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Workshop on Algebraic Geometry
报告人：Jia Jia(贾甲), Tsinghua University
摘要：Let X be a compact complex manifold in Fujiki's class C, i.e., admitting a big (1,1)-class [\alpha]. Consider Aut(X) the group of biholomorphic automorphisms and Aut_{[\alpha]}(X) the subgroup of automorphisms preserving the class [\alpha] via pullback. We show that X admits an Aut_{[\alpha]}(X)-equivariant Kähler model. I will talk several applications. We show that Aut_{[\alpha]}(X) is a Lie group with only finitely many components, which generalises an early result of Fujiki and Lieberman on the Kähler case. We also show that every torsion subgroup of Aut(X) is almost abelian, and Aut(X) is finite if it is a torsion group. This is based on a joint work with Sheng Meng.
时间：2023-12-23 16:00-17:00
地点：Room A-110, TSIMF
报告人：Zou Yu(邹瑜), Tsinghua University
摘要：In this talk, I will present our recent work concerning the explicit upper bound for anti-canonical volumes of e-lc Fano threefolds. More generally, We provide a reasonably small explicit upper bound with a sharp order, for the anti-canonical volumes of threefolds of e-lc Fano type (0＜e＜1/3). This is a joint work with Chen Jiang.
时间：2023-12-23 14:30-15:30
地点：Room A-110, TSIMF
报告人：Nanjun Yang(杨南君), Beijing Institute of Mathematical Sciences and Applications
摘要：Smooth projective Gm-varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting for- mula of such motives, which reduces the computation their Chow-Witt groups to that of their Chow groups and cohomologies of Witt sheaf. This a joint work with Jean Fasel.
时间：2023-12-23 09:00-10:00
地点：Room A-110, TSIMF
报告人：Chris Brav, Moscow Institute of Physics and Technology
摘要：We give an introduction to solid algebraic geometry, in the sense of Clausen-Scholze, a refinement of classical algebraic geometry built on spectra of solid rings, a certain category of “topological” rings including classical adic-like topological algebras. We show that the additional locality afforded by working with a larger collection of test spectra leads to a new construction of adelic decompositions of quasi-coherent sheaves, in the form of Beilinson-Parshin. This is joint work Grigory Konovalov.
时间：2023-12-23 10:30-11:30
地点：Room A-110, TSIMF
报告人：Chen Bingyi (陈炳仪）, YMSC, Tsinghua University
摘要：It was conjectured by McKernan and Shokurov that given a Fano fibration from X to Z, the singularities on Z are bounded in terms of those on X. Recently this conjecture was proved by Birkar. In this talk, I will discuss explicit bounds of singularities on Z in this conjecture in relative dimension one and in the toric case.
时间：2023-12-23 13:00-14:00
地点：Room A-110, TSIMF
报告人：Jeongseok Oh, lmperial College
摘要：“Quantum Lefschetz” is a pretentious name for understanding how moduli spaces -- and their virtual cycles and associated invariants -- change when we apply certain constraints. (The original application is to genus 0 curves in P^4 when we impose the constraint that they lie in the quintic 3-fold.) When it doesn’t work there are fixes (like the p-fields of Guffin-Sharpe-Witten/Chang-Li) for special cases associated with curve-counting. We will describe joint work with Richard Thomas developing a general theory.
时间：2023-12-24 09:00-10:00
地点：Room A-110, TSIMF
报告人：Artan Sheshmani, Beijing Institute of Mathematical Sciences and Applications
摘要：We elaborate on construction of a derived Lagrangian intersection theory on moduli spaces of divisors on compact Calabi Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We degenerate the CY3 into a normall crossing singular variety composed of Fano threefolds meeting along a K3. The deformation invariance arguments, together with derived Lagrangian intersection counts over the special fiber of the induced moduli space degeneration family, provides one with invariants of the generic CY fiber. This is report on several joint projects in progress with Ludmil Katzarkov, Tony Pantev, Vladimir Baranovsky and Maxim Kontsevich.
时间：2023-12-24 10:30-11:30
地点：Room A-110, TSIMF
报告人：Hossein Movasati, Instituto de Matematica Pura e Aplicada
摘要：In this talk I will review few conjectures which aim to detect which linear differential equations come from Gauss-Manin connections, that is, they are satisfied by periods of families of algebraic varieties. This includes conjectures due to Katz-Grothendieck, André and Bombieri-Dwork. I will discuss another finer criterion to detect differential equations coming from families of hypergeometric Calabi-Yau varieties. Finally, I will explain a classification list in the case of Heun and Painlevé VI equations (joint works with S. Reiter).
时间：2023-12-24 13:00-14:00
地点：Room A-110, TSIMF
报告人：Yuuji Tanaka , Kyoto University)
摘要：After mentioning some backgrounds, I'll talk about a blowup formula for sheaf-theoretic virtual enumerative invariants on projective surfaces and its applications at the level of the generating series of those invariants. For instance, we obtain Goettsche-Kool's conjectural blowup formulae for the generating series of the virtual Euler characteristics and virtual $\chi_y$-genera of the moduli spaces, in which modular forms appear in the same way as in Vafa-Witten's original paper in '94. This determines some of universal functions in the generating series of Vafa-Witten invariants on a projective surface, which were conjectured also by Goettsche-Kool and Goettsche-Kool-Laarakker. These are based on joint work arXiv:2107.08155 with Nikolas Kuhn and arXiv:2205.12953 with Nikolas Kuhn and Oliver Leigh.
时间：2023-12-24 14:30-15:30
地点：Room A-110, TSIMF
报告人：Bernhard Keller, Université Paris Cité
摘要：The Donovan-Wemyss conjecture from 2013 states that acompound Du Val singularity is determined up to isomorphism by the derived equivalence class of the "contraction algebra" associated with any crepant resolution. We will review the conjecture and its recent proof based on previous work by Wemyss, August, Hua-K and on the derived Auslander-Iyama correspondence, a deep result obtainedin August 2022 by Gustavo Jasso and Fernando Muro. The Donovan-Wemyss conjecture from 2013 states that acompound Du Val singularity is determined up to isomorphism by the derived equivalence class of the "contraction algebra" associated with any crepant resolution. We will review the conjecture and its recent proof based on previous work by Wemyss, August, Hua-K and on the derived Auslander-Iyama correspondence, a deep result obtained in August 2022 by Gustavo Jasso and Fernando Muro.
时间：2023-12-24 16:00-17:00
地点：Room A-110, TSIMF
报告人：Caucher Birkar, Tsinghua University
摘要：In this talk we will discuss recent results regarding singularities on fibrations, in particular, Fano and Calabi-Yau fibrations. We will give some of the main ideas of the proofs of these results.
时间：2023-12-25 09:00-10:00
地点：Room A-110, TSIMF
报告人：Liu Jihao(刘济豪), Northwestern University, USA
摘要：I will report the establishment of the minimal model program for algebraically integrable foliations on klt varieties and it applications, such as the minimal model program for generalized pairs and the canonical bundle formula. If time permits, I will discuss some related open problems and their connections to moduli theory. This talk is partially based on a series of joint works of myself with Guodu Chen, Jingjun Han, Fanjun Meng, and Lingyao Xie.
时间：2023-12-25 10:30-11:30
地点：Room A-110, TSIMF
报告人：Sheng Mao(盛茂), Tsinghua University
摘要：In this talk, I shall speak on a correspondence between the category of transversally foliated log smooth varieties over a fixed base in positive characteristic and the category of Higgs enhanced log smooth varieties over the same base. Stability for these objects will be also introduced.
时间：2023-12-25 13:00-14:00
地点：Room A-110, TSIMF
报告人：Seung-Joo Lee, Institute for Basic Science
摘要：Many instances have recently been found of the intriguing interplay between string landscape and algebraic geometry via the so-called swampland conjectures. In this talk, we will illustrate such an interplay with two concrete conjectures in physics. Specifically, to test the conjectures out for all possible effective QFT models of F-theory in (real) D = 8, 6, and 4 dimensions, we will address certain universal properties of compact elliptic Calabi-Yau d-folds for d=2, 3, and 4, respectively. In particular, several results will be discussed concerning (a) non-vanishing of specific enumerative invariants for d=3 (and 4), (b) characterization of the base Kahler geometries at infinite distance for d=4, and (c) explicit Weierstrass description of the Kulikov(-like) models at infinite distance for d=2 (and 3).
时间：2023-12-25 14:30-15:30
地点：Room A-110, TSIMF
报告人：Ivan Cheltsov, University of Edinburgh
摘要：I will report on a joint work with Yuri Tschinkel (Simons Foundation) and Zhijia Zhang (Courant Institute) on linearizability of actions of finite groups on singular cubic threefolds.
时间：2023-12-25 16:00-17:00
地点：Room A-110, TSIMF
报告人：Qu Santai(曲三太), Institute of Geometry and Physics, University of Science and Technology of China
摘要：In this talk, I will survey some recent progress about Kollar’s injectivity theorem on cohomologies. In the category of generalised pairs, we show that the injectivity theorem holds for projective generalised pairs with mild singularities when the nef part of the generalised pair is b-abundant. Moreover, by applying the methods from complex analytic geometry, we show that the injectivity theorem holds for generalised Kawamata log terminal generalised pairs on projective surfaces without any extra conditions on the nef parts of the generalised pairs.
时间：2023-12-26 09:00-10:00
地点：Room A-103, TSIMF
报告人：Jiao Junpeng(焦骏鹏), Tsinghua University
摘要：Given a family of log pairs over a smooth curve whose general fiber is a log Calabi--Yau pair in a fixed bounded family, suppose there exists a divisor on the family whose restriction on a general fiber is ample with bounded volume, we show that, if the total space of the family has relatively trivial log canonical divisor and the special fiber has slc singularities, then every irreducible component of the special fiber is birationally bounded.
时间：2023-12-26 10:30-11:30
地点：Room A-103, TSIMF
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