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Workshop on Algebraic Geometry
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
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