BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Kuznetsov (Steklov and HSE\, Moscow) DTSTART:20201201T160000Z DTEND:20201201T170000Z DTSTAMP:20260422T212609Z UID:DerSem/1 DESCRIPTION:Title: S imultaneous categorical resolutions of singularities\nby Alexander Kuz netsov (Steklov and HSE\, Moscow) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierrick Bousseau (University Paris-Saclay) DTSTART:20210112T160000Z DTEND:20210112T170000Z DTSTAMP:20260422T212609Z UID:DerSem/2 DESCRIPTION:Title: H olomorphic curves\, Lagrangians\, and coherent sheaves\nby Pierrick Bo usseau (University Paris-Saclay) as part of Derived seminar\n\nAbstract: T BA\n LOCATION:https://researchseminars.org/talk/DerSem/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Theo Raedschelders (Free University of Brussels) DTSTART:20210119T160000Z DTEND:20210119T170000Z DTSTAMP:20260422T212609Z UID:DerSem/3 DESCRIPTION:Title: A categorification of Galkin-Shinder's Y-F(Y) relation\nby Theo Raedsch elders (Free University of Brussels) as part of Derived seminar\n\n\nAbstr act\nFor a smooth cubic hypersurface Y\, Sergey Galkin and Evgeny Shinder exhibited a relation between the naive motives of Y\, the Fano variety F( Y) of lines and the Hilbert scheme Y^{[2]} of two points on Y. This relati on has been shown to persist both on the level of rational Chow motives an d integral Hodge structures. In a joint work with Pieter Belmans and Lie F u\, we lift this relation to derived categories by exhibiting a correspond ing semi-orthogonal decomposition for the derived category of Y^{[2]}. I w ill explain how to obtain this semi-orthogonal decomposition from a refine ment of Bondal-Orlov's results on derived categories of flips and how to f urther deduce an isomorphism of integral Chow motives using a recent resul t of Qingyuan Jiang.\n LOCATION:https://researchseminars.org/talk/DerSem/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jørgen Rennemo (University of Oslo) DTSTART:20210126T160000Z DTEND:20210126T170000Z DTSTAMP:20260422T212609Z UID:DerSem/4 DESCRIPTION:Title: K -theorietic sheaf-counting invariants of Quot^n(C^4)\nby Jørgen Renne mo (University of Oslo) as part of Derived seminar\n\n\nAbstract\nConsider the Quot scheme parametrising length n quotients of the rank r trivial bu ndle on C^4. There's a natural torus action on this scheme\, for which the fix points are labelled by r-tuples of solid partitions of total size n. Nekrasov and Piazzalunga have assigned rational function weights to these fix points and conjectured a formula for the generating function of weight ed counts of fix points. Oh and Thomas have defined general K-theoretic sh eaf counting invariants for Calabi-Yau 4-folds and proved a torus localisa tion formula for these. We show that Nekrasov-Piazzalunga's weights agree with weights coming from the Oh-Thomas localisation formula (matching up t he signs is the tricky part). We use this to prove that Nekrasov-Piazzalun ga's conjectured formula for the generating function is correct. This is j oint work with Martijn Kool.\n LOCATION:https://researchseminars.org/talk/DerSem/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Pertusi (University of Milan) DTSTART:20210202T160000Z DTEND:20210202T170000Z DTSTAMP:20260422T212609Z UID:DerSem/5 DESCRIPTION:Title: C ubic fourfolds and moduli spaces of O'Grady 10 type\nby Laura Pertusi (University of Milan) as part of Derived seminar\n\n\nAbstract\nIn this ta lk we study certain moduli spaces of semistable objects in the Kuznetsov c omponent of a cubic fourfold. We show that they admit a symplectic resolut ion \\tilde{M} which is a smooth projective hyperkaehler manifold deformat ion equivalent to the 10-dimensional example constructed by O’Grady. As a first application\, we construct a birational model of \\tilde{M} which is a compactification of the twisted intermediate Jacobian of the cubic fo urfold. Secondly\, we show that \\tilde{M} is the MRC quotient of the main component of the Hilbert scheme of elliptic quintic curves in the cubic f ourfold\, as conjectured by Castravet. This is a joint work with Chunyi Li and Xiaolei Zhao.\n LOCATION:https://researchseminars.org/talk/DerSem/5/ END:VEVENT BEGIN:VEVENT SUMMARY:David Stapleton (University of California\, San Diego) DTSTART:20210209T160000Z DTEND:20210209T170000Z DTSTAMP:20260422T212609Z UID:DerSem/6 DESCRIPTION:Title: S tudying Fano hypersurface with holomorphic forms\nby David Stapleton ( University of California\, San Diego) as part of Derived seminar\n\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ignacio Barros (University Paris-Saclay) DTSTART:20210216T160000Z DTEND:20210216T170000Z DTSTAMP:20260422T212609Z UID:DerSem/7 DESCRIPTION:Title: O n the irrationality of moduli spaces of K3 surfaces\nby Ignacio Barros (University Paris-Saclay) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Qingyuan Jiang (University of Edinburgh) DTSTART:20210223T160000Z DTEND:20210223T170000Z DTSTAMP:20260422T212609Z UID:DerSem/8 DESCRIPTION:Title: O n the derived categories of Quot-schemes of locally free quotients\nby Qingyuan Jiang (University of Edinburgh) as part of Derived seminar\n\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Bragg (University of California\, Berkeley) DTSTART:20210302T160000Z DTEND:20210302T170000Z DTSTAMP:20260422T212609Z UID:DerSem/9 DESCRIPTION:Title: C ompactifications of supersingular twistor spaces\nby Daniel Bragg (Uni versity of California\, Berkeley) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Gavril Farkas (Humboldt University of Berlin) DTSTART:20210309T160000Z DTEND:20210309T170000Z DTSTAMP:20260422T212609Z UID:DerSem/10 DESCRIPTION:Title: Moduli of K3 surfaces via cubic 4-folds\nby Gavril Farkas (Humboldt Un iversity of Berlin) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Alicia Lamarche (University of Utah) DTSTART:20210316T160000Z DTEND:20210316T170000Z DTSTAMP:20260422T212609Z UID:DerSem/11 DESCRIPTION:Title: Derived Categories\, Arithmetic\, and Rationality\nby Alicia Lamarche (University of Utah) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Lenny Taelman (University of Amsterdam) DTSTART:20210330T150000Z DTEND:20210330T160000Z DTSTAMP:20260422T212609Z UID:DerSem/12 DESCRIPTION:Title: Deformations of Calabi-Yau categories\nby Lenny Taelman (University of Amsterdam) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Stanford University) DTSTART:20210323T160000Z DTEND:20210323T170000Z DTSTAMP:20260422T212609Z UID:DerSem/13 DESCRIPTION:Title: The rational Chow rings of M_7\, M_8\, and M_9\nby Hannah Larson (Stan ford University) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrei Neguţ (MIT) DTSTART:20210406T150000Z DTEND:20210406T160000Z DTSTAMP:20260422T212609Z UID:DerSem/14 DESCRIPTION:Title: Lie algebra actions on the Chow ring of Hilb(K3)\nby Andrei Neguţ (MI T) as part of Derived seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Fei Xie (University of Edinburgh) DTSTART:20210413T150000Z DTEND:20210413T160000Z DTSTAMP:20260422T212609Z UID:DerSem/15 DESCRIPTION:Title: Nodal quintic del Pezzo threefolds and their derived categories\nby Fe i Xie (University of Edinburgh) as part of Derived seminar\n\nAbstract: TB A\n LOCATION:https://researchseminars.org/talk/DerSem/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Thorsten Beckmann (University of Bonn) DTSTART:20210420T150000Z DTEND:20210420T160000Z DTSTAMP:20260422T212609Z UID:DerSem/16 DESCRIPTION:Title: Derived categories of hyper-Kähler manifolds via the extended Mukai latti ce\nby Thorsten Beckmann (University of Bonn) as part of Derived semin ar\n\n\nAbstract\nThe derived category of a K3 surface is governed by its integral cohomology together with its Hodge structure and to objects we ca n functorially assign a Mukai vector in this lattice. We show an analogous picture for higher-dimensional hyper-Kähler manifolds using the extended Mukai lattice. In particular\, we construct a vector for certain objects in the derived category taking values in the extended Mukai lattice and we obtain a rank 25 integral lattice with a Hodge structure which is a deriv ed invariant for hyper-Kähler manifolds deformation-equivalent to the Hil bert scheme of n points on a K3 surface.\n LOCATION:https://researchseminars.org/talk/DerSem/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Halpern-Leistner (Cornell University) DTSTART:20210427T150000Z DTEND:20210427T160000Z DTSTAMP:20260422T212609Z UID:DerSem/17 DESCRIPTION:Title: Window categories and wall crossing\nby Daniel Halpern-Leistner (Corne ll University) as part of Derived seminar\n\n\nAbstract\nThe D-equivalence conjecture\, due to Bondal\, Orlov\, and Kawamata\, predicts that a birat ional equivalence between smooth projective varieties that preserves the c anonical bundle should induce an equivalence of derived categories of cohe rent sheaves. I will give an overview of "window categories" in equivarian t derived categories of coherent sheaves\, which can be used to construct derived equivalences for birational transformations coming from variation of GIT quotient. I will then discuss how these were used recently to prove the D-equivalence conjecture for projective Calabi-Yau manifolds in the b irational equivalence class of a moduli space of sheaves on a K3 surface.\ n LOCATION:https://researchseminars.org/talk/DerSem/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Lie Fu (Radboud University / Université Lyon 1) DTSTART:20210608T150000Z DTEND:20210608T160000Z DTSTAMP:20260422T212609Z UID:DerSem/18 DESCRIPTION:Title: Generalized Franchetta conjecture for certain families of K3 surfaces and hyper-Kähler varieties\nby Lie Fu (Radboud University / Université L yon 1) as part of Derived seminar\n\n\nAbstract\nIn 2013\, as an analogue of Franchetta's classical conjecture on the Picard group of the universal genus g curve\, O'Grady asked whether the Chow group of zero-cycles of the generic fiber of the universal genus-g K3 surface is cyclic. I will discu ss some recent progress that I obtained in collaboration with Laterveer an d Vial on this conjecture as well as its higher dimensional version for hy per-Kähler varieties. The main feature of our argument is the combination of the projective geometry of cubic fourfolds on one hand and moduli spac es of Bridgeland stable objects in their Kuznetsov components on the other hand.\n LOCATION:https://researchseminars.org/talk/DerSem/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Soheyla Feyzbakhsh (Imperial College) DTSTART:20210622T150000Z DTEND:20210622T160000Z DTSTAMP:20260422T212609Z UID:DerSem/20 DESCRIPTION:Title: Rank r DT theory from rank 1\nby Soheyla Feyzbakhsh (Imperial College) as part of Derived seminar\n\n\nAbstract\nFix a Calabi-Yau 3-fold X satis fying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda\, such as the quintic 3-fold. I will explain joint works in progress with Richard Thoma s that aim to express Joyce’s generalised DT invariants counting Gieseke r semistable sheaves of any rank r on X in terms of those counting sheaves of rank 1. By the MNOP conjecture\, the latter are determined by the Grom ov-Witten invariants of X. Our technique is to use wall-crossing with resp ect to weak Bridgeland stability conditions on X.\n LOCATION:https://researchseminars.org/talk/DerSem/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Perry (University of Michigan) DTSTART:20210629T150000Z DTEND:20210629T160000Z DTSTAMP:20260422T212609Z UID:DerSem/21 DESCRIPTION:Title: Serre functors of semiorthogonal components\nby Alexander Perry (Unive rsity of Michigan) as part of Derived seminar\n\n\nAbstract\nThe Serre fun ctor of a triangulated category is one of its most important invariants\, playing the role of the dualizing complex of a variety in noncommutative a lgebraic geometry. I will explain how to describe the Serre functors of ma ny semiorthogonal components of varieties in terms of spherical twists\, w ith applications to a dimension formula for Kuznetsov components of comple te intersections conjectured by Katzarkov and Kontsevich\, to the nonexist ence of Serre invariant stability conditions\, and to the construction of Calabi-Yau categories as crepant contractions. This is joint work with Ale xander Kuznetsov.\n LOCATION:https://researchseminars.org/talk/DerSem/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Addington (University of Oregon) DTSTART:20210601T150000Z DTEND:20210601T160000Z DTSTAMP:20260422T212609Z UID:DerSem/22 DESCRIPTION:Title: Derived autoequivalences of moduli spaces of sheaves on K3 surfaces\nb y Nicolas Addington (University of Oregon) as part of Derived seminar\n\nA bstract: TBA\n LOCATION:https://researchseminars.org/talk/DerSem/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Junliang Shen (MIT) DTSTART:20210504T150000Z DTEND:20210504T160000Z DTSTAMP:20260422T212609Z UID:DerSem/23 DESCRIPTION:Title: Geometry of the Gopakumar-Vafa theory.\nby Junliang Shen (MIT) as part of Derived seminar\n\n\nAbstract\nMotivated by classical enumerative geom etry and mathematical physics\, counting curves in Calabi-Yau 3-folds has been studied intensively for decades\, including Gromov-Witten theory and Donaldson-Thomas theory. In recent years\, mathematical theory (by Hosono- Saito-Takahashi\, Kiem-Li\, Maulik-Toda etc) has been developed to realize the idea of Gopakumar and Vafa to recover the curve-counting invariants u sing the geometry of 1-dimensional sheaves. These developments shed new li ght on both enumerative geometry and the classical geometry of the relevan t moduli spaces. I will discuss 3 particular cases (1) Higgs bundles (2) K 3 surfaces\, and (3) CP^2\, where the Gopakumar-Vafa theory interacts wi th some other structures and conjectures in a surprising way.\n LOCATION:https://researchseminars.org/talk/DerSem/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Georg Oberdieck (University of Bonn) DTSTART:20210615T150000Z DTEND:20210615T160000Z DTSTAMP:20260422T212609Z UID:DerSem/24 DESCRIPTION:Title: Another visit to the Donaldson-Thomas theory of K3xE\nby Georg Oberdie ck (University of Bonn) as part of Derived seminar\n\n\nAbstract\nIn this talk we consider the (reduced) Donaldson-Thomas theory of the product of a K3 surface and an elliptic curve. In rank 1\, these invariants can be vie wed as enumerating algebraic curves and are known for fiber classes over t he elliptic curve (work of Pandharipande and Thomas)\, and for classes pri mitive over the K3 (work of Pixton\, Shen and myself). I will explain how to extend these results to arbitrary curve classes. If time permits\, I wi ll also give an outlook on the higher rank case (work in progress).\n LOCATION:https://researchseminars.org/talk/DerSem/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Ed Segal (University College London) DTSTART:20210518T150000Z DTEND:20210518T160000Z DTSTAMP:20260422T212609Z UID:DerSem/25 DESCRIPTION:Title: Mirrors to surfaces and twisted derived categories\nby Ed Segal (Unive rsity College London) as part of Derived seminar\n\n\nAbstract\nPunctured surfaces are the simplest class of symplectic manifolds and there are many constructions of homological mirrors for them\, i.e. constructions in alg ebraic geometry of a category equivalent to the Fukaya category of the sur face. To make the Fukaya category Z-graded\, not just Z/2-graded\, you nee d to choose a line-field on the surface. I'll explain what this choice cor responds to in (some of) the mirror constructions\, it leads to a kind of twisted derived category which doesn't seem to have been widely studied.\n LOCATION:https://researchseminars.org/talk/DerSem/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Stellari (Università di Milano) DTSTART:20210511T150000Z DTEND:20210511T160000Z DTSTAMP:20260422T212609Z UID:DerSem/26 DESCRIPTION:Title: Uniqueness of enhancements for derived and geometric categories\nby Pa olo Stellari (Università di Milano) as part of Derived seminar\n\n\nAbstr act\nIn this talk we address several open questions and generalize the\nex isting results about the uniqueness of enhancements for triangulated\ncate gories which arise as derived categories of abelian categories or\nfrom ge ometric contexts. If time permits\, we will also discuss applications to t he description of exact equivalences. This is joint\nwork with A. Canonaco and A. Neeman.\n LOCATION:https://researchseminars.org/talk/DerSem/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitrii Pirozhkov (Université de Paris) DTSTART:20210525T150000Z DTEND:20210525T160000Z DTSTAMP:20260422T212609Z UID:DerSem/27 DESCRIPTION:Title: Stably semiorthogonally indecomposable varieties\nby Dmitrii Pirozhkov (Université de Paris) as part of Derived seminar\n\n\nAbstract\nA triang ulated category is said to be indecomposable if it admits no nontrivial se miorthogonal decompositions. For a derived category of coherent sheaves on a variety Y\, we propose a stronger condition\, which implies\, among oth er things\, that for any variety X\, any semiorthogonal decomposition of t he product X x Y is induced from a decomposition of X. For X = {pt} this i mplies the usual indecomposability. We show that varieties with finite Alb anese morphism\, e.g.\, curves of positive genus\, are stably semiorthogon ally indecomposable in this sense. From this\, we deduce the non-existence of phantom subcategories in the product surfaces C x P^1\, where C is a s mooth projective curve of positive genus\, and in some other examples as w ell.\n LOCATION:https://researchseminars.org/talk/DerSem/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Schnell (Stony Brook) DTSTART:20211012T150000Z DTEND:20211012T160000Z DTSTAMP:20260422T212609Z UID:DerSem/28 DESCRIPTION:Title: Finiteness for self-dual classes in variations of Hodge structure\nby Christian Schnell (Stony Brook) as part of Derived seminar\n\n\nAbstract\n I will talk about a new finiteness theorem for variations of Hodge structu re. It is a generalization of the Cattani-Deligne-Kaplan theorem from Hodg e classes to so-called self-dual (and anti-self-dual) 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 considerations in theoretical physi cs\, and the proof uses o-minimality and the definability of period mappin gs. This is joint work with Benjamin Bakker\, Thomas Grimm\, and Jacob Tsi merman.\n LOCATION:https://researchseminars.org/talk/DerSem/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastián Torres (IMSA) DTSTART:20211019T150000Z DTEND:20211019T160000Z DTSTAMP:20260422T212609Z UID:DerSem/29 DESCRIPTION:Title: The BGMN conjecture via windows and stable pairs\nby Sebastián Torres (IMSA) as part of Derived seminar\n\n\nAbstract\nLet C be a smooth projec tive curve of genus at least 2 and let N be the moduli space of stable ran k-two bundles on C of odd degree. We construct a semi-orthogonal decomposi tion in the derived category of N conjectured by Narasimhan and by Belmans \, Galkin and Mukhopadhyay. It contains two copies of the i-th symmetric p ower of C for i=0\,...\,g-2\, one copy of the (g-1)-st symmetric power\, a nd possibly a semi-orthogonal complement to all those blocks. This complem ent is expected to be trivial by the BGMN conjecture. Our approach is base d on an analysis of wall-crossing between moduli spaces of stable pairs\, combining classical vector bundles techniques with the method of windows. This is joint work with Jenia Tevelev.\n LOCATION:https://researchseminars.org/talk/DerSem/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoon-Joo Kim (Stony Brook) DTSTART:20211207T160000Z DTEND:20211207T170000Z DTSTAMP:20260422T212609Z UID:DerSem/30 DESCRIPTION:Title: The dual Lagrangian fibration of compact hyper-Kähler manifolds\nby Y oon-Joo Kim (Stony Brook) as part of Derived seminar\n\n\nAbstract\nA comp act hyper-Kähler manifold is a higher dimensional generalization of K3 su rfaces. An elliptic fibration of a K3 surface correspondingly generalizes to the so-called Lagrangian fibration of a compact hyper-Kähler manifold. It is known that an elliptic fibration of a K3 surface is always "self-du al" in a certain sense. This turns out to be not the case for higher-dimen sional Lagrangian fibrations. In this talk\, I will propose a construction for the dual Lagrangian fibration of all currently known examples of comp act hyper-Kähler manifolds.\n LOCATION:https://researchseminars.org/talk/DerSem/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Thomas (Imperial College London) DTSTART:20211109T160000Z DTEND:20211109T170000Z DTSTAMP:20260422T212609Z UID:DerSem/31 DESCRIPTION:Title: Higher rank DT theory from curve counts\nby Richard Thomas (Imperial C ollege London) as part of Derived seminar\n\n\nAbstract\nFix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The gen eralised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh using the weak stabilit y conditions of Bayer-Macrì -Toda to show these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP c onjecture the latter are determined by the GW invariants of X.\n LOCATION:https://researchseminars.org/talk/DerSem/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Pieter Belmans (University of Luxembourg) DTSTART:20211116T160000Z DTEND:20211116T170000Z DTSTAMP:20260422T212609Z UID:DerSem/32 DESCRIPTION:Title: The Hirzebruch isomorphism for exotic noncommutative surfaces\nby Piet er Belmans (University of Luxembourg) as part of Derived seminar\n\n\nAbst ract\nThe isomorphism between the first Hirzebruch surface and the blowup of the projective plane in a point is a well-known result\, due to Hirzebr uch. From a numerical classification of Grothendieck groups of rank 4 whic h behave like the Grothendieck group of a smooth projective surface we exp ect the existence of exotic noncommutative surfaces\, which are surfaces n ot obtained via deforming commutative surfaces. There exist two constructi ons: one as an asymmetric noncommutative P^1-bundle (due to de Thanhoffer- -Presotto)\, one as a fat point blowup (joint work with Presotto). I will explain how a Hirzebruch isomorphism for these two families of surfaces ex ists as an equivalence of (derived) categories\, and how this is related t o some very classical geometry of linear systems. This is joint work with Dennis Presotto and Michel Van den Bergh.\n LOCATION:https://researchseminars.org/talk/DerSem/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxim Smirnov (Augsburg and MPI Bonn) DTSTART:20211123T160000Z DTEND:20211123T170000Z DTSTAMP:20260422T212609Z UID:DerSem/33 DESCRIPTION:Title: Residual categories of Grassmannians\nby Maxim Smirnov (Augsburg and M PI Bonn) as part of Derived seminar\n\n\nAbstract\nWe will define residual categories of Lefschetz exceptional collections and discuss some conjectu ral relations between the structure of quantum cohomology and residual cat egories. We will illustrate this relationship in the case of some isotropi c Grassmannians. Based on joint works with Alexander Kuznetsov.\n LOCATION:https://researchseminars.org/talk/DerSem/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Špela Špenko (Vrije University Brussel) DTSTART:20211130T160000Z DTEND:20211130T170000Z DTSTAMP:20260422T212609Z UID:DerSem/34 DESCRIPTION:Title: Comparing commutative and noncommutative resolutions of singularities\ nby Špela Špenko (Vrije University Brussel) as part of Derived seminar\n \n\nAbstract\nQuotient varieties for reductive groups admit the Kirwan (pa rtial) resolution of singularities\, and quite often also a noncommutative crepant resolution (NCCR). We will construct a (Orlov's type) semi-orthog onal decomposition of the derived category of the Kirwan resolution which has the derived category of the NCCR as a component\, and where other comp onents also have a concrete (almost) geometric description. This is a join t work with Michel Van den Bergh.\n LOCATION:https://researchseminars.org/talk/DerSem/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Tony Yue Yu (Caltech) DTSTART:20211102T160000Z DTEND:20211102T170000Z DTSTAMP:20260422T212609Z UID:DerSem/35 DESCRIPTION:Title: Non-archimedean Quantum K-invariants\nby Tony Yue Yu (Caltech) as part of Derived seminar\n\n\nAbstract\nWe construct quantum K-invariants in no n-archimedean analytic geometry. Our approach differs from the classical o ne in algebraic geometry via perfect obstruction theory. Instead\, we buil d on our previous works on the foundation of derived non-archimedean geome try\, the representability theorem and Gromov compactness. We obtain a lis t of natural geometric relations between the stacks of stable maps\, direc tly at the derived level\, with respect to elementary operations on graphs \, namely\, products\, cutting edges\, forgetting tails and contracting ed ges. They imply immediately the corresponding properties of K-theoretic in variants. The derived approach produces highly intuitive statements and fu nctorial proofs. The flexibility of our derived approach to quantum K-inva riants allows us to impose not only simple incidence conditions for marked points\, but also incidence conditions with multiplicities. This leads to a new set of enumerative invariants. Our motivations come from non-archim edean enumerative geometry and mirror symmetry. Joint work with M Porta.\n LOCATION:https://researchseminars.org/talk/DerSem/35/ END:VEVENT END:VCALENDAR