log KSBA” compactifications\, but different c hoice of the extra divisors can lead to different log KSBA compactificatio ns.\nIn our talk\, based on our several recent papers (partially j.w.w. Yo shiki Oshima)\, we discuss the possibilities of still getting “canonical (geometric) compactifications” of the moduli of polarized K-trivial / CY varieties and corresponding "canonical limits"\, especially giving mor e explicit conjectures in hyperKahler / K3 case\, with certain confirmatio ns. This involves not only classical AG but also DG of collapsing CY metri cs\, symmetric space theory (Lie\, Cartan\, .. Satake..)\, non-archimedean /tropical geometry\, and some mirror symmetric phenomena. Examples and pic tures will be used for the illustration.\n LOCATION:https://researchseminars.org/talk/ZAG/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Takuzo Okada (Saga University) DTSTART:20201201T100000Z DTEND:20201201T110000Z DTSTAMP:20260422T225725Z UID:ZAG/73 DESCRIPTION:Title: K-s tability of birationally superrigid Fano 3-fold weighted hypersurfaces \nby Takuzo Okada (Saga University) as part of ZAG (Zoom Algebraic Geometr y) seminar\n\n\nAbstract\nFor Fano varieties\, birational superrigidity an d K-stability are completely different notions. On the other hand\, they a re both related to mildness of singularities of (pluri-)anticanonical divi sors/systems. In fact\, it is conjectured that a birational superrigid Fan o variety is K-stable. In my talk I will explain recent results that give a positive answer to the conjecture for Fano 3-fold weighted hypersurfaces . This is a joint work with In-Kyun Kim and Joonyeong Won.\n LOCATION:https://researchseminars.org/talk/ZAG/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Hulya Arguz (Versailles Saint-Quentin-en-Yvelines University) DTSTART:20201203T130000Z DTEND:20201203T140000Z DTSTAMP:20260422T225725Z UID:ZAG/74 DESCRIPTION:Title: Enu merating punctured log Gromov-Witten invariants from wall-crossing\nby Hulya Arguz (Versailles Saint-Quentin-en-Yvelines University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nPunctured log Gromov —Witten invariants of Abramovich—Chen--Gross—Siebert are obtained by counting of stable maps with prescribed tangency conditions (which are al lowed to be negative) relative to a not necessarily smooth divisor. In thi s talk we describe an algorithmic method to compute punctured log Gromov-W itten invariants of log Calabi-Yau varieties\, which are obtained by blowi ng-up of toric varieties along hypersurfaces on the toric boundary. For th is we use tropical geometry and wall-crossing computations. This is joint work with Mark Gross (arxiv:2007.08347).\n LOCATION:https://researchseminars.org/talk/ZAG/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Keiji Oguiso (University of Tokyo) DTSTART:20201208T110000Z DTEND:20201208T120000Z DTSTAMP:20260422T225725Z UID:ZAG/75 DESCRIPTION:Title: Smo oth projective rational varieties with non-finitely generated discrete aut omorphism group\nby Keiji Oguiso (University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ZAG/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Artan Sheshmani (Harvard University Center for Mathematical scienc es and Applications) DTSTART:20201210T150000Z DTEND:20201210T160000Z DTSTAMP:20260422T225725Z UID:ZAG/76 DESCRIPTION:Title: DT invariants from Gerstenhaber-BV structures\, and degeneration technique\nby Artan Sheshmani (Harvard University Center for Mathematical sciences and Applications) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA bstract\nWe discuss Donaldson-Thomas (DT) invariants of torsion sheaves wi th 2 dimensional support on a smooth projective surface in an ambient non- compact Calabi Yau fourfold given by the total space of a rank 2 bundle on the surface. We prove that in certain cases\, when the rank 2 bundle is c hosen appropriately\, the universal truncated Atiyah class of these codime nsion 2 sheaves reduces to one\, defined over the moduli space of such she aves realized as torsion codimension 1 sheaves in a noncompact divisor (th reefold) embedded in the ambient fourfold. Such reduction property of univ ersal Atiyah class enables us to relate our fourfold DT theory to a reduce d DT theory of a threefold and subsequently then to the moduli spaces of s heaves on the base surface. We finally make predictions about modularity o f such fourfold invariants when the base surface is an elliptic K3. There are connections between these invariants and birational properties of the base surface which we will discuss if time permits.\n LOCATION:https://researchseminars.org/talk/ZAG/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Sho Tanimoto (Kumamoto University) DTSTART:20201215T110000Z DTEND:20201215T120000Z DTSTAMP:20260422T225725Z UID:ZAG/77 DESCRIPTION:Title: Rat ional curves on Fano threefolds\nby Sho Tanimoto (Kumamoto University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nMori prov ed that a smooth Fano variety contains a lots of rational curves using fam ous Bend and Break technique. Thus it is natural to study the space of rat ional curves on a smooth Fano variety. Lines and conics on Fano threefolds are well studied\, and one may ask what one can say about higher degree r ational curves. Recently we established Movable Bend and Break for Fano th reefolds claiming that any free curve of high degree breaks into the union of two free curves. A proof is intricate\, and it relies on many properti es of three dimensional MMP such as Mori’s classification of divisorial contractions on smooth projective threefolds. In this talk I would like to explain some aspects of our proof of Movable Bend and Break as well as an application to Batyrev’s conjecture predicting a polynomial growth of t he number of components of bounded degree for the moduli space of rational curves. If time permits\, then I also explain a relation of our study to Geometric Manin’s conjecture which is an inspiration of our study. This is joint work with Roya Beheshti\, Brian Lehmann\, and Eric Riedl.\n LOCATION:https://researchseminars.org/talk/ZAG/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Harder (Lehigh University) DTSTART:20201217T160000Z DTEND:20201217T170000Z DTSTAMP:20260422T225725Z UID:ZAG/78 DESCRIPTION:Title: Log symplectic pairs and mixed Hodge structures\nby Andrew Harder (Lehigh University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nA log symplectic pair is a pair (X\,Y) consisting of a smooth projectiv e variety X and a divisor Y in X so that there is a non-degenerate log 2-f orm on X with poles along Y. I will discuss the relationship between log s ymplectic pairs and degenerations of hyperkaehler varieties\, and how this naturally leads to a class of log symplectic pairs called log symplectic pairs of "pure weight". I will talk about common properties of cohomology rings of log symplectic pairs of pure weight and type III degenerations of hyperkaehler varieties\, in particular\, the fact that both have the curi ous hard Lefschetz' (CHL) property discovered by Hausel and Rodriguez-Vill egas. Finally I will discuss partial results towards proving that in both of these cases\, the CHL property is a consequence of P=W type results. Pa rt of this is based on work with Li\, Shen\, and Yin.\n LOCATION:https://researchseminars.org/talk/ZAG/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Han-Bom Moon (Fordham University) DTSTART:20201222T150000Z DTEND:20201222T160000Z DTSTAMP:20260422T225725Z UID:ZAG/79 DESCRIPTION:Title: Poi nt configurations\, phylogenetic trees\, and dissimilarity vectors\nby Han-Bom Moon (Fordham University) as part of ZAG (Zoom Algebraic Geometry ) seminar\n\n\nAbstract\nIn 2004 Pachter and Speyer introduced the dissimi larity maps for phylogenetic trees and asked two important questions about their relationship with tropical Grassmannian. Multiple authors answered affirmatively the first of these questions\, showing that dissimilarity ve ctors lie on the tropical Grassmannian\, but the second question\, whether the set of dissimilarity vectors forms a tropical subvariety\, remained o pened. In this talk\, we present a weighted variant of the dissimilarity m ap and show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter-Speyer envis ioned. This tropical variety has a geometric interpretation in terms of po int configurations on rational normal curves. This is joint work with Ales sio Caminata\, Noah Giansiracusa\, and Luca Schaffler.\n LOCATION:https://researchseminars.org/talk/ZAG/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Hokuto Uehara (Tokyo Metropolitan University) DTSTART:20201224T100000Z DTEND:20201224T110000Z DTSTAMP:20260422T225725Z UID:ZAG/80 DESCRIPTION:Title: Exc eptional collections on the Hilzebruch surface of degree 2\nby Hokuto Uehara (Tokyo Metropolitan University) as part of ZAG (Zoom Algebraic Geom etry) seminar\n\n\nAbstract\nThe purpose of my talk is to clarify the stru cture of exceptional collections of the derived category of coherent sheav es on the Hirzebruch surface of degree 2 (a special weak del Pezzo surface )\, to the extent it is understood by Orlov and Kuleshov for del Pezzo sur faces.\n (1) First\, we prove that for any exceptional object in it\, one can find an autoequivalence which sends it to an exceptional vector bundle .\nThis result was conjectured by Shinnosuke Okawa and the speaker in 2015 .\n (2) Refining the method of the proof of the above result\, and based o n a deformation argument\, we prove that the braid group on 4 strands acts transitively (up to shifts) on the set of exceptional collections of leng th 4. This is a special case of an old conjecture by Bondal and Polishchuk .\n (3) We also prove that any exceptional collection can be extended to a full exceptional collection.\nMy talk is based on a joint work with Shinn osuke Okawa (Osaka) and Akira Ishii (Nagoya).\n LOCATION:https://researchseminars.org/talk/ZAG/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Jingjun Han (Johns Hopkins University) DTSTART:20201229T150000Z DTEND:20201229T160000Z DTSTAMP:20260422T225725Z UID:ZAG/81 DESCRIPTION:Title: The ACC for local volumes and boundedness of singularities\nby Jingjun Ha n (Johns Hopkins University) as part of ZAG (Zoom Algebraic Geometry) semi nar\n\n\nAbstract\nKawamata log terminal (klt) singularities form an impor tant class of singularities due to its fundamental roles in MMP\, K\\”ah ler-Einstein geometry\, and K-stability. Recently\, Chi Li introduced a ne w invariant called the local volume of a klt singularity which encodes lot s of interesting geometric and topological information. A folklore conject ure predicts that local volumes satisfy the ascending chain condition (ACC ) when the coefficients of the boundary divisors belong to a DCC set. In t his talk\, we will show the ACC conjecture for local volumes holds when th e ambient variety is fixed. We will also explore the relation between log canonical thresholds\, local volumes\, and delta-plt blow-ups. This is bas ed on ongoing joint work with Yuchen Liu and Lu Qi.\n LOCATION:https://researchseminars.org/talk/ZAG/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiromichi Takagi (Gakushuin University) DTSTART:20210107T100000Z DTEND:20210107T110000Z DTSTAMP:20260422T225725Z UID:ZAG/84 DESCRIPTION:Title: Key varieties for prime Q-Fano threefolds of codimension 4\nby Hiromichi Takagi (Gakushuin University) as part of ZAG (Zoom Algebraic Geometry) sem inar\n\n\nAbstract\nI talk about my construction of key varieties for prim e Q-Fano threefolds of codimension 4 related with (P^2)^2-fibrations.I dis cuss their relations with the cluster variety constructed by Coughlan and Ducat.\n LOCATION:https://researchseminars.org/talk/ZAG/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricio Gallardo (UC Riverside) DTSTART:20210112T180000Z DTEND:20210112T190000Z DTSTAMP:20260422T225725Z UID:ZAG/85 DESCRIPTION:Title: Com pactifications of the moduli space of cubic surfaces\nby Patricio Gall ardo (UC Riverside) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nWe discuss the interplay between geometric and Hodge theoretical compactifications for the moduli space of cubic surfaces. In particular\, we prove that Naruki's compactification is toroidal and has a modular int erpretation in terms of stable pairs. This last is joint work with Matt K err and Luca Schaffler. If time allows\, we will describe open questions and ongoing generalizations of such a relationship to the case of pairs in volving cubic surfaces and their anticanonical divisors.\n LOCATION:https://researchseminars.org/talk/ZAG/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiromu Tanaka (University of Tokyo) DTSTART:20210114T100000Z DTEND:20210114T110000Z DTSTAMP:20260422T225725Z UID:ZAG/86 DESCRIPTION:Title: On Mori fibre spaces in positive characteristic\nby Hiromu Tanaka (Univer sity of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstr act\nThe minimal model program conjecture predicts that any algebraic vari ety is birational to either a minimal model or a Mori fibre space.\nIn thi s talk\, we first summarise some results on Mori fibre spaces in positive characteristic.\nWe also discuss some open problems related to this topic. \n LOCATION:https://researchseminars.org/talk/ZAG/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Shihoko Ishii (University of Tokyo) DTSTART:20210119T090000Z DTEND:20210119T100000Z DTSTAMP:20260422T225725Z UID:ZAG/87 DESCRIPTION:Title: Uni form bound of the number of weighted blow-ups to compute the minimal log d iscrepancy for smooth 3-folds\nby Shihoko Ishii (University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn the tal k I will show that the minimal log discrepancy of every pair consisting of a smooth 3-fold and a "general" real ideal is computed by the divisor obt ained by at most two weighted blow ups.\n\nOur proof suggests the followi ng conjecture:\n\nEvery pair consisting of a smooth N-fold and a ``general ” real ideal is computed by a divisor obtained by at most N-1 weighted b low ups.\n\nThis is regarded as a weighted blow up version of Mustata-Naka mura’s conjecture.\n LOCATION:https://researchseminars.org/talk/ZAG/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Osamu Fujino (Osaka University) DTSTART:20210121T100000Z DTEND:20210121T110000Z DTSTAMP:20260422T225725Z UID:ZAG/88 DESCRIPTION:Title: On extremal contractions of log canonical pairs\nby Osamu Fujino (Osaka U niversity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\ nThe cone and contraction theorem holds for projective log canonical pairs . Let us consider an extremal contraction morphism of a log canonical pair . We prove that every irreducible component of the exceptional locus is un iruled. This result was first proved by Yujiro Kawamata for kawamata log t erminal pairs. His proof uses a relative Kawamata--Viehweg vanishing theor em for projective bimeromorphic morphisms of complex analytic spaces and d oes not work for log canonical pairs. Our approach is based on the theory of quasi-log schemes and can be applied to more general settings. We need a semipositivity theorem coming from the theory of variations of mixed Hod ge structure. We note that we do not use the minimal model program.\n LOCATION:https://researchseminars.org/talk/ZAG/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Frances Kirwan (University of Oxford) DTSTART:20210126T140000Z DTEND:20210126T150000Z DTSTAMP:20260422T225725Z UID:ZAG/89 DESCRIPTION:Title: Mod uli of unstable objects in algebraic geometry\nby Frances Kirwan (Univ ersity of Oxford) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nThe construction of the moduli spaces of stable curves of fixed ge nus is one of the classical applications of Mumford's geometric invariant theory (GIT)\, developed in the 1960s\; many other moduli spaces of 'stabl e' objects can be constructed using GIT\, as well as in other ways. The ai m of this talk is to explain how recent methods from a version of GIT for non-reductive group actions can help us to use suitable 'stability conditi ons' to stratify moduli stacks into locally closed strata such that not on ly the open 'stable' strata but also the 'unstable' strata have coarse mod uli spaces. In the case of moduli stacks of bundles over a nonsingular pro jective curve\, these stratifications refine the stratification by Harder- Narasimhan type. The talk is based on joint work with Gergely Berczi\, Vic ky Hoskins and Joshua Jackson.\n LOCATION:https://researchseminars.org/talk/ZAG/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Catanese (University of Bayreuth) DTSTART:20210128T140000Z DTEND:20210128T150000Z DTSTAMP:20260422T225725Z UID:ZAG/90 DESCRIPTION:Title: Var ieties of nodal surfaces\, Coding theory\, and cubic discriminants\nby Fabrizio Catanese (University of Bayreuth) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nNodal Hypersurfaces Y in projective spa ce are those whose singularities have nondegenerate Hessian. \nBasic nume rical invariants are the dimension n and the degree d of the hypersurfac e Y\, and the number \\nu of singular points. \nIf you fix those integers (n\, d\,\\nu) these hypersurfaces are parametrized by the so-called Noda l Severi varieties F(n\, d\, \\nu). \nThe first basic questions concernin g them are: \n1) for which triples is F(n\, d\, \\nu) nonempty ? \n2) Whe n is it irreducible ? \n\nAlready intriguing is the situation for surfaces \, indeed for n=2 the answer to 1) is known for d <= 6\, also the maximal number of nodes \\mu (d) that a nodal surface in 3-space of degree d can have is known only for d <= 6.\n\nThe known maximizing nodal surfaces (th ose with \\mu(d) nodes) are: the Cayley cubic\, the Kummer quartic surface s\, the Togliatti quintics\, the Barth sextic.\n\nAn important chapter in Coding theory is the theory of binary linear codes\, vector subspaces of a vector space (Z/2)^n.\n\nI will recall basic notions and methods of codi ng theory (e.g. the McWilliams identities) and describe some codes relate d to quadratic forms. \n\nNodal surfaces are related to coding theory via the first homology of their smooth part: it is a binary code K\, which wa s used by Beauville to show that\, for d=5 \, \\mu(d) = 31. Coding theory was also crucial in order to prove that \\mu(6) < = 65. \n\nOur main resu lts concern the cases d = 4\,5\,6 (d=2\,3 being elementary). \n\nTHM 1. Fo r d=4 the components of F(4\, \\nu) and their incidence correspondence ar e determined by their extended codes K’\, which are all the shortenings of the first Reed Muller code.\n\nWe extend this result to nodal K3 surfa ces of all degrees\, this sheds light on the case d=5.\n\nTHM 2. For d=5 the codes K occurring are classified\, up to a possible exception. F(5\ , \\nu) is irreducible for \\nu = 31\, and for \\nu = 29\,30\,31 these sur faces are discriminants of the projection of a cubic hypersurface in 5-s pace. \n\nTHM 3. For d=6 and \\nu = 65 the codes K\, K’ are uniquely d etermined\, and can be described explicitly via the Doro-Hall graph\, att ached to the group \\SigmaL(2\, 25)\, and the geometry of the Barth sextic . Every 65 nodal sextic occurs as discriminant of the projection of a cub ic hypersurface in 6-space with < = 33 nodes.\n\n\nIrreducibility for d =6\, and 65 nodes\, is related to the geometry of nodal cubic hypersurfac es in n-space\, and of the linear subspaces contained in them.\n\nWe pose the question whether\, in the case of even dimension n\, the cubic hypers urface with maximal number of singularities is\nprojectively equivalent to the Segre cubic s_1=s_3=0 (which is locally rigid).\n\nFor theorem 2 I b enefited of the cooperation of Sandro Verra\, for theorem 3 of Yonghwa Ch o\, Michael Kiermaier\, Sascha Kurz and the Linux Cluster of the Universi taet Bayreuth\, while Davide Frapporti and Stephen Coughlan cooperated f or the geometry of nodal cubic hypersurfaces.\n LOCATION:https://researchseminars.org/talk/ZAG/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Donaldson (Imperial College London and Simons Center for Geo metry and Physics) DTSTART:20210202T150000Z DTEND:20210202T160000Z DTSTAMP:20260422T225725Z UID:ZAG/91 DESCRIPTION:Title: Enu merative geometry\, Fredholm analysis and moduli spaces of surfaces of gen eral type\nby Simon Donaldson (Imperial College London and Simons Cent er for Geometry and Physics) as part of ZAG (Zoom Algebraic Geometry) semi nar\n\n\nAbstract\nIn the first part of the talk we will review some backg round in deformation theory\, comparing the points of view from algebraic geometric and differential geometry/global analysis. We will review in ou tline some known established examples in which a "virtual fundamental clas s" of a moduli space can be defined. In the second part of the talk we wil l explore the possibility that these ideas can be applied to moduli spaces of surfaces of general type using the KSBA compactification. We will make some standard observations about these moduli spaces\, whose dimension of ten differs from the virtual dimension. We will illustrate the discussion by a calculation in the case of sextic surfaces with a particular finite s ymmetry group.\n LOCATION:https://researchseminars.org/talk/ZAG/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Shinnosuke Okawa (Osaka University) DTSTART:20210204T110000Z DTEND:20210204T120000Z DTSTAMP:20260422T225725Z UID:ZAG/92 DESCRIPTION:Title: Mod uli space of semiorthogonal decompositions\nby Shinnosuke Okawa (Osaka University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nSemiorthogonal decomposition (SOD) of triangulated categories is quite interesting and of fundamental importance for various reasons. For example \, SOD of the derived category of coherent sheaves is closely related to t he geometry of varieties\, such as the minimal model program (MMP) among o thers. It is therefore desirable to understand the general properties of S ODs\, partly so as to classify SODs of as many triangulated categories as possible. The purpose of this talk is to explain certain moduli spaces of SODs which we introduced. To a smooth projective morphism of excellent sch emes f: X \\to B\, we associate an algebraic space over B which classifies the SODs of the derived categories of the fibers of f. We will discuss pr operties and various aspects of this moduli space including applications\, comparison to MMP\, and open problems.\n LOCATION:https://researchseminars.org/talk/ZAG/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrica Floris (Université de Poitiers) DTSTART:20210209T110000Z DTEND:20210209T120000Z DTSTAMP:20260422T225725Z UID:ZAG/93 DESCRIPTION:Title: Con nected algebraic groups acting on Fano fibrations over $\\mathbb P^1$\ nby Enrica Floris (Université de Poitiers) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLet G be a connected algebraic group and X a variety endowed with a regular action of G and a Mori fibre space X/P 1 whose fibre is a Fano variety of Picard rank at least 2. In this talk I will explain why there is a proper horizontal subvariety of X which is inv ariant under the action of G\, alongside with some applications of this re sult to the classification of connected algebraic subgroups of the Cremona group in dimension 4. This is a joint work with Jeremy Blanc.\n LOCATION:https://researchseminars.org/talk/ZAG/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasso de Fernex (University of Utah) DTSTART:20210211T180000Z DTEND:20210211T190000Z DTSTAMP:20260422T225725Z UID:ZAG/94 DESCRIPTION:Title: Mot ivic integration on Berkovic spaces\nby Tomasso de Fernex (University of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nT he purpose of the talk is to offer a new perspective on motivic integratio n. Working over a field with trivial norm\, I will introduce a motivic mea sure on the Berkovich analytification of an algebraic variety and define i ntegration in this setting. The construction is geometric with a similar s pirit as Kontsevich’s original definition\, and leads to the formulation of a functorial theory which mirrors\, in this aspect\, the functoriality of Cluckers and Loeser's approach via constructible motivic functions. Th e approach does not rely on model theory but rather on geometric propertie s such as resolution of singularities and the weak factorization theorem. The talk is based on joint work with Chung Ching Lau.\n LOCATION:https://researchseminars.org/talk/ZAG/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Yusuke Nakamura (University of Tokyo) DTSTART:20210216T110000Z DTEND:20210216T120000Z DTSTAMP:20260422T225725Z UID:ZAG/95 DESCRIPTION:Title: Inv ersion of adjunction for quotient singularities\nby Yusuke Nakamura (U niversity of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nThe minimal log discrepancy is an invariant of singularities def ined in birational geometry\, and it is related to the conjecture of termi nation of flips. In this talk\, we will discuss the minimal log discrepanc ies of quotient singularities. I will show that the PIA (precise inversion of adjunction) conjecture holds for quotient singularities. The main tool of this talk involves the theory of the arc space of a quotient singulari ty established by Denef and Loeser. This is joint work with Kohsuke Shibat a.\n LOCATION:https://researchseminars.org/talk/ZAG/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Frediani Paola (Università di Pavia) DTSTART:20210218T140000Z DTEND:20210218T150000Z DTSTAMP:20260422T225725Z UID:ZAG/96 DESCRIPTION:Title: A c anonical Hodge theoretic projective structure on compact Riemann surfaces< /a>\nby Frediani Paola (Università di Pavia) as part of ZAG (Zoom Algebra ic Geometry) seminar\n\n\nAbstract\nIn this talk we will show the existenc e of a canonical projective structure on every compact Riemann surface\, c oming from Hodge theory. We will show that it differs from the canonical p rojective structure produced by the uniformisation theorem. In fact the (0 \,1)- component of the differential of the corresponding sections of the m oduli space of projective structures over the moduli space of curves are d ifferent. The one corresponding to the projective structure coming from un iformisation was computed by Zograf and Takhtadzhyan as the Weil-Petersson Kaehler form on the moduli space of curves. Ours is the pullback via the Torelli map of a nonzero constant scalar multiple of the Siegel form on t he moduli space of principally polarised abelian varieties. These are resu lts obtained in collaboration with I. Biswas\, E. Colombo and G.P. Pirola. \n LOCATION:https://researchseminars.org/talk/ZAG/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Shing-Tung Yau (Harvard University) DTSTART:20210223T153000Z DTEND:20210223T163000Z DTSTAMP:20260422T225725Z UID:ZAG/97 DESCRIPTION:Title: Geo metry of Conifold Transitions\nby Shing-Tung Yau (Harvard University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nConifold t ransitions were introduced by Clemens\, Reid and Friedman to connect Calab i-Yau threefolds with different topologies. However\, this operation may p roduce a complex manifold with trivial canonical bundle which is non-Kahle r. I will discuss this transition from the point of view of metrics and di fferential geometry\, and propose a non-Kahler analog of Calabi-Yau metric s which originates in heterotic string theory. This talk will contain join t works with T.C. Collins\, J.-X. Fu\, J. Li\, and S. Picard.\n LOCATION:https://researchseminars.org/talk/ZAG/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Atsushi Ito (Nagoya University) DTSTART:20210225T100000Z DTEND:20210225T110000Z DTSTAMP:20260422T225725Z UID:ZAG/98 DESCRIPTION:Title: Lin ear systems on abelian varieties via M-regularity of Q-twisted sheaves \nby Atsushi Ito (Nagoya University) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nFor an ample line bundle $L$ on an abelian vari ety $X$\, it is known that $L^n$ is basepoint free if $n \\geq 2$\, projec tively normal if $n \\geq 3$\, and the ideal of $X$ embedded by $|L^n|$ is generated by quadrics if $n \\geq 4$. As a generalization of these result s\, Lazarsfeld conjectures that $L^n$ satisfies property $(N_p)$ if $n \\g eq p+3$.\nThis conjecture is affirmatively proved by Pareschi and strength en by Pareschi-Popa by the theory of M-regularity. Recently\, Jiang and Pa reschi consider (variants of) M-regularity of $\\mathbb{Q}$-twisted sheave s and it turns out that this is very useful when we study the linear syste m $|L|$ of $L$ itself\, not only $L^n$ for $n \\geq 2$. In this talk\, I w ill explain this topic and some recent results.\n LOCATION:https://researchseminars.org/talk/ZAG/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Cukierman (University of Buenos Aires) DTSTART:20210302T150000Z DTEND:20210302T160000Z DTSTAMP:20260422T225725Z UID:ZAG/99 DESCRIPTION:Title: Def ormations of exterior differential ideals and applications\nby Fernand o Cukierman (University of Buenos Aires) as part of ZAG (Zoom Algebraic Ge ometry) seminar\n\n\nAbstract\nThe main theme of this talk is the geometry of moduli spaces of algebraic singular foliations on smooth projective al gebraic varieties over the complex numbers. A motivating problem is the de termination of the irreducible components of such moduli spaces. We plan t o discuss some basic facts on deformations of exterior differential ideals . With these tools we study deformations of several types of Pfaff ideals\ , obtaining some new irreducible components of spaces of singular foliatio ns of any codimension. This is based on joint work with Cesar Massri.\n LOCATION:https://researchseminars.org/talk/ZAG/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Kiwamu Watanabe (Chuo University) DTSTART:20210304T100000Z DTEND:20210304T110000Z DTSTAMP:20260422T225725Z UID:ZAG/100 DESCRIPTION:Title: Po sitivity of the exterior power of the tangent bundles\nby Kiwamu Watan abe (Chuo University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n \nAbstract\nBy Mori's solution of the Hartshorne conjecture\, the only smo oth projective variety with ample tangent bundle is the projective space. As a generalization of the Hartshorne conjecture\, Demially\, Peternell an d Schneider studied smooth projective varieties with nef tangent bundle. T hey proved that such variety X admits an étale cover Y such that the Alba nese map Y \\to Alb(Y) is a smooth morphism whose fibers are smooth Fano v arieties with nef tangent bundle. In this talk\, we will study smooth proj ective varieties such that the r-th exterior power of the tangent bundle i s nef\, paying special attention to the case r=2. This talk is based on th e paper arXiv:2011.01427.\n LOCATION:https://researchseminars.org/talk/ZAG/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Shunsuke Takagi (University of Tokyo) DTSTART:20210309T110000Z DTEND:20210309T120000Z DTSTAMP:20260422T225725Z UID:ZAG/101 DESCRIPTION:Title: De formations of F-pure and F-regular singularities\nby Shunsuke Takagi ( University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nF-regular and F-pure singularities are singularities in positiv e characteristic defined in terms of Frobenius splitting properties. Ma an d Schwede recently proved that a normal Q-Gorenstein complex variety has l og terminal singularities if its reduction modulo p has F-regular singular ities for a single prime p. I will discuss the analog of their result for log canonical singularities. I will also explain how F-regular singulariti es behave under equal and mixed characteristic deformations. This talk is based on joint work with Kenta Sato.\n LOCATION:https://researchseminars.org/talk/ZAG/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolina Araujo (IMPA) DTSTART:20210311T150000Z DTEND:20210311T160000Z DTSTAMP:20260422T225725Z UID:ZAG/102 DESCRIPTION:Title: Bi rational geometry of Calabi-Yau pairs and 3-dimensional Cremona transforma tions\nby Carolina Araujo (IMPA) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nAbstract: Recently\, Oguiso addressed the follo wing question\, attributed to Gizatullin: ``Which automorphisms of a smoot h quartic K3 surface $D\\subset \\mathbb{P}^3$ are induced by Cremona tran sformations of the ambient space $\\mathbb{P}^3$?'' When $D\\subset \\math bb{P}^3$ is a quartic surface\, $(\\mathbb{P}^3\,D)$ is an example of a \ \emph{Calabi-Yau pair}\, that is\, a pair $(X\,D)$ consisting of a normal projective variety $X$ and an effective Weil divisor $D$ on $X$ such that $K_X+D\\sim 0$. In this talk\, I will explain a general framework to study the birational geometry of mildly singular Calabi-Yau pairs. Then I will focus on the case of singular quartic surfaces $D\\subset \\mathbb{P}^3$. Our results illustrate how the appearance of increasingly worse singularit ies in $D$ enriches the birational geometry of the pair $(\\mathbb{P}^3\, D)$\, and lead to interesting subgroups of the Cremona group of $\\mathbb{ P}^3$. This is a joint work with Alessio Corti and Alex Massarenti.\n LOCATION:https://researchseminars.org/talk/ZAG/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Taro Sano (Kobe University) DTSTART:20210316T100000Z DTEND:20210316T110000Z DTSTAMP:20260422T225725Z UID:ZAG/103 DESCRIPTION:Title: Bi rational boundedness of some Calabi-Yau hypersurfaces\nby Taro Sano (K obe University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst ract\nIt is well-known that complex projective K3 surfaces are connected b y analytic deformations\, but they are algebraically unbounded. Neverthele ss\, Reid\, Iano-Fletcher and Kollar-Johnson showed the finiteness of weig hted Calabi-Yau hypersurfaces. Motivated by this\, we study plt Calabi-Yau pairs (X\,D) and show finiteness of D in some cases. In particular\, we s how that anticanonical K3 surfaces form a birationally bounded family. We also exhibit examples of K3 surfaces of a fixed degree whose birational co ntractions form an unbounded family\, thus the birational boundedness is o ptimal in a sense.\n LOCATION:https://researchseminars.org/talk/ZAG/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Lazda (University of Warwick) DTSTART:20210318T150000Z DTEND:20210318T160000Z DTSTAMP:20260422T225725Z UID:ZAG/104 DESCRIPTION:Title: A Neron-Ogg-Shafarevich criterion for K3 surfaces\nby Chris Lazda (Unive rsity of Warwick) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nThe naive analogue of the Néron-Ogg-Shafarevich criterion fails f or K3 surfaces\, that is\, there exist K3 surfaces over Henselian\, discre tely valued fields K\, with unramified etale cohomology groups\, but which do not admit good reduction over K. Assuming potential semi-stable reduct ion\, I will show how to correct this by proving that a K3 surface has goo d reduction if and only if is second cohomology is unramified\, and the as sociated Galois representation over the residue field coincides with the s econd cohomology of a certain “canonical reduction” of X. This is join t work with B. Chiarellotto and C. Liedtke.\n LOCATION:https://researchseminars.org/talk/ZAG/104/ END:VEVENT BEGIN:VEVENT SUMMARY:John Lesieutre (Pennsylvania State University) DTSTART:20210323T100000Z DTEND:20210323T110000Z DTSTAMP:20260422T225725Z UID:ZAG/105 DESCRIPTION:Title: Ra tional surface automorphisms without periodic curves\nby John Lesieutr e (Pennsylvania State University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlthough there are many examples known of infinite -order automorphisms of rational surfaces\, in most cases these automorphi sms have at least one periodic curve C (a curve for which f^n(C) = C for s ome n). I will explain the construction of a class of rational surfaces w hich admit a large group of automorphisms with no invariant curves. The e xample makes use of several classical constructions\, and the surfaces adm it contructions down to three different Coble surfaces.\n LOCATION:https://researchseminars.org/talk/ZAG/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulia Sacca (Columbia University) DTSTART:20210325T150000Z DTEND:20210325T160000Z DTSTAMP:20260422T225725Z UID:ZAG/106 DESCRIPTION:Title: Fa no manifolds associated to hyperkahler manifolds\nby Giulia Sacca (Col umbia University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nIt is known that to some Fano manifolds whose cohomology looks lik e that of a K3 surface\, one can associate\, via geometric constructions\, examples of hyperkahler manifolds. In this talk I will report on the firs t steps of a program whose aim is to reverse this construction: starting f rom a hyperkahler manifold how to recover geometrically a Fano manifold? T his is joint work with L. Flapan\, E. Macri\, and K. O'Grady.\n LOCATION:https://researchseminars.org/talk/ZAG/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Katsuhisa Furukawa (Josai University) DTSTART:20210330T100000Z DTEND:20210330T110000Z DTSTAMP:20260422T225725Z UID:ZAG/107 DESCRIPTION:Title: On the singular loci of higher secant varieties of Veronese embeddings\n by Katsuhisa Furukawa (Josai University) as part of ZAG (Zoom Algebraic Ge ometry) seminar\n\n\nAbstract\nFor a projective variety X in P^N\, the k-s ecant variety \\sigma_k(X) is defined to be the closure of the union of k- planes in P^N spanned by k-points of X. It is well known that \\sigma_{k-1 }(X) is contained in the singular locus of \\sigma_k(X). Let us consider t he case when X is the image of the Veronese embedding P^n to P^N of degree d\, where N = \\binom{d+N}{d}-1. In the case of k=3\, K. Han showed that \\Sing(\\sigma_3(X)) = \\sigma_2(X)\, except when d=4 and n > 2. In the ex ceptional case\, \\Sing(\\sigma_3(X)) is the union of \\sigma_2(X) and D\, where D is an irreducible subset. In this talk\, we first give a geometri c description of this D for k = 3\, and next study the case of k > 3. In p articular\, I will explain projective techniques with respect to an explic it calculation of the Gauss map of X and the projection from the incidence correspondence of \\sigma_k(X). This is a joint work with Kangjin Han.\n LOCATION:https://researchseminars.org/talk/ZAG/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Vyacheslav Shokurov (Johns Hopkins University) DTSTART:20210401T150000Z DTEND:20210401T160000Z DTSTAMP:20260422T225725Z UID:ZAG/108 DESCRIPTION:Title: Ar ound a-n-complements\nby Vyacheslav Shokurov (Johns Hopkins University ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA genera l conjecture about a-n-complements will be discussed in connection with st rict $\\delta$-lc singularities\, generalized pairs and McKernan conjectur e.\n LOCATION:https://researchseminars.org/talk/ZAG/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Takehiko Yasuda (Osaka University) DTSTART:20210406T100000Z DTEND:20210406T110000Z DTSTAMP:20260422T225725Z UID:ZAG/109 DESCRIPTION:Title: St ringy motives and local fundamental groups of klt surface singularities in arbitrary characteristic\nby Takehiko Yasuda (Osaka University) as pa rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this talk\, I will speak about an application of stringy motives to local fundamental groups of klt surface singularities. Xu proved that klt singularities in c haracteristic zero have finite local fundametal groups. I will explain how to prove that the same is true in arbitrary characteristic and in dimensi on two\, which had been unknown in characteristics two and three. The key of the proof is to study the behavior of stringy motives under quasi-etale Galois covers of klt singularities. This is a joint work with Javier Carv ajal-Rojas.\n LOCATION:https://researchseminars.org/talk/ZAG/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Langer (Institute of Mathematics\, University of Warsaw\, P oland) DTSTART:20210408T130000Z DTEND:20210408T140000Z DTSTAMP:20260422T225725Z UID:ZAG/110 DESCRIPTION:Title: Ch ern classes of vector bundles\nby Adrian Langer (Institute of Mathemat ics\, University of Warsaw\, Poland) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nI will talk about various restrictions on Chern classes of vector bundles on algebraic varieties. One of the most import ant is Bogomolov's inequality saying that the degree of the discriminant of a semistable vector bundle on a smooth complex algebraic variety is non -negative. The degree zero case essentially corresponds to flat vector bu ndles. There are also versions of this inequality for Higgs bundles and i n positive characteristic. I will talk about some applications of Bogomolo v's inequality and its possible variants in the Chow ring of the variety.\ n LOCATION:https://researchseminars.org/talk/ZAG/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Karl Schwede (University of Utah) DTSTART:20210413T170000Z DTEND:20210413T180000Z DTSTAMP:20260422T225725Z UID:ZAG/111 DESCRIPTION:Title: Re cent progress in mixed characteristic higher dimensional algebraic geometr y\nby Karl Schwede (University of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn characteristic zero birational algebr aic geometry\, Kawamata-Viehweg vanishing is a centrally important tool. For some applications in characteristic p > 0\, one may use Frobenius and perturbations as a replacement for resolution of singularities and Kawamat a-Viehweg vanishing. This talk will show how to use Bhatt's vanishing the orem for absolute integral closures mixed characteristic as a replacement for resolutions and Kawamata-Viehweg vanishing theorems in a number of app lications. This is joint work with B. Bhatt\, L. Ma\, Z. Patakfalvi\, K. Tucker\, J. Waldron and J. Witaszek.\n LOCATION:https://researchseminars.org/talk/ZAG/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Yasunari Nagai (Waseda University) DTSTART:20210415T100000Z DTEND:20210415T110000Z DTSTAMP:20260422T225725Z UID:ZAG/112 DESCRIPTION:Title: Ra tional normal quintic curves on a cubic fourfold\nby Yasunari Nagai (W aseda University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nWe study the moduli of rational normal quintic curves on a cubic f ourfold and its compactifications with a view toward projective symplectic geometry. This is a work in progress with Manfred Lehn and Duco van Strat en.\n LOCATION:https://researchseminars.org/talk/ZAG/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Witaszek (University of Michigan) DTSTART:20210420T170000Z DTEND:20210420T180000Z DTSTAMP:20260422T225725Z UID:ZAG/113 DESCRIPTION:Title: Re lative semiampleness in mixed characteristic.\nby Jakub Witaszek (Univ ersity of Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nIn this talk we will discuss the existence of contractions and b ase point freeness of line bundles in mixed characteristic in the context of the arithmetic Minimal Model Program.\n LOCATION:https://researchseminars.org/talk/ZAG/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandor Kovacs (University of Washington) DTSTART:20210422T170000Z DTEND:20210422T180000Z DTSTAMP:20260422T225725Z UID:ZAG/114 DESCRIPTION:Title: Ho dge sheaves for singular families\nby Sandor Kovacs (University of Was hington) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nT his is a report on joint work with Behrouz Taji. Given a flat projective m orphism [f:X\\to B] of complex varieties\, assuming that [B] is smooth\, we construct a system of reflexive Hodge sheaves on [B] . If in addition [X] is also smooth then this system gives an extension of the Hodge bundl e underlying the VHS of the smooth locus of [f] . This in turn provides a criterion that all VHSs of geometric origin must satisfy. As an independen t application we prove a singular version of Viehweg's conjecture about ba se spaces of families of maximal variation.\n LOCATION:https://researchseminars.org/talk/ZAG/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Tschinkel (Courant Institute of Mathematical Sciences\, New Y ork University) DTSTART:20210427T150000Z DTEND:20210427T160000Z DTSTAMP:20260422T225725Z UID:ZAG/115 DESCRIPTION:Title: Eq uivariant birational types\nby Yuri Tschinkel (Courant Institute of Ma thematical Sciences\, New York University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will discuss joint work with A. Kresch and B. Hassett concerning new invariants in equivariant birational geometr y and their applications.\n LOCATION:https://researchseminars.org/talk/ZAG/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Margarida Melo (University of Roma Tre) DTSTART:20210429T120000Z DTEND:20210429T130000Z DTSTAMP:20260422T225725Z UID:ZAG/116 DESCRIPTION:Title: On the top weight cohomology of the moduli space of abelian varieties\nb y Margarida Melo (University of Roma Tre) as part of ZAG (Zoom Algebraic G eometry) seminar\n\n\nAbstract\nThe moduli space of abelian varieties Ag a dmits well behaved toroidal compactifications whose dual complex can be gi ven a tropical interpretation. Therefore\, one can use the techniques rece ntly developed by Chan-Galatius-Payne in order to understand part of the t opology of Ag via tropical geometry. In this talk\, which is based in join t work with Madeleine Brandt\, Juliette Bruce\, Melody Chan\, Gwyneth More land and Corey Wolfe\, I will explain how to use this setup\, and in parti cular computations in the perfect cone compactification of Ag\, in order t o describe its top weight cohomology for g up to 7.\n LOCATION:https://researchseminars.org/talk/ZAG/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Pe Pereira (Universidad Complutense de Madrid) DTSTART:20210504T140000Z DTEND:20210504T150000Z DTSTAMP:20260422T225725Z UID:ZAG/117 DESCRIPTION:Title: Mo derately Discontinuous Algebraic Topology\nby Maria Pe Pereira (Univer sidad Complutense de Madrid) as part of ZAG (Zoom Algebraic Geometry) semi nar\n\n\nAbstract\nAn algebraic or complex analytic subset in C^n has 2 na tural metrics: the outer metric (restriction of the euclidean metric) and the inner metric (natural extension of the riemannian metric on the smooth part). These metrics considered up to bilipschitz mappings are analytic i nvariants\, that is\, they do not depend on the complex analytic embedding .\nRecently there is an intense activity in bilipschitz geometry of germs and degenerations\, enriching and providing finer information on\nproblems that were studied previously from the topological viewpoint (for multipli city invariance of the germ or certain equisingularity notions).\nIn the w orks [1] and [2] we develop a new metric algebraic topology\, called the M oderately Discontinuous Homology and Homotopy\, in the context of subanaly tic germs in R^n (with a supplementary metric structure) and more generall y of (degenerating) subanalytic families. This theory captures bilipschitz information\, or in other words\, quasi isometric invariants\, and aims t o codify\, in an algebraic way\, part of the bilipschitz geometry.\nA suba nalytic germ is topologically a cone over its link and the moderately disc ontinuous theory captures the different speeds\, with respect to the dista nce to the origin\, in which the topology of the link collapses towards th e origin. Similarly\, in a degenerating subanalytic family\, it captures t he different speeds of collapsing with respect to the family parameter.\nT he MD algebraic topology satisfies all the analogues of the usual theorems in Algebraic Topology: long exact sequences for the relative case\, Mayer Vietoris and Seifert van Kampen for special coverings...\nIn this talk\, I will present the most important concepts in the theory and some results or applications that we got until the present.\n[1] (with J. Fernandez de Bobadilla\, S. Heinze\, E. Sampaio) Moderately discontinuous homology. To appear in Comm. Pure App. Math.. Available in arXiv: 1910.12552\n[2] (with J. Fernández de Bobadilla\, S. Heinze) Moderately discontinuous hom otopy. Submitted. Available in ArXiv:2007.01538\n LOCATION:https://researchseminars.org/talk/ZAG/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Mara Ungureanu (University of Freiburg) DTSTART:20210506T140000Z DTEND:20210506T150000Z DTSTAMP:20260422T225725Z UID:ZAG/118 DESCRIPTION:Title: Co unts of secant planes to varieties\, Virasoro algebras\, and universal pol ynomials\nby Mara Ungureanu (University of Freiburg) as part of ZAG (Z oom Algebraic Geometry) seminar\n\n\nAbstract\nFor a curve in projective s pace\, the varieties parametrising its secant planes are among the most st udied objects in classical enumerative geometry. We shall start with an i ntroduction to secant varieties and explain the role of degeneration argum ents in understanding their geometry. We shall then explore the connectio n between the enumerative geometry of secant varieties and Virasoro algebr as on one side\, and tautological integrals on the other.\n LOCATION:https://researchseminars.org/talk/ZAG/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Kebekus (University of Freiburg) DTSTART:20210511T130000Z DTEND:20210511T140000Z DTSTAMP:20260422T225725Z UID:ZAG/119 DESCRIPTION:Title: Br auer-Manin obstruction on a simply connected fourfold and a Mordell theore m in the orbifold setting\nby Stefan Kebekus (University of Freiburg) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlmost one decade ago\, Poonen constructed the first examples of algebraic varieties over global fields for which Skorobogatov's etale Brauer-Manin obstructio n does not explain the failure of the Hasse principle. By now\, several co nstructions are known\, but they all share common geometric features such as large fundamental groups. In this paper\, we construct simply connected fourfolds over global fields of positive characteristic for which the Bra uer-Manin machinery fails. Contrary to earlier work in this direction\, ou r construction does not rely on major conjectures. Instead\, we establish a new diophantine result of independent interest: a Mordell-type theorem f or Campana's "geometric orbifolds" over function fields of positive charac teristic. Along the way\, we also construct the first example of simply co nnected surface of general type over a global field with a non-empty\, but non-Zariski dense set of rational points. This is joint work with Jorge P ereira (IMPA) and Arne Smeets (Nijmegen)\n LOCATION:https://researchseminars.org/talk/ZAG/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Rogers (University of Manchester) DTSTART:20210513T140000Z DTEND:20210513T150000Z DTSTAMP:20260422T225725Z UID:ZAG/120 DESCRIPTION:Title: K- stability of smooth Fano SL2-threefolds\nby Jack Rogers (University of Manchester) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nThere has been much interest in K-stability since it was shown to be eq uivalent to the existence of Kähler-Einstein metrics by Chen-Donaldson-Su n. The theory of K-stability is now well developed\, but practical methods to check whether a given variety is K-stable are hard to come by. Equivar iant K-stability\, introduced by Datar-Székelyhidi\, makes finding such c riteria easier for varieties with large automorphism groups.\n\nIf an alge braic group G acts on a variety X\, the complexity of the action is the mi nimal codimension in X of the orbits of a Borel subgroup B of G (e.g. if T is a torus\, the complexity zero T-varieties are the toric varieties). Co nditions for K-stability have been found for toric varieties by Wang-Zhu\, for complexity one T-varieties by Ilten-Süss and for all complexity zero varieties by Delcroix.\n\nWe will discuss the combinatorial description d ue to Timashev of complexity one G-varieties\, and describe a practical me thod to check K-stability in the particular case of smooth Fano SL2-threef olds. In particular\, this method proves the K-stability of several variet ies not previously known to be K-stable\, e.g. projective 3-space blown up along three disjoint lines. This is joint work with Hendrik Süss.\n LOCATION:https://researchseminars.org/talk/ZAG/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Jørgen Vold Rennemo (University of Oslo) DTSTART:20210518T110000Z DTEND:20210518T120000Z DTSTAMP:20260422T225725Z UID:ZAG/121 DESCRIPTION:Title: K- theoretic sheaf counting invariants on C^4\nby Jørgen Vold Rennemo (U niversity of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA bstract\nOh and Thomas have recently defined a K-theoretic sheaf counting invariant for moduli spaces of sheaves on a Calabi-Yau 4-fold. One of the simplest examples of such a moduli scheme is the Hilbert scheme of n point s on C^4. The topic of this talk is a proof of a formula for the generatin g functions of invariants of these Hilbert schemes\, confirming a conjectu re of Nekrasov (as well a generalisation to Quot schemes of C^4\, conjectu red by Nekrasov and Piazzalunga). This is joint work with Martijn Kool.\n LOCATION:https://researchseminars.org/talk/ZAG/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Pieropan (Utrecht University) DTSTART:20210520T150000Z DTEND:20210520T160000Z DTSTAMP:20260422T225725Z UID:ZAG/122 DESCRIPTION:Title: Ca mpana points on Fano varieties\nby Marta Pieropan (Utrecht University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe call C ampana points an arithmetic notion of points on Campana's orbifolds that h as been first studied by Campana and Abramovich\, and that interpolates be tween the notions of rational and integral points. In this talk we introdu ce Campana points and a Manin type conjecture for Campana points on Fano v arieties\, and we present results for equivariant compactifications of vec tor groups (joint work with A. Smeets\, S. Tanimoto\, T. Várilly-Alvarado ) and for toric varieties (joint work with D. Schindler).\n LOCATION:https://researchseminars.org/talk/ZAG/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendan Hassett (Brown University) DTSTART:20210525T150000Z DTEND:20210525T160000Z DTSTAMP:20260422T225725Z UID:ZAG/123 DESCRIPTION:Title: Ra tionality of even-dimensional intersections of two real quadrics\nby B rendan Hassett (Brown University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe consider rationality constructions for smooth c omplete intersections of two quadrics over nonclosed fields. Over the real numbers\, we establish a criterion for rationality in dimension four and discuss open cases in higher dimensions. (joint with János Kollár and Yu ri Tschinkel)\n LOCATION:https://researchseminars.org/talk/ZAG/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Varilly-Alvarado (Rice University) DTSTART:20210527T150000Z DTEND:20210527T160000Z DTSTAMP:20260422T225725Z UID:ZAG/124 DESCRIPTION:Title: Qu asi-hyperbolicity via explicit symmetric differentials\nby Anthony Var illy-Alvarado (Rice University) as part of ZAG (Zoom Algebraic Geometry) s eminar\n\n\nAbstract\nA surface X is algebraically quasi-hyperbolic if it contains finitely many curves of genus 0 or 1. In 2006\, Bogomolov and de Oliveira used asymptotic computations to show that sufficiently nodal sur faces of high degree in projective three-space carry symmetric differentia ls\, and they used this to prove quasi-hyperbolicity of these surfaces. W e explain how a granular analysis of their ideas\, combined with computati onal tools and insights\, yield explicit results for the existence of symm etric differentials\, and we show how these results can be used to give co nstraints on the locus of rational curves on surfaces like the Barth Decic \, Buechi's surface\, and certain complete intersections of general type\, including the surface parametrizing perfect cuboids\, and the surface par ametrizing magic squares of squares. This is joint work with Nils Bruin a nd Jordan Thomas.\n LOCATION:https://researchseminars.org/talk/ZAG/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Livia Campo (University of Birmingham) DTSTART:20210601T110000Z DTEND:20210601T120000Z DTSTAMP:20260422T225725Z UID:ZAG/125 DESCRIPTION:Title: Fa no 3-folds and double covers\nby Livia Campo (University of Birmingham ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will p ropose a method to explicitly construct 52 deformation families of termina l Q-Fano 3-folds in codimension 4 and Fano index 2. Their structure descen ds from suitably crafted double covers. If time allows\, I will briefly di scuss the non-solidity of some of such families (in a joint work in progre ss with T. Guerreiro).\n LOCATION:https://researchseminars.org/talk/ZAG/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrico Fatighenti (Sapienza - Università di Roma) DTSTART:20210603T160000Z DTEND:20210603T170000Z DTSTAMP:20260422T225725Z UID:ZAG/126 DESCRIPTION:Title: Fa no varieties from homogeneous vector bundles\nby Enrico Fatighenti (Sa pienza - Università di Roma) as part of ZAG (Zoom Algebraic Geometry) sem inar\n\n\nAbstract\nThe idea of classifying Fano varieties using homogeneo us vector bundles was behind Mukai's classification of prime Fano 3-folds. In this talk\, we give a survey of some recent progress along the same li nes\, including a biregular rework of the non-prime Mori-Mukai 3-folds cla ssification and some examples of higher-dimensional Fano varieties with sp ecial Hodge-theoretical properties.\n LOCATION:https://researchseminars.org/talk/ZAG/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Lev Borisov (Rutgers University) DTSTART:20210608T150000Z DTEND:20210608T160000Z DTSTAMP:20260422T225725Z UID:ZAG/127 DESCRIPTION:Title: Ex plicit equations of surfaces of general type\nby Lev Borisov (Rutgers University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nI will talk about progress in finding equations of special surfaces of g eneral type\, notably fake projective planes. This work was done over the last several years\, in a series of joint papers with JongHae Keum\, Sai K ee Yeung\, Enrico Fatighenti and Anders Buch.\n LOCATION:https://researchseminars.org/talk/ZAG/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Fumiaki Suzuki (UCLA Mathematics) DTSTART:20210610T160000Z DTEND:20210610T170000Z DTSTAMP:20260422T225725Z UID:ZAG/128 DESCRIPTION:Title: An O-acyclic variety of even index\nby Fumiaki Suzuki (UCLA Mathematics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will co nstruct a family of Enriques surfaces parametrized by P^1 such that any mu lti-section has even degree over the base P^1. Over the function field of a complex curve\, this gives the first example of an O-acyclic variety (H^ i(X\,O)=0 for i>0) whose index is not equal to one\, and an affirmative an swer to a question of Colliot-Thélène and Voisin. I will also discuss ap plications to related problems\, including the integral Hodge conjecture a nd Murre’s question on universality of the Abel-Jacobi maps. This is joi nt work with John Christian Ottem.\n LOCATION:https://researchseminars.org/talk/ZAG/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Eveline Legendre (Institut de Mathématiques de Toulouse) DTSTART:20210615T110000Z DTEND:20210615T120000Z DTSTAMP:20260422T225725Z UID:ZAG/129 DESCRIPTION:Title: Va luative stability for polarised varieties\nby Eveline Legendre (Instit ut de Mathématiques de Toulouse) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will talk about a recent joint work with Ruadhai Dervan where we introduced a notion of valuative stability for polarised variety. This extends Fujita's valuative stability of Fano varieties. We s how that valuative stability is equivalent to K-stability with respect to test configurations with integral central fibre.\n LOCATION:https://researchseminars.org/talk/ZAG/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Cascini (Imperial College London) DTSTART:20210617T160000Z DTEND:20210617T170000Z DTSTAMP:20260422T225725Z UID:ZAG/130 DESCRIPTION:Title: Bi rational geometry of foliations on a complex threefold\nby Paolo Casci ni (Imperial College London) as part of ZAG (Zoom Algebraic Geometry) semi nar\n\n\nAbstract\nMany results in the classical minimal model program\, s uch as the existence of flips and the base point free theorem\, admit a na tural generalisation to the category of foliations defined over a complex threefold. Other results\, instead\, seem to behave differently\, such as existence of flops and canonical models. I will survey about some of the r ecent progress in this direction. Joint work with C. Spicer.\n LOCATION:https://researchseminars.org/talk/ZAG/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Krishna Hanumanthu (Chennai Mathematical Institute) DTSTART:20210622T110000Z DTEND:20210622T120000Z DTSTAMP:20260422T225725Z UID:ZAG/131 DESCRIPTION:Title: Ra tionality questions on Seshadri constants.\nby Krishna Hanumanthu (Che nnai Mathematical Institute) as part of ZAG (Zoom Algebraic Geometry) semi nar\n\n\nAbstract\nLet X be a projective variety and let L be an ample lin e bundle on X. For a point x in X\, the Seshadri constant of L at x is the infimum\, over all curves C passing through x\, of the ratios (L.C)/m\, w here (L.C) denotes the intersection product of L and C and m is the multip licity of C at x. These constants were defined by J.-P. Demailly in 1990 and they shed light on the local behaviour of L at x and even say somethin g about the nature of L and X. An important question about Seshadri const ants is whether they can be irrational. They are expected to be irrational often\, even though currently no examples are known. In this talk\, we wi ll focus on rational surfaces. We will discuss certain conjectures on line ar systems of plane curves and show that Seshadri constants of some ample line bundles are irrational if these conjectures are true. This talk is ba sed on joint works with B. Harbourne\, \\L. Farnik\, J. Huizenga\, D. Schm itz and T. Szemberg.\n LOCATION:https://researchseminars.org/talk/ZAG/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Howard Nuer (Technion\, Israel Institute of Technology) DTSTART:20210624T110000Z DTEND:20210624T120000Z DTSTAMP:20260422T225725Z UID:ZAG/132 DESCRIPTION:Title: Th e cohomology of the general stable sheaf on a K3 surface\nby Howard N uer (Technion\, Israel Institute of Technology) as part of ZAG (Zoom Algeb raic Geometry) seminar\n\n\nAbstract\nLet X be a K3 surface of Picard rank one and degree 2n with ample generator H. Let M_H(v) be the moduli space of Gieseker semistable sheaves on X with Mukai vector v. In this talk\, we consider the weak Brill-Noether property for v\, namely that the general sheaf in M_H(v) has at most one nonzero cohomology group. We show that g iven any positive rank r\, there are only finitely many Mukai vectors of r ank r failing weak Brill-Noether over all K3 surfaces of Picard rank one. We discuss our algorithm for finding the potential counterexamples and dem onstrate the utility of our approach by discussing how we were able to cla ssify all such counterexamples up to rank 20 and calculate the cohomology of the general sheaf in each case. Moreover\, for fixed rank r\, we give sharp bounds on n\, d\, and a that guarantee that a Mukai vector v=(r\,dH\ ,a) satisfies weak Brill-Noether. As a corollary\, we provide another pro of of the classification of Ulrich bundles on K3 surfaces of Picard rank o ne. In addition\, we discuss the question of when the general sheaf in M_H (v) is globally generated. This joint work with Izzet Coskun and Kota Yosh ioka makes crucial use of Bridgeland stability conditions and wall-crossin g.\n LOCATION:https://researchseminars.org/talk/ZAG/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Javier Fernandez de Bobadilla (Basque Center for Applied Mathemati cs) DTSTART:20210629T110000Z DTEND:20210629T120000Z DTSTAMP:20260422T225725Z UID:ZAG/133 DESCRIPTION:Title: Th e Brasselet-Schurmann-Yokura conjecture for L-classes on singular varietie s\nby Javier Fernandez de Bobadilla (Basque Center for Applied Mathema tics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe Brasselet-Schurmann-Yokura conjecture predicts the equality between the Ho dge L-class and the Goresky-MacPherson L-class for compact complex algebra ic varieties that are rational homology manifolds. In this talk\, we give two different proofs of this conjecture. The first proof is for projective varieties\, and it is based on cubical hyperresolutions\, the Decompositi on Theorem\, and classical Hodge theory. This is a joint work with I. Pall ares. The second proof is for general compact algebraic varieties by using the theory of mixed Hodge modules. This is a joint work with I. Pallares and M. Saito.\n LOCATION:https://researchseminars.org/talk/ZAG/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Sheng Meng (Korea Institute for Advanced Study) DTSTART:20210701T110000Z DTEND:20210701T120000Z DTSTAMP:20260422T225725Z UID:ZAG/134 DESCRIPTION:Title: Au tomorphism group and its Jordan property\nby Sheng Meng (Korea Institu te for Advanced Study) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nA group is said to have Jordan property if there exists a Jor dan constant J such that any finite subgroup has an abelian subgroup with index bounded by J. I will survey known results for Jordan property on cer tain automorphism groups and birational automorphism groups of varieties. I will also explain our recent progress on automorphism groups of compact spaces in Fujiki’s class C. This is a joint work with Fabio Perroni and De-Qi Zhang.\n LOCATION:https://researchseminars.org/talk/ZAG/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Taku Suzuki (Utsunomiya University) DTSTART:20210706T100000Z DTEND:20210706T110000Z DTSTAMP:20260422T225725Z UID:ZAG/135 DESCRIPTION:Title: Hi gher order minimal families of rational curves on Fano manifolds\nby T aku Suzuki (Utsunomiya University) as part of ZAG (Zoom Algebraic Geometry ) seminar\n\n\nAbstract\nThe purpose of my talk is to introduce the notion of higher order minimal families of rational curves on Fano manifolds and to explain two results concerning it. One is that Fano manifolds are cove red by higher rational manifolds if their Chern characters satisfy some po sitivity conditions. The other is a classification of embedded Fano manifo lds covered by higher linear spaces.\n LOCATION:https://researchseminars.org/talk/ZAG/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Aline Zanardini (Leiden University) DTSTART:20210708T150000Z DTEND:20210708T160000Z DTSTAMP:20260422T225725Z UID:ZAG/136 DESCRIPTION:Title: St ability of pencils of plane curves\nby Aline Zanardini (Leiden Univers ity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn th is talk I will discuss some recent results on the problem of classifying p encils of plane curves up to projective equivalence. We will see how the s tability of a pencil is related to the stability of its generators\, to th e log canonical threshold\, and to the multiplicities of a base point. In particular\, I will present complete stability criteria for certain pencil s of plane sextics called Halphen pencils of index two.\n LOCATION:https://researchseminars.org/talk/ZAG/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Zheng Zhang (ShanghaiTech) DTSTART:20210713T100000Z DTEND:20210713T110000Z DTSTAMP:20260422T225725Z UID:ZAG/137 DESCRIPTION:Title: Th e moduli space of cubic surface pairs via the intermediate Jacobians of Ec kardt cubic threefolds\nby Zheng Zhang (ShanghaiTech) as part of ZAG ( Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe study the moduli space of pairs consisting of a smooth cubic surface and a transverse plane via a period map. More specifically\, the construction associates to a cubic su rface pair a so-called Eckardt cubic threefold which admits an involution\ , and the period map sends the pair to the anti-invariant part of the inte rmediate Jacobian. Our main result is that the global Torelli theorem hold s for the period map (in other words\, the period map is injective). The k ey ingredients of the proof include a description of the anti-invariant pa rt of the intermediate Jacobian as a Prym variety of a branched cover and a detailed study of certain positive dimensional fibers of the correspondi ng Prym map. This is joint work with S. Casalaina-Martin.\n LOCATION:https://researchseminars.org/talk/ZAG/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicole Lemire (University of Western Ontario) DTSTART:20210715T160000Z DTEND:20210715T170000Z DTSTAMP:20260422T225725Z UID:ZAG/138 DESCRIPTION:Title: Co dimension 2 cycles of classifying spaces of low-dimensional algebraic tori \nby Nicole Lemire (University of Western Ontario) as part of ZAG (Zoo m Algebraic Geometry) seminar\n\n\nAbstract\nLet T be an algebraic torus o ver a field F\, and let CH^2(BT) be the Chow group of codimension 2 cycles in its classifying space. Following work of Blinstein and Merkurjev on th e structure of the torsion part of CH^2(BT)\, Scavia\, in a recent preprin t\, found an example of an algebraic torus with non-trivial torsion in CH^ 2(BT). In joint work with Alexander Neshitov\, we show computationally tha t the group CH^2(BT) is torsion-free for all algebraic tori of dimension a t most 5 and determine the conjugacy classes of finite subgroups of GL_6(Z ) which correspond to 6-dimensional tori with nontrivial torsion in CH^2(B T). Some interesting properties of the structure of low-dimensional algebr aic tori are involved.\n LOCATION:https://researchseminars.org/talk/ZAG/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Eiji Inoue (RIKEN iTHEMS) DTSTART:20210720T110000Z DTEND:20210720T120000Z DTSTAMP:20260422T225725Z UID:ZAG/139 DESCRIPTION:Title: Pe relman's entropy and optimal degeneration\nby Eiji Inoue (RIKEN iTHEMS ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlgebrai c optimal degeneration of Fano variety along Kahler-Ricci flow was origina lly constructed by Chen-Sun-Wang and was deepened by Dervan-Szekelyhidi\, Han-Li and recent Blum-Liu-Xu-Zhuang. The degeneration is a substantial in termediate for studying a Fano variety with Kahler-Ricci soliton appearing in the Gromov-Hausdorff limit of Kahler-Ricci flow. The degeneration is c haracterized by a valuation which maximizes `H-entropy' among all valuatio ns. Motivated by these works\, I would like to explain my ongoing attempt to optimal degeneration of polarized variety with respect to `mu-entropy'. The mu-entropy appears in my study on mu-cscK metrics and muK-stability\, which I introduced to understand cscK metrics and Kahler-Ricci soliton in a unified way. Going deep into the story\, we encounter Perelman's entrop y\, which turns out to be the origin of our story.\n LOCATION:https://researchseminars.org/talk/ZAG/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Swarnava Mukhopadhyay (Tata Institute of Fundamental Research) DTSTART:20210722T110000Z DTEND:20210722T120000Z DTSTAMP:20260422T225725Z UID:ZAG/140 DESCRIPTION:Title: Hi tchin connection for parabolic bundles\nby Swarnava Mukhopadhyay (Tata Institute of Fundamental Research) as part of ZAG (Zoom Algebraic Geometr y) seminar\n\n\nAbstract\nIn a fundamental paper in1990\, Hitchin consider ed the space of non-abelian theta functions/conformal blocks/Verlinde spac es from the view point of geometric-quantization (Konstant-Kirillov-Sourea u) for the moduli space of principal bundles on a smooth projective curv e. Hitchin found a flat projective connection that can be interpreted as i dentification of these spaces via a parallel transport along a path joinin g different curves in the Teichmuller space. In this talk\, we will discus s a generalization of Hitchin's construction to the parabolic set-up. Name ly we consider punctured curves and the moduli space of parabolic $G$ bund les and produce a flat projective connection that identifies sections of p arabolic determinant bundles as the puncture curve varies. This is a joint work with Indranil Biswas and Richard Wentworth.\n LOCATION:https://researchseminars.org/talk/ZAG/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenneth Ascher (Princeton University) DTSTART:20210727T160000Z DTEND:20210727T170000Z DTSTAMP:20260422T225725Z UID:ZAG/141 DESCRIPTION:Title: K- stability and birational geometry of moduli spaces of quartic K3 surfaces< /a>\nby Kenneth Ascher (Princeton University) as part of ZAG (Zoom Algebra ic Geometry) seminar\n\n\nAbstract\nWe discuss various compactifications o f moduli spaces of quartic K3 surfaces constructed using GIT\, hodge theor y\, and K-stability. This is based on joint work with Kristin DeVleming an d Yuchen Liu.\n LOCATION:https://researchseminars.org/talk/ZAG/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Anand Sawant (Tata Institute of Fundamental Research) DTSTART:20210729T110000Z DTEND:20210729T120000Z DTSTAMP:20260422T225725Z UID:ZAG/142 DESCRIPTION:Title: Ne ar-rationality properties of norm varieties\nby Anand Sawant (Tata Ins titute of Fundamental Research) as part of ZAG (Zoom Algebraic Geometry) s eminar\n\n\nAbstract\nThe standard norm varieties played a crucial role in Voevodsky's proof of the Bloch-Kato conjecture. I will discuss various n ear-rationality concepts for smooth projective varieties and describe know n near-rationality results for standard norm varieties. I will then outli ne an argument showing that a standard norm variety over a field of charac teristic 0 is universally R-trivial after passing to the algebraic closure of the base field. The talk is based on joint work with Chetan Balwe and Amit Hogadi.\n LOCATION:https://researchseminars.org/talk/ZAG/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Fanelli (Institut de Mathématiques de Bordeaux) DTSTART:20210902T110000Z DTEND:20210902T120000Z DTSTAMP:20260422T225725Z UID:ZAG/143 DESCRIPTION:Title: Ra tional simple connectedness and Fano threefolds\nby Andrea Fanelli (In stitut de Mathématiques de Bordeaux) as part of ZAG (Zoom Algebraic Geome try) seminar\n\n\nAbstract\nThe notion of rational simple connectedness ca n be seen as an algebro-geometric analogue of simple connectedness in topo logy. The work of de Jong\, He and Starr has already produced several rece nt studies to understand this notion. \nIn this talk I will discuss the jo int project with Laurent Gruson and Nicolas Perrin to study rational simpl e connectedness for Fano threefolds via explicit methods from birational g eometry.\n LOCATION:https://researchseminars.org/talk/ZAG/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Schnell (Stony Brook University) DTSTART:20210907T090000Z DTEND:20210907T100000Z DTSTAMP:20260422T225725Z UID:ZAG/144 DESCRIPTION:Title: A new finiteness theorem for variations of Hodge structure\nby Christian Schnell (Stony Brook University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will talk about a new finiteness theorem for var iations of Hodge structure. It is a generalization of the Cattani-Deligne- Kaplan theorem from Hodge classes to so-called self-dual (and anti-self-du al) classes. For example\, among integral cohomology classes of degree 4\, those of type (4\,0) + (2\,2) + (0\,4) are self-dual\, and those of type (3\,1) + (1\,3) are anti-self-dual. The result is suggested by considerati ons in theoretical physics\, and the proof uses o-minimality and the defin ability of period mappings. This is joint work with Benjamin Bakker\, Thom as Grimm\, and Jacob Tsimerman.\n LOCATION:https://researchseminars.org/talk/ZAG/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Filipazzi (École polytechnique fédérale de Lausanne) DTSTART:20210909T150000Z DTEND:20210909T160000Z DTSTAMP:20260422T225725Z UID:ZAG/145 DESCRIPTION:Title: On the boundedness of elliptically fibered varieties\nby Stefano Filipaz zi (École polytechnique fédérale de Lausanne) as part of ZAG (Zoom Alge braic Geometry) seminar\n\n\nAbstract\nIn this talk\, we will survey some ideas to address the boundedness of varieties admitting an elliptic fibrat ion. After introducing general ideas\, we will discuss how they apply conc retely to special classes of varieties: n-folds of Kodaira dimension n-1\, and elliptic Calabi--Yau varieties. Part of this talk is based on current work in progress joint with C.D. Hacon and R. Svaldi.\n LOCATION:https://researchseminars.org/talk/ZAG/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaroslaw Wisniewski (Institute of Mathematics\, University of Wars aw) DTSTART:20210914T140000Z DTEND:20210914T150000Z DTSTAMP:20260422T225725Z UID:ZAG/146 DESCRIPTION:Title: Ra tional maps via C* actions\nby Jaroslaw Wisniewski (Institute of Mathe matics\, University of Warsaw) as part of ZAG (Zoom Algebraic Geometry) se minar\n\n\nAbstract\nI will recall old results and present new facts linki ng varieties with C^* action to birational maps. I particular I will talk about recent results obtained together with Michalek\, Monin\, Occhetta\, Romano\, and Sola Conde.\n LOCATION:https://researchseminars.org/talk/ZAG/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Geordie Williamson (Sydney Mathematical Research Institute) DTSTART:20210916T210000Z DTEND:20210916T220000Z DTSTAMP:20260422T225725Z UID:ZAG/147 DESCRIPTION:Title: Ge ometric extensions\nby Geordie Williamson (Sydney Mathematical Researc h Institute) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nThe Decomposition Theorem is probably my favourite theorem. I'll start by recalling the statement and trying to explain a little of why it is so remarkable. One consequence is that one could imagine an alternate history of the subject\, in which intersection cohomology complexes were discover ed without knowing about perverse sheaves. I'll explain how this might hav e occurred\, and how it led Soergel and Juteau-Mautner-Williamson to the s tudy of parity sheaves. Parity sheaves need strong parity vanishing assump tions\, which somewhat restrict their utility (particularly for applicatio ns outside of geometric representation theory). The final goal of my talk is to explain a recent theorem (joint with Chris Hone) which proves the ex istence and uniqueness of "geometric extensions" in broad generality. The upshot is that parity sheaves probably don't need parity after all.\n LOCATION:https://researchseminars.org/talk/ZAG/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Perry (University of Michigan) DTSTART:20210921T130000Z DTEND:20210921T140000Z DTSTAMP:20260422T225725Z UID:ZAG/148 DESCRIPTION:Title: Se rre functors of semiorthogonal components\nby Alexander Perry (Univers ity of Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbs tract\nThe Serre functor of a triangulated category is one of its most imp ortant invariants\, playing the role of the dualizing complex of a variety in noncommutative algebraic geometry. I will explain how to describe the Serre functors of many semiorthogonal components of varieties in terms of spherical twists. In the case of Kuznetsov components of Fano complete int ersections\, this leads to a proof of a conjecture of Katzarkov and Kontse vich on the dimensions of such categories\, and implies the nonexistence o f Serre invariant stability conditions when the degrees of the complete in tersection do not all coincide. This is joint work with Alexander Kuznetso v.\n LOCATION:https://researchseminars.org/talk/ZAG/148/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton University) DTSTART:20210923T150000Z DTEND:20210923T160000Z DTSTAMP:20260422T225725Z UID:ZAG/149 DESCRIPTION:Title: Lo rentzian polynomials\nby June Huh (Princeton University) as part of ZA G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLorentzian polynomials link continuous convex analysis and discrete convex analysis via tropical geometry. The tropical connection is used to produce Lorentzian polynomial s from discrete convex functions. Specific examples can be constructed fro m graphs\, convex bodies\, stable polynomials\, irreducible representation s of general linear groups\, and in particular\, projective varieties. I w ill explain the main ideas from the viewpoint of algebraic geometry. Based on joint work with Petter Branden.\n LOCATION:https://researchseminars.org/talk/ZAG/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulia Sacca (Columbia University) DTSTART:20210928T150000Z DTEND:20210928T160000Z DTSTAMP:20260422T225725Z UID:ZAG/150 DESCRIPTION:Title: Co mpactification of Lagrangian fibrations\nby Giulia Sacca (Columbia Uni versity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nL agrangian fibered Hyper-Kahler manifolds are the natural generalization of elliptic K3 surfaces and have been used to study and construct examples o f compact Hyper-Kahler manifolds and (possibly singular) symplectic variet ies. In this talk I will talk about some recent compactification technique s I introduced for quasi-projective Lagrangian fibrations\, with applicati ons to the study of Prym\, Intermediate Jacobian\, and Albanese fibrations .\n LOCATION:https://researchseminars.org/talk/ZAG/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Neeman (Australian National University) DTSTART:20210930T210000Z DTEND:20210930T220000Z DTSTAMP:20260422T225725Z UID:ZAG/151 DESCRIPTION:Title: Un iqueness theorems for dg enhancements\nby Amnon Neeman (Australian Nat ional University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nAbstract: The study of Fourier-Mukai transforms has led to many fa scinating developments\, and in this talk we will focus on just one of the m. In a 2004 article Bondal\, Larsen and Lunts made the daring conjecture that geometric categories should have unique enhancements\, and this remar kable conjecture turns out to be true. We will describe the series of theo rems that have come out of this conjecture. The recent work\, which we wil l get to at the end of the talk\, is joint with Alberto Canonaco and Paolo Stellari.\n LOCATION:https://researchseminars.org/talk/ZAG/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Caraiani (Imperial College London) DTSTART:20211005T100000Z DTEND:20211005T110000Z DTSTAMP:20260422T225725Z UID:ZAG/152 DESCRIPTION:Title: On the cohomology of Hilbert modular varieties with torsion coefficients \nby Ana Caraiani (Imperial College London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nShimura varieties are certain moduli spa ces equipped with many symmetries\, that play an important role in the Lan glands programme. For example\, Hilbert modular varieties are quotients of the product of several copies of the upper-half plane by certain arithmet ic groups. I will discuss a general conjecture on the cohomology of Shimur a varieties with torsion coefficients\, which states that the non-degenera te part of their cohomology is concentrated in the middle degree. I will g ive an overview of an approach to this conjecture introduced in joint work with Peter Scholze. This approach relies on the geometry of the Hodge-Tat e period morphism\, which I will describe\, and on certain technical compu tations. I will then specialise to the case of Hilbert modular varieties a nd explain a modified version of this approach that relies on an instance of geometric Jacquet-Langlands functoriality for the fibers of the Hodge-T ate period morphism. This is joint work with Matteo Tamiozzo.\n LOCATION:https://researchseminars.org/talk/ZAG/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Yongnam Lee (Korea Advanced Institute of Science and Technology) DTSTART:20211007T110000Z DTEND:20211007T120000Z DTSTAMP:20260422T225725Z UID:ZAG/153 DESCRIPTION:Title: Do minant rational maps from a very general hypersurface\nby Yongnam Lee (Korea Advanced Institute of Science and Technology) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThere has been recent interest in studying measures of irrationality for hypersurfaces $X$ of high degree in $\\mathbb P^{n+1}$. The degree of irrationality of $X$ is defined as t he minimal degree of dominant rational maps from $X$ to $\\mathbb P^n$. It is known that the degree of irrationality of $X$ is $d-1$ if $X$ is a ver y general hypersurface of degree $d\\ge 2n+1$. In this talk\, from a diffe rent point of view we will discuss dominant rational maps of finite degree from a very general hypersurface $X$ of degree $d\\ge n+3$ in $\\mathbb P ^{n+1}$ to any smooth projective variety $Z$. The finite theorem states th at these form a finite set\, up to birational equivalence of $Z$\, if $Z$ is a variety of general type. It is an interesting question to determine $ Z$ when $Z$ is not birational to $X$. It is conjecturally expected that $Z $ is rationally connected if $X$ is a very general hypersurface of degree $d\\ge n+3$. In this talk\, I will present some partial results for this e xpectation. This talk combines the joint work with Gian Pietro Pirola and the joint work with De-Qi Zhang.\n LOCATION:https://researchseminars.org/talk/ZAG/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Thomas (Imperial College London) DTSTART:20211012T160000Z DTEND:20211012T170000Z DTSTAMP:20260422T225725Z UID:ZAG/154 DESCRIPTION:Title: Hi gher rank DT theory from curve counting\nby Richard Thomas (Imperial C ollege London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstr act\nFix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistabl e bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh s howing these generalised DT invariants in any rank r can be written in ter ms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These in variants are predicted by S-duality to be governed by (vector-valued\, moc k) modular forms.\n LOCATION:https://researchseminars.org/talk/ZAG/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Fei Hu (University of Oslo) DTSTART:20211014T120000Z DTEND:20211014T130000Z DTSTAMP:20260422T225725Z UID:ZAG/155 DESCRIPTION:Title: A dynamical approach to generalized Weil's Riemann hypothesis\nby Fei Hu (University of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n \nAbstract\nInspired by a result of Esnault and Srinivas on automorphisms of surfaces and recent advances in complex dynamics\, Truong raised a ques tion on the comparison of two dynamical degrees\, which are defined using pullback actions of dynamical correspondences on numerical cycle class gro ups and cohomology groups\, respectively. An affirmative answer to his que stion would surprisingly imply Weil’s Riemann hypothesis. In this talk\, I shall discuss some partial results in the cases of Abelian varieties an d surfaces. This is based on joint work with Tuyen Truong.\n LOCATION:https://researchseminars.org/talk/ZAG/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Ronan Terpereau (Université de Bourgogne) DTSTART:20211019T150000Z DTEND:20211019T160000Z DTSTAMP:20260422T225725Z UID:ZAG/156 DESCRIPTION:Title: Re al structures on almost homogeneous varieties\nby Ronan Terpereau (Uni versité de Bourgogne) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nIn this talk\, we will be interested in the real structures o n the almost homogeneous varieties\; these are the complex algebraic varie ties X endowed with an action of a reductive algebraic group G such that G acts on X with a dense open orbit. We will see how to determine when a re al structure on X exists and\, if so\, how to describe and count all of th em. In particular\, we will try to illustrate our approach on two classica l families of almost homogeneous varieties: the horospherical varieties (w hich include toric manifolds and flag varieties) and the SL(2)-almost homo geneous threefolds (which include the Fano threefolds P3\, Q3\, V5\, and V 22). This is a joint work with Lucy Moser-Jauslin (IMB\, Dijon).\n LOCATION:https://researchseminars.org/talk/ZAG/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Donu Arapura (Purdue University) DTSTART:20211021T170000Z DTEND:20211021T180000Z DTSTAMP:20260422T225725Z UID:ZAG/157 DESCRIPTION:Title: Eu ler characteristics of aspherical Kähler manifolds\nby Donu Arapura ( Purdue University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA bstract\nThis is joint work with Botong Wang. I want to start by recalling the Hopf-Singer conjecture on the sign of the Euler characteristic of a c ompact aspherical manifold. In the K\\”ahler setting\, we have a stronge r conjecture involving Euler characteristics of perverse sheaves. Our resu lts are that the stronger conjecture holds when X is compact K\\”ahler w ith nonpositive curvature\, or X is aspherical projective with a faithfu l rigid local system. I will sketch the proofs\, and describe with some il lustrative examples.\n LOCATION:https://researchseminars.org/talk/ZAG/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Fenglong You (University of Oslo) DTSTART:20211026T130000Z DTEND:20211026T140000Z DTSTAMP:20260422T225725Z UID:ZAG/158 DESCRIPTION:Title: De generations\, fibrations and mirror symmetry\nby Fenglong You (Univers ity of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nGiven a Tyurin degeneration of a Calabi-Yau variety to a union of two q uasi-Fano varieties\, Doran-Harder-Thompson conjectured that the Landau-Gi nzburg models of two quasi-Fano varieties can be glued to the mirror Calab i-Yau variety which admits a P^1-fibration. I will talk about a generaliza tion of this conjecture to degenerations of quasi-Fano varieties. I will e xplain some evidence of this conjecture including a gluing formula for (re lative) periods.\n LOCATION:https://researchseminars.org/talk/ZAG/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Viatcheslav Kharlamov (University of Strasbourg) DTSTART:20211028T140000Z DTEND:20211028T150000Z DTSTAMP:20260422T225725Z UID:ZAG/159 DESCRIPTION:Title: Ne w examples of surgery invariant counts in real algebraic geometry\nby Viatcheslav Kharlamov (University of Strasbourg) as part of ZAG (Zoom Alge braic Geometry) seminar\n\n\nAbstract\nInitial Welschinger invariants\, as well as their various generalizations\, are very sensitive\, in general \ , to a change of topology of the underlying real structure. However\, it w as soon noticed that some natural combinations of them have a stronger inv ariance property (remaining also non-trivial in many interesting cases)\, the property that I call "surgery invariance": for a given complex defor mation class of a variety\, they no more depend on a chosen real structure . The starting example is the signed count of real lines on cubic surf aces in accordance with B.~Segre's division of such lines in 2 kinds\, hy perbolic and elliptic. It is this example that originated a discovery of similar counts on higher dimensional hypersurfaces and complete intersect ions\, and served as one of the impulses for a development of an integer valued real Schubert calculus. In this talk (based on a work in progress\, joint with Sergey Finashin) I intend to discuss extending of the above cu bic surface example in a bit different direction: from lines on a cubic su rface to lines\, and even higher degree rational curves\, on other del Pez zo surfaces.\n LOCATION:https://researchseminars.org/talk/ZAG/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Elana Kalashnikov (Harvard University) DTSTART:20211102T170000Z DTEND:20211102T180000Z DTSTAMP:20260422T225725Z UID:ZAG/160 DESCRIPTION:Title: Un doing toric degenerations: an analogue of Greene-Plesser mirror symmetry f or the Grassmannian\nby Elana Kalashnikov (Harvard University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe most basic co nstruction of mirror symmetry compares the Calabi–Yau hypersurfaces of p rojective space and projective space quotient a finite group G. There is a natural analogue of this finite group action on the Grassmannian Gr(n\, r ). In this talk\, I'll explain how toric degenerations\, blow-ups\, variat ion of GIT and mirror symmetry relate the Calabi–Yau hypersurfaces of Gr (n\,r) and Gr(n\,r)/G. This is joint work with Tom Coates and Charles Dora n.\n LOCATION:https://researchseminars.org/talk/ZAG/160/ END:VEVENT BEGIN:VEVENT SUMMARY:François Loeser (Sorbonne Université) DTSTART:20211104T140000Z DTEND:20211104T150000Z DTSTAMP:20260422T225725Z UID:ZAG/161 DESCRIPTION:Title: A motivic version of topological mirror symmetry\nby François Loeser (S orbonne Université) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nHausel and Thaddeus have conjectured that the moduli spaces of twisted SL_n- and PGL_n-Higgs bundles on a smooth projective curve have th e same (twisted) stringy Hodge numbers. This was recently proven by Groech enig\, Wyss and Ziegler using $p$-adic integration. In this talk we shall explain how we can prove using motivic integration that the result holds i n the Grothendieck ring of rational Chow motives. This is joint work with D. Wyss.\n LOCATION:https://researchseminars.org/talk/ZAG/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Farbod Shokrieh (University of Washington) DTSTART:20211109T170000Z DTEND:20211109T180000Z DTSTAMP:20260422T225725Z UID:ZAG/162 DESCRIPTION:Title: He ights and moments of abelian varieties\nby Farbod Shokrieh (University of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst ract\nWe give a formula which\, for a principally polarized abelian variet y $(A\, \\lambda)$ over a number field (or a function field)\, relates the stable Faltings height of $A$ with the N\\'eron--Tate height of a symmetr ic theta divisor on $A$. Our formula involves invariants arising from trop ical geometry. We also discuss the case of Jacobians in some detail\, wher e graphs and electrical networks will play a key role. (Based on joint wor ks with Robin de Jong.)\n LOCATION:https://researchseminars.org/talk/ZAG/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosa Winter (King's College London) DTSTART:20211111T130000Z DTEND:20211111T140000Z DTSTAMP:20260422T225725Z UID:ZAG/163 DESCRIPTION:Title: Co ncurrent exceptional curves on del Pezzo surfaces of degree one and torsio n points on elliptic fibrations\nby Rosa Winter (King's College London ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLet S be a del Pezzo surface of degree one. Then S contains 240 exceptional curves over an algebraically closed field. After blowing up a specific point one obtains an elliptic surface E\, where the exceptional curves correspond t o 240 sections. At most 16 exceptional curves gan go through the same poin t on S\, and when this happens\, the corresponding point on E is torsion o n its fiber. In this talk I will consider the question how many exceptiona l curves can go through a point on S for which the corresponding point on E is non-torsion on its fiber. First of all I will explain how this questi on came up when studying the density of the set of rational points on del Pezzo surfaces of degree one. I will then show that if at least 9 exceptio nal curves intersect in a point on~S\, the corresponding point on E is tor sion on its fiber. This is less trivial than one might think by looking at the Mordell--Weil rank of E. Finally\, in joint work with Julie Desjardin s we show that 7 exceptional curves can go through a non-torsion point\, a nd the question if 8 exceptional curves can go through a non-torsion point is still work in progress. I will show how one might try to tackle this.\ n LOCATION:https://researchseminars.org/talk/ZAG/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Gross (University of Cambridge) DTSTART:20211116T150000Z DTEND:20211116T160000Z DTSTAMP:20260422T225725Z UID:ZAG/164 DESCRIPTION:Title: Op en FJRW theory\nby Mark Gross (University of Cambridge) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will describe joint wo rk with Tyler Kelly and Ran Tessler. FJRW (Fan-Jarvis-Ruan-Witten) theory is an enumerative theory of quasi-homogeneous singularities\, or alternati vely\, of Landau-Ginzburg models. It associates to a potential W:C^n -> C given by a quasi-homogeneous polynomial moduli spaces of (orbi-)curves of some genus and marked points along with some extra structure\, and these m oduli spaces carry virtual fundamental classes as constructed by Fan-Jarvi s-Ruan. Here we specialize to the case W=x^r+y^s and construct an analogou s enumerative theory for disks. We show that these open invariants provide perturbations of the potential W in such a way that mirror symmetry becom es manifest. Further\, these invariants are dependent on certain choices o f boundary conditions\, but satisfy a beautiful wall-crossing formalism.\n LOCATION:https://researchseminars.org/talk/ZAG/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Oscar Garcia-Prada (ICMAT) DTSTART:20211118T150000Z DTEND:20211118T160000Z DTSTAMP:20260422T225725Z UID:ZAG/165 DESCRIPTION:Title: Hi ggs bundles and higher Teichmüller spaces\nby Oscar Garcia-Prada (ICM AT) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIt is well-known that the Teichmüller space of a compact real surface can be id entified with a connected component of the moduli space of representations of the fundamental group of the surface in PSL(2\,R). Higher Teichmüller spaces are generalizations of this\, where PSL(2\,R) is replaced by cert ain simple non-compact real Lie groups of higher rank. As for the usual Te ichmüller space\, these spaces consist entirely of discrete and faithful representations. Several cases have been identified over the years. First\ , the Hitchin components for split groups\, then the maximal Toledo invari ant components for Hermitian groups\, and more recently certain components for SO(p\,q). In this talk\, I will describe a general construction of al l possible higher Teichmüller spaces\, and a parametrization of them usin g the theory of Higgs bundles\, given in joint work with Bradlow\, Collier \, Gothen and Oliveira.\n LOCATION:https://researchseminars.org/talk/ZAG/165/ END:VEVENT BEGIN:VEVENT SUMMARY:Sung Rak Choi (Yonsei University) DTSTART:20211123T100000Z DTEND:20211123T110000Z DTSTAMP:20260422T225725Z UID:ZAG/166 DESCRIPTION:Title: Su badditivity theorem for Okounkov bodies\nby Sung Rak Choi (Yonsei Univ ersity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe will investigate the subadditivity theorem of Okounkov bodies for algebra ic fiber spaces. As an application\, we obtain some numerical variants of the Iitaka conjecture. As a byproduct\, we also obtain a criterion of bir ational isotriviality in terms of Okounkov bodies when the general fiber i s of general type. We expect that our results will provide a new approach toward the Iitaka conjecture. This is a joint work with Jinhyung Park.\n LOCATION:https://researchseminars.org/talk/ZAG/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Urech (École polytechnique fédérale de Lausanne) DTSTART:20211125T150000Z DTEND:20211125T160000Z DTSTAMP:20260422T225725Z UID:ZAG/167 DESCRIPTION:Title: Ac tions of Cremona groups on CAT(0) cube complexes\nby Christian Urech ( École polytechnique fédérale de Lausanne) as part of ZAG (Zoom Algebrai c Geometry) seminar\n\n\nAbstract\nRecently\, in geometric group theory\, isometric actions of groups on CAT(0) cube complexes have turned out to be powerful tools to study a broad range of groups. In this talk\, I will ex plain the construction of CAT(0) cube complexes on which groups of biratio nal transformations act by isometries and explain how to use these actions to deduce new and old group theoretical and dynamical results about Cremo na groups. This is joint work with Anne Lonjou.\n LOCATION:https://researchseminars.org/talk/ZAG/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatemeh Rezaee (Loughborough University) DTSTART:20211130T150000Z DTEND:20211130T160000Z DTSTAMP:20260422T225725Z UID:ZAG/168 DESCRIPTION:Title: Wa ll-crossing pathologies in dimension three\nby Fatemeh Rezaee (Loughbo rough University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nRunning wall-crossing (with respect to Bridgeland stability condit ions)\, I will describe the geometry of associated moduli spaces to canoni cal genus four curves\, including the moduli space of PT stable pairs and the Hilbert scheme. Along the way\, I will introduce a new wall-crossing p henomenon that induces non-Q-factorial singularities\; hence\, it cannot b e detected as an operation in the Minimal Model Program of the correspondi ng moduli space\, unlike the case for many surfaces.\n LOCATION:https://researchseminars.org/talk/ZAG/168/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Lehmann (Boston College) DTSTART:20211202T130000Z DTEND:20211202T140000Z DTSTAMP:20260422T225725Z UID:ZAG/169 DESCRIPTION:Title: Ra tional curves on del Pezzo surfaces in characteristic p\nby Brian Lehm ann (Boston College) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nTesta classified the components of the moduli space of rational curves on a del Pezzo surface over an algebraically closed field of chara cteristic 0. In characteristic p\, new pathologies can appear. I will expl ain how such pathologies are predicted by Geometric Manin's Conjecture and how this perspective leads to a description of "problematic" surfaces. Wh en no pathologies occur\, we can completely classify the components of the moduli space of rational curves. This is joint work with Roya Beheshti\, Eric Riedl\, and Sho Tanimoto.\n LOCATION:https://researchseminars.org/talk/ZAG/169/ END:VEVENT BEGIN:VEVENT SUMMARY:Jun-Muk Hwang (Korea Institute for Advanced Study) DTSTART:20211207T100000Z DTEND:20211207T110000Z DTSTAMP:20260422T225725Z UID:ZAG/170 DESCRIPTION:Title: Mi nimal rational curves and 1-flat irreducible G-structures\nby Jun-Muk Hwang (Korea Institute for Advanced Study) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\n1-flat irreducible G-structures\, equiva lently\, irreducible G-structures admitting torsion-free affine connection s\, have been studied extensively in differential geometry\, especially i n connection with the theory of affine holonomy groups. In a joint work wi th Qifeng Li\, we study them in a setting in algebraic geometry\, where th ey arise from varieties of minimal rational tangents (VMRT) associated to families of minimal rational curves on uniruled projective manifolds. We p rove that such a structure is locally symmetric when the dimension of the uniruled projective manifold is at least 5. By the classification result o f Merkulov and Schwachhoefer on irreducible affine holonomy\, the problem is reduced to the case when the VMRT at a general point of the uniruled pr ojective manifold is isomorphic to a subadjoint variety. In the latter sit uation\, we prove a stronger result that\, without the assumption of 1-fla tness\, the structure arising from VMRT is always locally flat.\n LOCATION:https://researchseminars.org/talk/ZAG/170/ END:VEVENT BEGIN:VEVENT SUMMARY:Helge Ruddat (University of Hamburg) DTSTART:20211209T150000Z DTEND:20211209T160000Z DTSTAMP:20260422T225725Z UID:ZAG/171 DESCRIPTION:Title: Fa no manifolds from smoothing toroidal crossing varieties\nby Helge Rudd at (University of Hamburg) as part of ZAG (Zoom Algebraic Geometry) semina r\n\n\nAbstract\nI am reporting on a joint work with Corti\, Felten\, Petr acci where we put particular singular log structures on toroidal crossing spaces. We prove various properties of the resulting reflexive log differe ntial forms from using local log smooth log crepant resolutions. The prope rties give the ingredients to conclude the Hodge to de Rham degeneration a nd the smoothability of the toroidal crossing Fano variety. All Fanos with very amply anticanonical divisor are obtained from so called "admissible" log singularties by this method. We believe that yet more general log sin gularities give all Fano manifolds with non-empty anticanonical class by s imilar methods.\n LOCATION:https://researchseminars.org/talk/ZAG/171/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Schaposnik (University of Illinois at Chicago) DTSTART:20211214T150000Z DTEND:20211214T160000Z DTSTAMP:20260422T225725Z UID:ZAG/172 DESCRIPTION:Title: Th e geometry of Generalized Hyperpolygons\, Hitchin systems and other scient ific advances\nby Laura Schaposnik (University of Illinois at Chicago) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this t alk we will introduce generalized hyperpolygons\, which arise as Nakajima- type representations of a comet-shaped quiver\, following recent work join t with Steven Rayan. After showing how to identify these representations w ith pairs of polygons\, we shall associate to the data an explicit meromor phic Higgs bundle on a genus-g Riemann surface\, where g is the number of loops in the comet. We shall see that\, under certain assumptions on flag types\, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system. Having made the connection to Hitchin moduli spaces\, we will consider different geometric methods d eveloped within that set up to study geometric properties of integrable sy stems and their dualities. Finally\, we shall conclude the talk mentioning other directions in which one can apply geometric insights to make scient ific advances.\n LOCATION:https://researchseminars.org/talk/ZAG/172/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Ballard (University of South Carolina) DTSTART:20211216T150000Z DTEND:20211216T160000Z DTSTAMP:20260422T225725Z UID:ZAG/173 DESCRIPTION:Title: St ratified Mukai flops revisited\nby Matthew Ballard (University of Sout h Carolina) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nWe will describe how constructing Fourier-Mukai kernels for stratified M ukai flops fits into a general framework. Joint with N. Chidambaram and D. Favero.\n LOCATION:https://researchseminars.org/talk/ZAG/173/ END:VEVENT BEGIN:VEVENT SUMMARY:Linquan Ma (Purdue University) DTSTART:20211221T170000Z DTEND:20211221T180000Z DTSTAMP:20260422T225725Z UID:ZAG/174 DESCRIPTION:Title: Th e cohomology table of coherent sheaves on singular projective varieties\nby Linquan Ma (Purdue University) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nThe cohomology table of a coherent sheaf on a p rojective variety is numerical data of the dimension of each cohomoogy gro up of each twist of the sheaf. Eisenbud--Schreyer give a description of th e cone of cohomology table of vector bundles and coherent sheaves on proje ctive spaces. This leads to their proof of the Boij--Soderberg theory whic h describes the cone spanned by the Betti tables of graded modules over po lynomial rings. In this talk\, we give some extensions of these results of Eisenbud--Schreyer to singular projective varieties and singular standard graded rings. Our central technique is to use a sequence of coherent shea ves that behave like an Ulrich sheave asymptotically. We call such sequenc e a lim Ulrich sequence of sheaves and we can prove their existence in pos itive characteristic. This talk is largely based on joint work in progress with Srikanth Iyengar and Mark Walker.\n LOCATION:https://researchseminars.org/talk/ZAG/174/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrei Okounkov (Columbia University) DTSTART:20220203T090000Z DTEND:20220203T100000Z DTSTAMP:20260422T225725Z UID:ZAG/175 DESCRIPTION:Title: Th e unramified Eisenstein spectrum\nby Andrei Okounkov (Columbia Univers ity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI wil l report on joint work with David Kazhdan\, in which we determine the unra mified Eisenstein spectrum for\nall split reductive groups over a global f ield. Our methods are rooted in topology and algebraic geometry.\nSpecific ally\, we relate the spectral decomposition to a decomposition of $T^*(B \ \backslash G / B)$ in in a certain cobordism group\, where $G$ is the Lang lands dual group. This works equally well for fields of positive and zero characteristic.\n LOCATION:https://researchseminars.org/talk/ZAG/175/ END:VEVENT BEGIN:VEVENT SUMMARY:Takumi Murayama (Princeton University) DTSTART:20220111T170000Z DTEND:20220111T180000Z DTSTAMP:20260422T225725Z UID:ZAG/176 DESCRIPTION:Title: Th e Kawamata–Viehweg vanishing theorem for schemes\nby Takumi Murayama (Princeton University) as part of ZAG (Zoom Algebraic Geometry) seminar\n \n\nAbstract\nIn 1953\, Kodaira proved what is now called the Kodaira vani shing theorem\, which states that if L is an ample divisor on a complex pr ojective manifold X\, then H^i(X\,-L) = 0 for all i < dim(X). Since then\, Kodaira's theorem and its generalizations for complex projective varietie s – in particular\, the Kawamata–Viehweg vanishing theorem and its rel ative version due to Kawamata–Matsuda–Matsuki – have become indispen sable tools in algebraic geometry over fields of characteristic zero\, in particular in birational geometry and the minimal model program. However\, while the goal in the minimal model program is to study birational equiva lences between projective varieties\, recent progress in the minimal model program has shown that it would be very useful to have a version of the K awamata–Viehweg vanishing theorem that holds for schemes that are not ne cessarily projective varieties. Recently\, I proved the relative Kawamata –Viehweg vanishing theorem for schemes of equal characteristic zero. My results are optimal given known counterexamples to vanishing theorems in p ositive and mixed characteristic\, and have many applications to both alge braic geometry and commutative algebra. In this talk\, I will discuss my v anishing theorem and several of its applications.\n LOCATION:https://researchseminars.org/talk/ZAG/176/ END:VEVENT BEGIN:VEVENT SUMMARY:Kris Shaw (University of Oslo) DTSTART:20220113T150000Z DTEND:20220113T160000Z DTSTAMP:20260422T225725Z UID:ZAG/177 DESCRIPTION:Title: A tropical approach to the enriched count of bitangents to quartic curves\nby Kris Shaw (University of Oslo) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nUsing A1 enumerative geometry Larson and Vogt h ave provided an enriched count of the 28 bitangents to a quartic curve. In this talk\, I will explain how these enriched counts can be computed comb inatorially using tropical geometry. I will also introduce an arithmetic a nalogue of Viro’s patchworking for real algebraic curves which\, in some cases\, retains enough data to recover the enriched counts. This talk is based on joint work with Hannah Markwig and Sam Payne.\n LOCATION:https://researchseminars.org/talk/ZAG/177/ END:VEVENT BEGIN:VEVENT SUMMARY:Eunjeong Lee (Institute for Basic Science\, Center for Geometry an d Physics) DTSTART:20220118T100000Z DTEND:20220118T110000Z DTSTAMP:20260422T225725Z UID:ZAG/178 DESCRIPTION:Title: On smooth toric Richardson varieties\nby Eunjeong Lee (Institute for Bas ic Science\, Center for Geometry and Physics) as part of ZAG (Zoom Algebra ic Geometry) seminar\n\n\nAbstract\nSchubert varieties and Richardson vari eties are some of the most interesting subvarieties of the full flag varie ties. A maximal torus acts on the full flag variety and these subvarieties are stable under the action. Considering the restriction of the moment ma p on Richardson varieties\, we obtain Bruhat interval polytopes. The combi natorics of Bruhat interval polytopes play an important role in studying t oric Richardson varieties. In this talk\, we consider an interesting famil y of smooth toric Richardson varieties each element of which is associated with a cubic Bruhat interval polytope\, called a toric variety \\textit{o f Catalan type}. We study the relationship between the isomorphism classes of toric varieties of Catalan type and polygon triangulations. Moreover\, we consider the isomorphism classes of toric Schubert varieties which may not be of Catalan type. This talk is based on joint work with Mikiya Masu da and Seonjeong Park.\n LOCATION:https://researchseminars.org/talk/ZAG/178/ END:VEVENT BEGIN:VEVENT SUMMARY:Ehud Hrushovski (University of Oxford) DTSTART:20220120T113000Z DTEND:20220120T123000Z DTSTAMP:20260422T225725Z UID:ZAG/179 DESCRIPTION:Title: Ol d and new results in the model theory of finite fields\nby Ehud Hrusho vski (University of Oxford) as part of ZAG (Zoom Algebraic Geometry) semin ar\n\n\nAbstract\nAx's determination of the first-order theory of finite fields in 1968 was the starting point of a rich chapter of model theory\ ; highlights include the Denef-Loeser connection between definable sets ov er pseudo-finite fields and motives\, their use in motivic integration\, the Chatzidakis-Van den Dries-Macintyre measure theory\, the strong Sze meredi regularity lemma for definable sets and applications to expansion d ue to Terry Tao. I will sketch a path through some of this material\, ai ming to touch on recent work of Levi and Chevalier on higher regularity\ , and on open problems that arise when an additive character is added to the structure.\n LOCATION:https://researchseminars.org/talk/ZAG/179/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Stanford University) DTSTART:20220125T170000Z DTEND:20220125T180000Z DTSTAMP:20260422T225725Z UID:ZAG/180 DESCRIPTION:Title: Th e rational Chow rings of M_7\, M_8\, and M_9\nby Hannah Larson (Stanfo rd University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstr act\nThe rational Chow ring of the moduli space M_g of curves of genus g i s known for g up to 6. In each of these cases\, the Chow ring is tautologi cal (generated by certain natural classes known as kappa classes). In join t work with Sam Canning\, we prove that the rational Chow ring of M_g is t autological for g = 7\, 8\, 9\, thereby determining the Chow rings by earl ier work of Faber. In this talk\, I will give an overview of our approach\ , with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).\n LOCATION:https://researchseminars.org/talk/ZAG/180/ END:VEVENT BEGIN:VEVENT SUMMARY:Sukmoon Huh (Sungkyunkwan Universityok) DTSTART:20220127T100000Z DTEND:20220127T110000Z DTSTAMP:20260422T225725Z UID:ZAG/181 DESCRIPTION:Title: To relli problem on logarithmic sheaves\nby Sukmoon Huh (Sungkyunkwan Uni versityok) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\ nThe logarithmic sheaf associated to a reduced divisor\, is the sheaf of d ifferential 1-forms with logarithmic poles along the divisor\, and it was introduced by P. Deligne to define a mixed Hodge structure on the compleme nt of the divisor. There have been a great deal of study on this subject\, and one of the questions is whether the sheaf determines the divisor or n ot\, which we call the Torelli problem. In case of general hyperplane arra ngements on projective spaces\, I. Dolgachev and M. Kapranov gave a positi ve answer to the Torelli problem when the number of hyperplanes is big eno ugh\, and then later J. Valles gave a complete answer. In this talk we giv e several other results on the Torelli problem\, and report our recent res ult\, in which we introduce two different approachs to have a positive ans wer on the problem. This is a joint work with S. Marchesi\, J. Pons-Llopis and J. Valles.\n LOCATION:https://researchseminars.org/talk/ZAG/181/ END:VEVENT BEGIN:VEVENT SUMMARY:Soheyla Feyzbakhsh (Imperial College London) DTSTART:20220201T150000Z DTEND:20220201T160000Z DTSTAMP:20260422T225725Z UID:ZAG/182 DESCRIPTION:Title: Mo duli spaces of stable objects in the Kuznetsov component of cubic threefol ds\nby Soheyla Feyzbakhsh (Imperial College London) as part of ZAG (Zo om Algebraic Geometry) seminar\n\n\nAbstract\nWe will first discuss a gene ral criterion that ensures a fractional Calabi-Yau category of dimension l ess than or equal to 2 admits a unique Serre-invariant stability condition up to the action of the universal cover of GL+(2\, R). This result can be applied to a certain triangulated subcategory (called the Kuznetsov compo nent) of the bounded derived category of coherent sheaves on a cubic three fold. As an application\, we will prove (i) a categorical version of the T orelli theorem holds for cubic threefolds\, and (ii) the moduli space of U lrich bundles of fixed rank r greater than or equal to 2 on a cubic threef old is irreducible. The talk is based on joint work with Laura Pertusi and a group project with A. Bayer\, S.V. Beentjes\, G. Hein\, D. Martinelli\, F. Rezaee and B. Schmidt.\n LOCATION:https://researchseminars.org/talk/ZAG/182/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Keel (The University of Texas at Austin) DTSTART:20220208T170000Z DTEND:20220208T180000Z DTSTAMP:20260422T225725Z UID:ZAG/183 DESCRIPTION:Title: Mi rror symmetry and analytic disks\nby Sean Keel (The University of Texa s at Austin) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac t\nI will explain my recent construction\, joint with Tony Yu\, of the mir ror to an affine log CY manifold as the spectrum of an algebra with a cano nical basis and structure constants naive counts of Berkovich analytic dis ks. I wont assume any previous knowledge of Berkovich geometry.\n LOCATION:https://researchseminars.org/talk/ZAG/183/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Kummer (TU Dresden) DTSTART:20220210T150000Z DTEND:20220210T160000Z DTSTAMP:20260422T225725Z UID:ZAG/184 DESCRIPTION:Title: Se cant varieties of real curves\nby Mario Kummer (TU Dresden) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAfter an introductio n to hyperbolic polynomials and their relevance in convex optimization\, I will explain a construction of hyperbolic polynomials using secant variet ies of curves. Further\, I will relate this to the theory of Ulrich sheave s.\n LOCATION:https://researchseminars.org/talk/ZAG/184/ END:VEVENT BEGIN:VEVENT SUMMARY:Alena Pirutka (Courant Institute of Mathematical Sciences\, New Yo rk University) DTSTART:20220215T150000Z DTEND:20220215T160000Z DTSTAMP:20260422T225725Z UID:ZAG/185 DESCRIPTION:Title: On local-global principles and Galois cohomology\nby Alena Pirutka (Cour ant Institute of Mathematical Sciences\, New York University) as part of Z AG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this talk we will r eview several questions of local-global type for schemes of dimension 3 in the arithmetic (curves over semi-global fields) and geometric (threefolds over a finite field) settings.\n LOCATION:https://researchseminars.org/talk/ZAG/185/ END:VEVENT BEGIN:VEVENT SUMMARY:David Favero (University of Alberta) DTSTART:20220217T160000Z DTEND:20220217T170000Z DTSTAMP:20260422T225725Z UID:ZAG/186 DESCRIPTION:Title: Pa th Homotopy Quiver Algebras and Mirror Symmetry\nby David Favero (Univ ersity of Alberta) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA bstract\nGiven a quiver (directed graph) embedded in a topological space\, one can consider the algebra of directed paths up to homotopy. Conversel y\, given a certain type of algebra\, I will construct a quiver and a topo logical space which recovers this algebra by the above procedure. These c onstructions induce an equivalence between the derived category of the alg ebra and a certain subcategory of the derived category of sheaves on the t opological space. As applications\, I will recover some examples of homol ogical mirror symmetry for Berglund-Hubsch-Krawitz mirrors and for toric v arieties following work of Bondal and Fan-Lui-Treumann-Zaslow.\n LOCATION:https://researchseminars.org/talk/ZAG/186/ END:VEVENT BEGIN:VEVENT SUMMARY:Alicia Dickenstein (Universidad de Buenos Aires) DTSTART:20220222T150000Z DTEND:20220222T160000Z DTSTAMP:20260422T225725Z UID:ZAG/187 DESCRIPTION:Title: It erated and mixed discriminants\nby Alicia Dickenstein (Universidad de Buenos Aires) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra ct\nClassical work by Salmon and Bromwich classified singular intersection s of two quadric surfaces. The basic idea of these results was already pur sued by Cayley in connection with tangent intersections of conics in the p lane and used by Schafli for the study of hyperdeterminants. More recently \, the problem has been revisited with similar tools in the context of geo metric modeling and a generalization to the case of two higher dimensional quadric hypersurfaces was given by Ottaviani. In joint work with Sandra d i Rocco and Ralph Morrison\, we propose and study a generalization of this question for systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case\, the closure of the locus of co efficients giving a non-degenerate multiple root of the system is defined by a polynomial called the mixed discriminant. We define a related polynom ial called the multivariate iterated discriminant. This iterated discrimin ant is easier to compute and we prove that it is always divisible by the m ixed discriminant. We show that tangent intersections can be computed via iteration if and only if the singular locus of a corresponding dual variet y has sufficiently high codimension. We also study when point configuratio ns corresponding to Segre-Veronese varieties and to the lattice points of planar smooth polygons\, have their iterated discriminant equal to their m ixed discriminant.\n LOCATION:https://researchseminars.org/talk/ZAG/187/ END:VEVENT BEGIN:VEVENT SUMMARY:Diane Maclagan (University of Warwick) DTSTART:20220224T150000Z DTEND:20220224T160000Z DTSTAMP:20260422T225725Z UID:ZAG/188 DESCRIPTION:Title: To ric and tropical Bertini theorems in arbitrary characteristic\nby Dian e Maclagan (University of Warwick) as part of ZAG (Zoom Algebraic Geometry ) seminar\n\n\nAbstract\nThe classical Bertini theorem on irreducibility w hen intersecting by hyperplanes is a standard part of the algebraic geomet ry toolkit. This was generalised recently\, in characteristic zero\, by Fu chs\, Mantova\, and Zannier to a toric Bertini theorem for subvarieties of an algebraic torus\, with hyperplanes replaced by subtori. I will discuss joint work with Gandini\, Hering\, Mohammadi\, Rajchgot\, Wheeler\, and Y u in which we give a different proof of this theorem that removes the char acteristic assumption. An application is a tropical Bertini theorem.\n LOCATION:https://researchseminars.org/talk/ZAG/188/ END:VEVENT BEGIN:VEVENT SUMMARY:Georg Oberdieck (Hausdorff Center for Mathematics) DTSTART:20220301T110000Z DTEND:20220301T120000Z DTSTAMP:20260422T225725Z UID:ZAG/189 DESCRIPTION:Title: Ho lomorphic anomaly equations for the Hilbert schemes of points of a K3 surf ace\nby Georg Oberdieck (Hausdorff Center for Mathematics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nHolomorphic anomaly e quations are certain structural properties predicted by physics for the Gr omov-Witten theory of Calabi-Yau manifolds. In this talk I will explain th e conjectural form of these equations for the Hilbert scheme of points of a K3 surface\, and explain how to prove them for genus 0 and up to three m arkings. As a corollary\, for fixed n\, the (reduced) quantum cohomology o f Hilb^n K3 is determined up to finitely many coefficients.\n LOCATION:https://researchseminars.org/talk/ZAG/189/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Nordstrom (University of Bath) DTSTART:20220303T110000Z DTEND:20220303T120000Z DTSTAMP:20260422T225725Z UID:ZAG/190 DESCRIPTION:Title: K3 surfaces and twisted connected sum G2-manifolds\nby Johannes Nordstro m (University of Bath) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nThe twisted connected sum construction of Kovalev produces ma ny examples of closed Riemannian 7-manifolds with holonomy group G_2 (a sp ecial class of Ricci-flat manifolds)\, starting from complex algebraic geo metry data like Fano 3-folds. If the pieces admit automorphisms\, then add ing an extra twist to the construction yields examples with a wider variet y of topological features. I will outline the constructions\, and describe how a good understanding of moduli of K3 surfaces appearing as anticanoni cal divisors in Fano 3-folds is used in a crucial way to match the pieces in the gluing procedure. This is joint work with Diarmuid Crowley and Seba stian Goette.\n LOCATION:https://researchseminars.org/talk/ZAG/190/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Bragg (University of California\, Berkeley) DTSTART:20220308T170000Z DTEND:20220308T180000Z DTSTAMP:20260422T225725Z UID:ZAG/191 DESCRIPTION:Title: Co mpact supersingular twistor spaces\nby Daniel Bragg (University of Cal ifornia\, Berkeley) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nSupersingular twistor spaces are certain families of K3 surfaces over A^1 associated to a supersingular K3 surface. We will describe a geo metric construction that produces families of K3 surfaces over P^1 which c ompactify supersingular twistor spaces. The key input is a construction re lating Brauer classes of order p on a scheme of characteristic p to certai n sheaves of twisted differential operators. We will give some results on the geometry of compactified supersingular twistor spaces\, and some appli cations.\n LOCATION:https://researchseminars.org/talk/ZAG/191/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Yves Welschinger (Institut Camille Jordan\, Université Lyon 1) DTSTART:20220310T150000Z DTEND:20220310T160000Z DTSTAMP:20260422T225725Z UID:ZAG/192 DESCRIPTION:Title: Sh ellable tilings on simplicial complexes\nby Jean-Yves Welschinger (Ins titut Camille Jordan\, Université Lyon 1) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will introduce a notion of shellable ti lings on finite simplicial complexes\, prove their existence after finitel y many stellar subdivisions and discuss their relations with discrete Mors e theory and h-vectors. Every shelled tiling computes the (co)homology of the complex via two spectral sequences. As a consequence\, I deduce the ex istence of piecewise-linear pinched handle decompositions for all closed t riangulated manifolds.\n LOCATION:https://researchseminars.org/talk/ZAG/192/ END:VEVENT BEGIN:VEVENT SUMMARY:Guolei Zhong (Institute for Basic Science) DTSTART:20220315T090000Z DTEND:20220315T100000Z DTSTAMP:20260422T225725Z UID:ZAG/193 DESCRIPTION:Title: Co mpact Kähler threefolds with the action of an abelian group of maximal dy namical rank\nby Guolei Zhong (Institute for Basic Science) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLet X be a compact K aehler manifold. It is proved by Dinh and Sibony that\, for any abelian su bgroup G of the automorphism group Aut(X)\, if G is of positive entropy\, then G is free abelian with rank no more than dim(X)-1. In the past decade \, when X is projective\, the extremal case rank(G)=dim(X)-1 (being maxima l) has been intensively studied by Zhang. In this talk\, we consider the c ase when X is a general compact Kaehler 3-fold and rank(G)=2. By running t he G-equivariant log minimal model program\, we show that such X is either rationally connected\, or bimeromorphic to a quasi-etale quotient of a co mplex 3-torus.\n LOCATION:https://researchseminars.org/talk/ZAG/193/ END:VEVENT BEGIN:VEVENT SUMMARY:Lawrence Jack Barrott (University of Leiden) DTSTART:20220317T150000Z DTEND:20220317T160000Z DTSTAMP:20260422T225725Z UID:ZAG/194 DESCRIPTION:Title: Fi brations and degenerations of Calabi-Yau varieties via tropical geometry\nby Lawrence Jack Barrott (University of Leiden) as part of ZAG (Zoom A lgebraic Geometry) seminar\n\n\nAbstract\nOne expectation from the Doran-H arder-Thompson is that certain degenerations of Calabi-Yau's should corres pond under mirror symmetry to fibrations by lower dimensional Calabi-Yau's . I will make this expectation precise\, and explain how to prove it under certain assumptions using the Gross-Siebert program. The proof uses an ol d result of Deligne-Illusie together with modern deformation theory from C han-Leung-Ma and Felten-Filip-Ruddat.\n LOCATION:https://researchseminars.org/talk/ZAG/194/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Bridgeland (University of Sheffield) DTSTART:20220322T140000Z DTEND:20220322T150000Z DTSTAMP:20260422T225725Z UID:ZAG/195 DESCRIPTION:Title: Ge ometric structures on spaces of quadratic differentials\nby Tom Bridge land (University of Sheffield) as part of ZAG (Zoom Algebraic Geometry) se minar\n\n\nAbstract\nThis talk is part of a long-running saga which aims t o encode the Donaldson-Thomas invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of examples of such categories whose stability spaces are known to parameteri se compact Riemann surfaces equipped with quadratic differentials. I will explain exactly what geometric structure we should look for on these space s\, and then use moduli spaces of Higgs bundles\, flat connections\, etc t o construct it.\n LOCATION:https://researchseminars.org/talk/ZAG/195/ END:VEVENT BEGIN:VEVENT SUMMARY:Masafumi Hattori (Kyoto University) DTSTART:20220324T100000Z DTEND:20220324T110000Z DTSTAMP:20260422T225725Z UID:ZAG/196 DESCRIPTION:Title: On K-stability of Calabi-Yau fibrations\nby Masafumi Hattori (Kyoto Univ ersity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn K-stability\, the characterization of K-stable varieties is well-studied when K_X is ample or X is a Calabi-Yau or Fano variety. However\, K-stabil ity of Fano fibrations or Calabi-Yau fibrations (i.e.\, K_X is relatively trivial) is not known much in algebraic geometry. On the other hand\, cscK problems on fibrations are studied by Fine\, Jian-Shi-Song and Dervan-Sek tnan in Kahler geometry. We introduce adiabatic K-stability (If f:(X\,H)\\ to (B\,L) is a fibration of polarized varieties\, this means that K-stabil ity of (X\,aH+L) for sufficiently small a) and show that adiabatic K-semis tability of Calabi-Yau fibration implies log-twisted K-semistability of th e base variety by applying the canonical bundle formula. If the base is a curve\, we also obtain a partial converse. In this talk\, I would like to explain our main results and their applications to rational elliptic surfa ces and the conjecture of Miranda on Chow-stability of rational Weierstras s fibrations.\n LOCATION:https://researchseminars.org/talk/ZAG/196/ END:VEVENT BEGIN:VEVENT SUMMARY:Tristan Collins (Massachusetts Institute of Technology) DTSTART:20220329T140000Z DTEND:20220329T150000Z DTSTAMP:20260422T225725Z UID:ZAG/197 DESCRIPTION:Title: SY Z mirror symmetry for some Calabi-Yau surface pairs\nby Tristan Collin s (Massachusetts Institute of Technology) as part of ZAG (Zoom Algebraic G eometry) seminar\n\n\nAbstract\nI will discuss a proof of a strong form of the SYZ mirror symmetry conjecture for Calabi-Yau surfaces pairs construc ted from del Pezzo surfaces and rational elliptic surfaces. Time permittin g\, I will also mention some applications\, including to the Torelli theor em for ALH* gravitational instantons. This is joint work with A. Jacob and Y.-S. Lin.\n LOCATION:https://researchseminars.org/talk/ZAG/197/ END:VEVENT BEGIN:VEVENT SUMMARY:Julius Ross (University of Illinois Chicago) DTSTART:20220331T160000Z DTEND:20220331T170000Z DTSTAMP:20260422T225725Z UID:ZAG/198 DESCRIPTION:Title: Ho dge-Riemann Classes and Schur Polynomials\nby Julius Ross (University of Illinois Chicago) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nThe classical Hodge-Riemann bilinear relations are statements a bout the intersection form associated to the self-wedge product of a K\\"a hler form on a compact complex manifold. Gromov initiated the question a s to whether there are other cohomology that give rise these same bilinear relations\, and proved that this is the case for the intersection of (pos sibly different) K\\"ahler classes. In this talk I will discuss joint wo rk with Matei Toma in which we prove that the Schur classes of ample vecto r bundles have the Hodge-Riemann bilinear relations (at least on $H^{1\,1} $). This gives rise to a number of new inequalities among characteristic classes of ample vector bundles that should be thought of as generalizati ons of the Khovanskii-Tessier inequalities. And if time allows I will als o discuss how this extends to the non-projective case and beyond.\n LOCATION:https://researchseminars.org/talk/ZAG/198/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Codogni (Università di Roma Tor Vergata) DTSTART:20220405T110000Z DTEND:20220405T120000Z DTSTAMP:20260422T225725Z UID:ZAG/199 DESCRIPTION:Title: Am ple cone of KSB and K- moduli spaces\nby Giulio Codogni (Università d i Roma Tor Vergata) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nI will present some quantitative results about the ample cone of the moduli spaces of KSB stable and K-stable varieties of any dimension. These results follow from various higher dimensional generalizations of th e Xiao-Cornalba-Harris slope inequality. Our proofs combine some new Noeth er and Castelnuovo inequalities with a careful study of the Harder-Narasim han filtration of the push-forward of the log pluri-canonical bundles. The talk is based on a joint work with Luca Tasin and Filippo Viviani.\n LOCATION:https://researchseminars.org/talk/ZAG/199/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Laface (Universidad de Concepción) DTSTART:20220407T150000Z DTEND:20220407T160000Z DTSTAMP:20260422T225725Z UID:ZAG/200 DESCRIPTION:Title: On effective cones of rational surfaces\nby Antonio Laface (Universidad de Concepción) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst ract\nEffective cones of rational surfaces have been intensively studied i n the past few years\, especially in the context of Nagata conjecture and Seshadri constants. After reviewing recent results on blow-ups of the proj ective plane at points in very general position\, I will focus on blow-ups of toric surfaces at a general point\, discussing examples of polyhedral and non-polyhedral effective cones. This is joint work with A-M. Castravet \, J. Tevelev and L. Ugaglia.\n LOCATION:https://researchseminars.org/talk/ZAG/200/ END:VEVENT BEGIN:VEVENT SUMMARY:Jose Ignacio Burgos Gil (Instituto de Ciencias Matemáticas) DTSTART:20220412T140000Z DTEND:20220412T150000Z DTSTAMP:20260422T225725Z UID:ZAG/201 DESCRIPTION:Title: Ch ern-Weil theory and Hilbert-Samuel theorem for semi-positive singular toro idal metrics on line bundles\nby Jose Ignacio Burgos Gil (Instituto de Ciencias Matemáticas) as part of ZAG (Zoom Algebraic Geometry) seminar\n \n\nAbstract\nIn this talk I will report on joint work with A. Botero\, D. Holmes and R. de Jong. Using the theory of b-divisors and non-pluripolar products we show that Chen-Weil theory and a Hilbert Samuel theorem can be extended to a wide class of singular semi-positive metrics. We apply the techniques relating semipositive metrics on line bundles to b-divisors to study the line bundle of Siegel-Jacobi forms with the Peterson metric. On the one hand we prove that the ring of Siegel-Jacobi forms of constant pos itive relative index is never finitely generated\, and we recover a formul a of Tai giving the asymptotic growth of the dimension of the spaces of Si egel-Jacobi modular forms.\n LOCATION:https://researchseminars.org/talk/ZAG/201/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Lieblich (University of Washington) DTSTART:20220414T170000Z DTEND:20220414T180000Z DTSTAMP:20260422T225725Z UID:ZAG/202 DESCRIPTION:Title: In finite rank vector bundles and applications\nby Max Lieblich (Universi ty of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb stract\nThis is a report on joint work with Johan de Jong and Minseon Shin . Grothendieck famously asked whether the Brauer group and cohomological B rauer group of a scheme coincide\, a question which still lacks a good ans wer. Modern methods reduce this question to a question about the existence of non-zero vector bundles of finite rank on certain stacks. I will discu ss what happens if one allows vector bundles of infinite rank\, and how th is infinite-rank version of the question is related to the resolution prop erty for schemes. I will also discuss some basic questions about vector bu ndles of infinite rank on varieties\, including the potential existence of some mysterious invariants.\n LOCATION:https://researchseminars.org/talk/ZAG/202/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Paemurru (International Center for Mathematical Sciences – Sofia) DTSTART:20220419T140000Z DTEND:20220419T150000Z DTSTAMP:20260422T225725Z UID:ZAG/203 DESCRIPTION:Title: Co unting Divisorial Contractions with Centre a cAn-singularity\nby Erik Paemurru (International Center for Mathematical Sciences – Sofia) as par t of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nFirst\, we simpl ify the existing classification due to Kawakita and Yamamoto of 3-dimensio nal divisorial contractions with centre a cA_n-singularity. Next we consid er divisorial contractions of discrepancy at least 2 to a fixed variety wi th centre a cA_n-singularity. We show that if there exists one such diviso rial contraction\, then there exist uncountably many such divisorial contr actions.\n LOCATION:https://researchseminars.org/talk/ZAG/203/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva Elduque (Universidad Autónoma de Madrid) DTSTART:20220426T120000Z DTEND:20220426T130000Z DTSTAMP:20260422T225725Z UID:ZAG/204 DESCRIPTION:Title: Ei genspace decomposition of mixed Hodge structures on Alexander modules\ nby Eva Elduque (Universidad Autónoma de Madrid) as part of ZAG (Zoom Alg ebraic Geometry) seminar\n\n\nAbstract\nIn previous work jointly with Gesk e\, Herradón Cueto\, Maxim and Wang\, we constructed a mixed Hodge struct ure (MHS) on the torsion part of Alexander modules\, which generalizes the MHS on the cohomology of the Milnor fiber for weighted homogeneous polyno mials. The cohomology of a Milnor fiber carries a monodromy action\, whose semisimple part is an isomorphism of MHS. The natural question of whether this result still holds for Alexander modules was then posed. In this tal k\, we will talk about the solution to this question\, as well as some con sequences and explicit computations. Joint work with Moises Herradón Cuet o.\n LOCATION:https://researchseminars.org/talk/ZAG/204/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodoros Papazachariou (University of Essex) DTSTART:20220426T140000Z DTEND:20220426T150000Z DTSTAMP:20260422T225725Z UID:ZAG/205 DESCRIPTION:Title: K- moduli for log Fano complete intersections\nby Theodoros Papazachariou (University of Essex) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nAn important category of geometric objects in algebraic geome try is smooth Fano varieties\, which have positive curvature. These have b een classified in 1\, 10 and 105 families in dimensions 1\, 2 and 3 respec tively\, while in higher dimensions the number of Fano families is yet unk nown\, although we know that their number is bounded. An important problem is compactifying these families into moduli spaces via K-stability. In th is talk\, I will describe the compactification of the family of Fano three folds\, which is obtained by blowing up the projective space along a compl ete intersection of two quadrics which is an elliptic curve\, into a K-mod uli space using Geometric Invariant Theory (GIT). A more interesting setti ng occurs in the case of pairs of varieties and a hyperplane section where the K-moduli compactifications tessellate depending on a parameter. In th is case it has been shown recently that the K-moduli decompose into a wall -chamber decomposition depending on a parameter\, but wall-crossing phenom ena are still difficult to describe explicitly. Using GIT\, I will descri be an explicit example of wall-crossing in the K-moduli spaces\, where bot h variety and divisor differ in the deformation families before and after the wall\, given by log pairs of Fano surfaces of degree 4 and a hyperplan e section.\n LOCATION:https://researchseminars.org/talk/ZAG/205/ END:VEVENT BEGIN:VEVENT SUMMARY:Arman Sarikyan (University of Edinburgh) DTSTART:20220428T100000Z DTEND:20220428T110000Z DTSTAMP:20260422T225725Z UID:ZAG/206 DESCRIPTION:Title: Eq uivariant pliability of the projective space\nby Arman Sarikyan (Unive rsity of Edinburgh) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n Abstract\nWe classify finite subgroups $G\\subset\\mathrm{PGL}_4(\\mathbb{ C})$ such that $\\mathbb{P}^3$ is not $G$-birational to conic bundles and del Pezzo fibrations\, and explicitly describe all $G$-Mori fibre spaces t hat are $G$-birational to $\\mathbb{P}^3$ for these subgroups. This is a j oint work with I. Cheltsov\n LOCATION:https://researchseminars.org/talk/ZAG/206/ END:VEVENT BEGIN:VEVENT SUMMARY:Kyoung-Seog Lee (University of Miami) DTSTART:20220503T150000Z DTEND:20220503T160000Z DTSTAMP:20260422T225725Z UID:ZAG/207 DESCRIPTION:Title: De rived categories and motives of moduli spaces of vector bundles on curves< /a>\nby Kyoung-Seog Lee (University of Miami) as part of ZAG (Zoom Algebra ic Geometry) seminar\n\n\nAbstract\nDerived categories and motives are imp ortant invariants of algebraic varieties invented by Grothendieck and his collaborators around the 1960s. In 2005\, Orlov conjectured that they will be closely related and now there are several evidences supporting his con jecture. On the other hand\, moduli spaces of vector bundles on curves pro vide attractive and important examples of algebraic varieties and there ha ve been intensive works studying them. In this talk\, I will discuss deriv ed categories and motives of moduli spaces of vector bundles on curves and how they are related. Part of this talk is based on several joint works w ith I. Biswas\, T. Gomez\, H.-B. Moon and M. S. Narasimhan.\n LOCATION:https://researchseminars.org/talk/ZAG/207/ END:VEVENT BEGIN:VEVENT SUMMARY:Ariyan Javanpeykar (Johannes Gutenberg University of Mainz) DTSTART:20220505T100000Z DTEND:20220505T110000Z DTSTAMP:20260422T225725Z UID:ZAG/208 DESCRIPTION:Title: Sh afarevich's conjecture for canonically polarized varieties revisited\n by Ariyan Javanpeykar (Johannes Gutenberg University of Mainz) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: Arakelov-Pa rshin proved Shafarevich's conjecture for the (actual) moduli space M_g o f curves of genus g (g>1). Namely\, for every curve C\, the set of isomorp hism classes of non-isotrivial morphisms C \\to M_g is finite. This finite ness result is similar to the theorem of De Franchis: for every hyperbolic curve X\, the set of non-constant morphisms C->X is finite. Interestingly \, M_g is hyperbolic (in any reasonable sense of the word "hyperbolic"). I s maybe the theorem of Arakelov-Parshin and De Franchis an instance of a m ore general finiteness property for hyperbolic varieties/stacks? The answe r is no. The conclusion of the theorem of De Franchis fails for hyperbolic surfaces (such as X x X) and the conclusion of Arakelov-Parshin's theorem fails for the moduli space of canonically polarized surfaces (because it contains copies of X x X). How to remedy this? Guided by finiteness proper ties of compact hyperbolic varieties\, we establish new finiteness propert ies for the moduli space CanPol of canonically polarized varieties by prov ing rigidity properties of pointed maps. Applications include bounds on di mensions of moduli spaces of maps to CanPol. Joint work with Steven Lu\, R uiran Sun\, and Kang Zuo.\n LOCATION:https://researchseminars.org/talk/ZAG/208/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Brakkee (University of Amsterdam) DTSTART:20220510T120000Z DTEND:20220510T130000Z DTSTAMP:20260422T225725Z UID:ZAG/209 DESCRIPTION:Title: Ge neral type results for moduli of hyperkahler varieties\nby Emma Brakke e (University of Amsterdam) as part of ZAG (Zoom Algebraic Geometry) semin ar\n\n\nAbstract\nIn 2007\, Gritsenko\, Hulek and Sankaran proved that the moduli space of K3 surfaces of degree 2d is of general type when d>61. Th eir strategy is to reduce the question to the existence of a certain cusp form for an orthogonal modular variety. This method has been applied succe ssfully to prove general type results for\, among others\, some moduli of higher-dimensional hyperkähler varieties. In this talk\, we sketch the re duction argument and give general type results for some more types of hype rkähler moduli spaces. We also explain what the challenges are when tryin g to imitate the strategy for other moduli spaces of hyperkähler varietie s. This is joint work in progress with I. Barros\, P. Beri and L. Flapan.\ n LOCATION:https://researchseminars.org/talk/ZAG/209/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Chan (UNSW Sydney) DTSTART:20220512T210000Z DTEND:20220512T220000Z DTSTAMP:20260422T225725Z UID:ZAG/210 DESCRIPTION:Title: Th e minimal model program for arithmetic surfaces enriched by a Brauer class \nby Daniel Chan (UNSW Sydney) as part of ZAG (Zoom Algebraic Geometry ) seminar\n\n\nAbstract\nMori's minimal model program is a major organisin g principle for studying and classifying varieties $X$. It has been genera lised in many directions\, and in this talk\, we examine a ``noncommutativ e'' one where $X$ is enriched by a Brauer class $\\beta \\in K(X)$. We foc us on some new results where $X$ is a surface whose residue fields are fin ite. When the order of $\\beta$ is a prime >5\, we recover most of standar d surface theory including existence of terminal resolutions\, Castelnuovo contraction and Zariski factorisation. However\, interesting new examples of terminal singularities and Castelnuovo contractions appear\, which hav e no characteristic zero analogue.\n LOCATION:https://researchseminars.org/talk/ZAG/210/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Claudon (Université de Rennes 1) DTSTART:20220517T100000Z DTEND:20220517T110000Z DTSTAMP:20260422T225725Z UID:ZAG/211 DESCRIPTION:Title: Nu merical characterization of complex tori\nby Benoit Claudon (Universit é de Rennes 1) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst ract\nIn this talk I will explain how to recognize complex tori among Kahl er klt spaces (smooth in codimension 2) in terms of vanishing of Chern num bers. It requires first to define Chern classes on singular spaces (a rath er unstable notion). On the way\, we will establish a singular version of the Bogomolov--Gieseker inequality for stable sheaves and study what can b e said in the equality case. Joint work with Patrick Graf and Henri Guenan cia.\n LOCATION:https://researchseminars.org/talk/ZAG/211/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Bakker (University of Illinois at Chicago) DTSTART:20220524T220000Z DTEND:20220524T230000Z DTSTAMP:20260422T225725Z UID:ZAG/212 DESCRIPTION:Title: Pe riod integrals of algebraic varieties\nby Benjamin Bakker (University of Illinois at Chicago) as part of ZAG (Zoom Algebraic Geometry) seminar\n \n\nAbstract\nPeriod integrals on complex algebraic varieties are the inte grals of algebraic differential forms along topological cycles. They are at the heart of Hodge theory. In this talk I will survey some recent resu lts on the behavior of the functions obtained by taking period integrals i n algebraic families\, including their transcendence\, their relation to t he derivatives of the associated period map\, and some geometric applicati ons. This is joint work with J. Pila and J. Tsimerman.\n LOCATION:https://researchseminars.org/talk/ZAG/212/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne-Sophie Kaloghiros (Brunel University) DTSTART:20220519T140000Z DTEND:20220519T150000Z DTSTAMP:20260422T225725Z UID:ZAG/213 DESCRIPTION:Title: 1- dimensional K-moduli spaces of Fano 3-folds\nby Anne-Sophie Kaloghiros (Brunel University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nRecent advances in the study of K-stability have shown that the re is a projective good moduli space of K-polystable Q-Gorenstein smoothab le Q-Fano varieties of dimension n and volume V. The classification of smo oth Fano 3-folds is due to Iskovshikh\, Mori and Mukai and dates back to t he 80s. While the classification is non-modular\, it contains rich informa tion on the geometry of Fano 3-folds. Fano 3-folds offer a rich source of examples in which we can explicitly construct and understand some K-moduli spaces. In this talk\, I will discuss some examples of 1-dimensional K-mo duli spaces of Fano 3-folds. This is joint work with Abban\, Cheltsov\, Ji ao\, Martinez-Garcia\, Papazachariou and Sarikyan.\n LOCATION:https://researchseminars.org/talk/ZAG/213/ END:VEVENT BEGIN:VEVENT SUMMARY:Evgeny Shinder (University of Sheffield) DTSTART:20220526T140000Z DTEND:20220526T150000Z DTSTAMP:20260422T225725Z UID:ZAG/214 DESCRIPTION:Title: Mo tivic invariants of birational maps\nby Evgeny Shinder (University of Sheffield) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\ nI will introduce invariants of birational maps with values in the Grothen dieck ring of varieties and their applications to groups of birational iso morphisms\, in particular the Cremona groups. This is joint work with Hsue h-Yung Lin.\n LOCATION:https://researchseminars.org/talk/ZAG/214/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Shepherd-Barron (King’s College London) DTSTART:20220531T100000Z DTEND:20220531T110000Z DTSTAMP:20260422T225725Z UID:ZAG/215 DESCRIPTION:Title: Pe riods of elliptic surfaces\nby Nicholas Shepherd-Barron (King’s Coll ege London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract \nThe derivative of the period map for elliptic surfaces has a description in terms of where the j-invariant ramifies. This leads to a natural ortho normal basis of the (1\,1) part of the primitive cohomology\, expressed in terms of meromorphic 2-forms of the 2nd kind\, and to a generic Torelli t heorem. This extends to certain other families of varieties fibred in Cala bi-Yau varieties.\n LOCATION:https://researchseminars.org/talk/ZAG/215/ END:VEVENT END:VCALENDAR