BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ana-Maria Castravet (Université Paris-Saclay\, UVSQ) DTSTART:20201207T130000Z DTEND:20201207T140000Z DTSTAMP:20260422T212747Z UID:EDGE2020/1 DESCRIPTION:Title: Blown-up toric surfaces with non-polyhedral effective cone\nby Ana-Ma ria Castravet (Université Paris-Saclay\, UVSQ) as part of EDGE 2020 (onli ne)\n\n\nAbstract\nI will report on recent joint work with Antonio Laface\ , Jenia Tevelev and Luca Ugaglia. We construct examples of projective tori c surfaces whose blow-up at a general point has a non-polyhedral effective cone\, both in characteristic 0 and in prime characteristic. As a conseq uence\, we prove that the effective cone of the Grothendieck-Knudsen modul i space of stable\, n-pointed\, rational stable curves\, is not polyhedra l if n>=10 in characteristic 0 and in positive characteristic for an infi nite set of primes of positive density. In particular\, these moduli space s are not Mori dream spaces even in positive characteristic.\n LOCATION:https://researchseminars.org/talk/EDGE2020/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruadhaí Dervan (University of Cambridge) DTSTART:20201207T141500Z DTEND:20201207T151500Z DTSTAMP:20260422T212747Z UID:EDGE2020/2 DESCRIPTION:Title: The complex geometry of Bridgeland stability conditions\nby Ruadhaí Dervan (University of Cambridge) as part of EDGE 2020 (online)\n\n\nAbstra ct\nI will discuss geometric partial differential equations on holomorphic vector bundles that one can associate to Bridgeland stability conditions. The setup can be seen as a generalisation of the Hitchin-Kobayashi corres pondence\, which relates slope stability of vector bundles with the existe nce of Hermite-Einstein metrics. I will then describe some foundational re sults concerning these new equations. The algebraic geometry involved will be light on technicalities\; triangulated categories will not appear. Thi s is joint work with John McCarthy and Lars Sektnan.\n LOCATION:https://researchseminars.org/talk/EDGE2020/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenyang Xu (Princeton University) DTSTART:20201207T153000Z DTEND:20201207T163000Z DTSTAMP:20260422T212747Z UID:EDGE2020/3 DESCRIPTION:Title: On positivity of the CM line bundle\nby Chenyang Xu (Princeton Univer sity) as part of EDGE 2020 (online)\n\n\nAbstract\n(Joint with Ziquan Zhua ng) The K-moduli which parametrizes K-polystable Fano varieties is conject urally to be projective. In this talk\, I will discuss the result we obtai ned for the positivity of the CM line bundle on the K-moduli. In particula r\, it implies the (proper) component parametrizing smoothable K-polystabl e Fano varieties is projective.\n LOCATION:https://researchseminars.org/talk/EDGE2020/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Nivedita Viswanathan (University of Edinburgh) DTSTART:20201208T130000Z DTEND:20201208T140000Z DTSTAMP:20260422T212747Z UID:EDGE2020/4 DESCRIPTION:Title: On K-stability of some singular del Pezzo surfaces\nby Nivedita Viswa nathan (University of Edinburgh) as part of EDGE 2020 (online)\n\n\nAbstra ct\nThere has been a lot of development recently in understanding the exis tence of Kahler-Einstein metrics on Fano manifolds due to the Yau-Tian-Don aldson conjecture\, which gives us a way of looking at this problem in ter ms of the notion of K-stability. In particular\, this problem is solved in totality for smooth del Pezzo surfaces by Tian. For del Pezzo surfaces wi th quotient singularities\, there are partial results. In this talk\, we w ill consider singular del Pezzo surfaces which are quasi-smooth\, well-for med hypersurfaces in weighted projective space\, and understand what we ca n say about their K-stability. This is joint work with In-Kyun Kim and Joo nyeong Won.\n LOCATION:https://researchseminars.org/talk/EDGE2020/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolina Araujo (IMPA) DTSTART:20201208T141500Z DTEND:20201208T151500Z DTSTAMP:20260422T212747Z UID:EDGE2020/5 DESCRIPTION:Title: Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona transfo rmations\nby Carolina Araujo (IMPA) as part of EDGE 2020 (online)\n\n\ nAbstract\nRecently\, Oguiso addressed the following question\, attributed to Gizatullin: ``Which automorphisms of a smooth quartic K3 surface $D\\s ubset \\mathbb{P}^3$ are induced by Cremona transformations of the ambient space $\\mathbb{P}^3$?'' When $D\\subset \\mathbb{P}^3$ is a quartic sur face\, $(\\mathbb{P}^3\,D)$ is an example of a \\emph{Calabi-Yau pair}\, t hat is\, a pair $(X\,D)$\, consisting of a normal projective variety $X$ a nd an effective Weil divisor $D$ on $X$ such that $K_X+D\\sim 0$. Gizatull in's question is about birational properties of the Calabi-Yau pair $(\\ma thbb{P}^3\,D)$. 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 joint work with Alessio Corti and Alex Massarenti.\n LOCATION:https://researchseminars.org/talk/EDGE2020/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Constantin Shramov (Higher School of Economics) DTSTART:20201208T153000Z DTEND:20201208T163000Z DTSTAMP:20260422T212747Z UID:EDGE2020/6 DESCRIPTION:Title: Birational automorphisms of Severi-Brauer surfaces.\nby Constantin Sh ramov (Higher School of Economics) as part of EDGE 2020 (online)\n\n\nAbst ract\nIn 2009\, I.Dolgachev and V.Iskovskikh classified finite subgroups o f the birational automorphism groups of the projective plane over an algeb raically closed field of characteristic zero. I will explain an analog of their result for birational automorphism groups of Severi-Brauer surfaces\ , i.e.\, surfaces that become isomorphic to the projective plane after pas sing to the algebraic closure of the base field. The classification is obt ained by using geometric techniques based on the Minimal Model Program tog ether with some theory of central simple algebras.\n LOCATION:https://researchseminars.org/talk/EDGE2020/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Hoskins (Radboud University Nijmegen) DTSTART:20201209T130000Z DTEND:20201209T140000Z DTSTAMP:20260422T212747Z UID:EDGE2020/7 DESCRIPTION:Title: Constructing new moduli space via non-reductive geometric invariant theor y\nby Victoria Hoskins (Radboud University Nijmegen) as part of EDGE 2 020 (online)\n\n\nAbstract\nThere are some moduli problems where non-reduc tive groups naturally appear: for example\, moduli of hypersurfaces in tor ic varieties\, which may have non-reductive automorphism groups\, and modu li of certain unstable objects\, such as vector bundles of fixed Harder-Na rasimhan type\, where there is naturally a parabolic group action. In this talk\, I will give an introduction to non-reductive GIT and explain how t o construct quotients when the unipotent radical is 'graded' by a copy of the multiplicative group. I will then report on joint work in progress wit h G. Berczi\, J. Jackson and F. Kirwan on the construction of moduli space s of sheaves of fixed Harder-Narasimhan type.\n LOCATION:https://researchseminars.org/talk/EDGE2020/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Gergely Bérczi (Aarhus University) DTSTART:20201209T153000Z DTEND:20201209T163000Z DTSTAMP:20260422T212747Z UID:EDGE2020/8 DESCRIPTION:Title: Enumerative applications of non-reductive GIT\nby Gergely Bérczi (Aa rhus University) as part of EDGE 2020 (online)\n\n\nAbstract\nPolynomial r eparametrisation groups form the symmetries of jets of holomorphic curves in complex manifolds. They play central role in various classical problems in geometry. I report on recent work in two\, seemingly unrelated questio ns: (i) degeneracy loci of holomorphic maps between complex manifolds and Thom polynomials of singularities and (ii) the Green-Griffiths-Land and Ko bayashi hyperbolicity conjectures. I will explain why moduli of jets is a link between the two\, and how recently developed intersection theory of n on-reductive GIT quotients led to the proof of the polynomial Kobayashi co njecture\, and resulted in new formulas for Thom polynomials.\n LOCATION:https://researchseminars.org/talk/EDGE2020/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Eloise Hamilton (University of Oxford) DTSTART:20201209T141500Z DTEND:20201209T151500Z DTSTAMP:20260422T212747Z UID:EDGE2020/9 DESCRIPTION:Title: Cohomology of GIT quotients\, reductive and non-reductive\nby Eloise Hamilton (University of Oxford) as part of EDGE 2020 (online)\n\n\nAbstrac t\nGeometric Invariant Theory (GIT) is a powerful tool not only for constr ucting quotients in algebraic geometry\, but also for studying the geometr y of these quotients. The aim of this talk is to explain how to calculate the (rational) cohomology of quotients constructed on the one hand using c lassical GIT\, and on the other using a recent generalisation of GIT\, cal led Non-Reductive GIT. As its name suggests\, Non-Reductive GIT enables th e construction of quotients by a certain class of non-reductive group acti ons. After reviewing existing methods for computing the Poincare series of classical GIT quotients when the initial variety is smooth\, we will show how similar methods can be used to compute the Poincare series of non-red uctive GIT quotients.\n LOCATION:https://researchseminars.org/talk/EDGE2020/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sébastien Boucksom (École Polytechnique) DTSTART:20201210T130000Z DTEND:20201210T140000Z DTSTAMP:20260422T212747Z UID:EDGE2020/10 DESCRIPTION:Title: Non-Archimedean pluripotential theory and K-stability\nby Sébastien Boucksom (École Polytechnique) as part of EDGE 2020 (online)\n\n\nAbstra ct\nNon-Archimedean pluripotential theory interprets test configurations a s plurisubharmonic functions on a space of valuations\, and provides a pow erful analytic framework to study and compare various completions of the s et of test configurations\, phrased in terms of filtrations\, valuations\, etc... I will review the main features of this theory\, which is joint wo rk with Mattias Jonsson.\n LOCATION:https://researchseminars.org/talk/EDGE2020/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiano Spotti (Aarhus University) DTSTART:20201210T141500Z DTEND:20201210T151500Z DTSTAMP:20260422T212747Z UID:EDGE2020/11 DESCRIPTION:Title: On relations between K-moduli and symplectic geometry\nby Cristiano Spotti (Aarhus University) as part of EDGE 2020 (online)\n\n\nAbstract\nA natural intriguing question is the following: how much the moduli spaces o f certain polarized varieties know about the symplectic geometry of the un derneath manifold? After giving an overview\, I will discuss joint work wi th T. Baier\, G. Granja and R. Sena-Dias where we investigate some relatio ns between the topology of the moduli spaces of certain varieties\, of the symplectomorphism group and of the space of compatible integrable complex structures. In particular\, using results of J. Evans\, we show that the space of such complex structures for monotone del Pezzo surfaces of degree four and five is weakly homotopically contractible.\n LOCATION:https://researchseminars.org/talk/EDGE2020/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Codogni (Università degli Studi Tor Vergata) DTSTART:20201210T153000Z DTEND:20201210T163000Z DTSTAMP:20260422T212747Z UID:EDGE2020/12 DESCRIPTION:Title: Ample cone of KSB moduli spaces and higher dimensional slope inequalitie s\nby Giulio Codogni (Università degli Studi Tor Vergata) as part of EDGE 2020 (online)\n\n\nAbstract\nI will present some quantitative results about the ample cone of KSB moduli spaces. These results follow from vari ous higher dimensional generalizations of the Xiao-Cornalba-Harris slope i nequality. Our proofs combine some new Noether inequalities\, and a carefu l study of the Harder-Narasimhan filtration of the push-forward of the log pluri-canonical bundles. The talk is based on a work in progress joint wi th Luca Tasin and Filippo Viviani.\n LOCATION:https://researchseminars.org/talk/EDGE2020/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Milena Hering (University of Edinburgh) DTSTART:20201211T130000Z DTEND:20201211T140000Z DTSTAMP:20260422T212747Z UID:EDGE2020/13 DESCRIPTION:Title: T-Stability of Toric Tangent bundles\nby Milena Hering (University o f Edinburgh) as part of EDGE 2020 (online)\n\n\nAbstract\nIn this talk I w ill give a brief introduction to slope stability and present a combinatori al criterion for the tangent bundle on a polarised toric variety to be st able in terms of the lattice polytope corresponding to the polarisation. I will then give some applications to toric surfaces and toric varieties of Picard rank 2. This is joint work with Benjamin Nill and Hendrik Süss\n LOCATION:https://researchseminars.org/talk/EDGE2020/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Petracci (Freie Universität Berlin) DTSTART:20201211T141500Z DTEND:20201211T151500Z DTSTAMP:20260422T212747Z UID:EDGE2020/14 DESCRIPTION:Title: Toric geometry and singularities on K-moduli\nby Andrea Petracci (Fr eie Universität Berlin) as part of EDGE 2020 (online)\n\n\nAbstract\nAn i mmediate consequence of Kodaira-Akizuki-Nakano vanishing is that smooth Fa no varieties have unobstructed deformations. The same holds for singular F ano varieties with mild singularities and small dimension.\nIn this talk I will show how to use the combinatorics of lattice polytopes to construct examples of K-polystable toric Fano varieties with obstructed deformations \, dimension at least 3\, and canonical singularities. This method produce s singularities (even reducible and non-reduced) on K-moduli stacks and K- moduli spaces of Fano varieties.\nThis is joint work with Anne-Sophie Kalo ghiros.\n LOCATION:https://researchseminars.org/talk/EDGE2020/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik Süß (University of Manchester) DTSTART:20201211T153000Z DTEND:20201211T163000Z DTSTAMP:20260422T212747Z UID:EDGE2020/15 DESCRIPTION:Title: Beta-invariants on T-varieties\nby Hendrik Süß (University of Manc hester) as part of EDGE 2020 (online)\n\n\nAbstract\nIn my talk I am prese nting previous results on the K-stability of T-varieties in the new packag ing of beta-invariants. The main result will be that for T-varieties of co mplexity 1 Kento Fujita's divisorial polystability is (almost) equivalent to K-polystability. One practical implication will be that for testing K-p olystability of such T-varieties it is sufficient to calculate beta-invari ants only for a finite number number of "special" T-invariant prime diviso rs on the variety itself.\n LOCATION:https://researchseminars.org/talk/EDGE2020/15/ END:VEVENT END:VCALENDAR