（All seminars will be held in Conference Room 3, Jinchunyuan West Building on Wednesday at 15:30, unless marked in red. ）
Upcoming Talk:
Title: Cubic threefolds with an involution and their intermediate Jacobians
Speaker: Zheng Zhang 张正 (ShanghaiTech University)
Time: Wednesday at 15:30, May 31, 2023
Place: Conference Room 3, Jinchunyuan West Building
Abstract:
We study the moduli space of cubic threefolds admitting an involution via the period map sending such a cubic threefold to the invariant/anti-invariant part of the intermediate Jacobian. Our main result is global Torelli holds for the period map. Key ingredients of the proof include a description of the invariant/anti-invariant part of the intermediate Jacobian as a Prym variety and a detailed study of certain positive dimensional fibers of the corresponding Prym map. The proof also relies on the results of Donagi-Smith, Ikeda and Naranjo-Ortega on related Prym maps. This is joint work with S. Casalaina-Martin and L. Marquand.
Past Talks：
Title: Universal meromorphic functions with slow growth
Speaker: Songyan Xie (CAS)
Time: Wednesday at 15:30, May 24, 2023
Place: Conference Room 3, Jinchunyuan West Building
Abstract:
I will show a solution to a problem asked by Dinh and Sibony in their open problem list, about minimal growth of universal meromorphic functions. This is joint work with Dinh Tuan Huynh and Zhangchi Chen. If time permits, I will also discuss my recent joint work with my Ph.D. student Bin Guo, about the existence of universal holomorphic functions in several variables with slow growth.
Title: On attractor points on the moduli space of Calabi-Yau threefolds
Speaker: Emanuel Scheidegger (BICMR)
Time: Wednesday at 15:30, May 17, 2023
Place: Conference Room 3, Jinchunyuan West Building
Abstract:
We briefly review the origin in physics of attractor points on the moduli space of Calabi-Yau threefolds. We turn to their mathematical interpretation as special cases of Hodge loci. This leads to fascinating conjectures on the modularity of the Calabi-Yau threefolds at these points in terms of their periods and L-functions. For hypergeometric one-parameter families of Calabi-Yau threefolds, these conjectures can be verified at least numerically to very high precision.
Title: stable (parabolic) holomorphic vector bundles over complex curves and instanton Floer homology
Speaker: 谢羿（北京大学）
Time: Wednesday at 15:30, Apr 26, 2023
Place: Conference Room 3, Jinchunyuan West Building
Abstract:
Stable holomorphic bundles are objects in algebraic geometry which have been studied by many people. Instanton Floer homology is an invariant of 3-manifolds, which has been used to solve many problems in the low dimensional topology. It turns out the two things are closely related: knowledge on the moduli space of stable bundles can help the calculation of Instanton Floer homology. In this talk, I will explain this relationship and its generalization to stable parabolic bundles. This is joint work with Boyu Zhang.
Title: On the cohomology of BG
Speaker: 李时璋（中科院晨兴数学中心）
Time: Wednesday at 15:30, Apr 19, 2023
Place: Conference Room 3, Jinchunyuan West Building
Abstract:
In this talk, if time permits, we will discuss:
(1) classify order p group schemes over Spec(char p alg closed field) using Dieudonne modules;
(2) a new way of understanding Dieudonne modules in terms of cohomology of BG (due to Mondal);
(3) an attempt of using BG to construct a counterexample that Deligne--Illusie asked for (work of Antieau--Bhatt--Mathew);
(4) why this attempt cannot succeed (joint work in progress with Kubrak--Mondal), and how this attempt can be made successful (due to Petrov).
Title: Tropicalization of curves and applications
Speaker: Xiang He (YMSC, Tsinghua)
Time: Wednesday at 15:30, Apr 12, 2023
Place: Conference Room 3, Jinchunyuan West Building
Abstract:
The tropicalization process assigns to an algbraic variety a polyhedral complex with extra structure that records certain degeneration data. In this talk, I will introduce the tropicalization of (a family of) algebraic curves and explain the connection between the geometry of the algebro-geometric side and the tropical side. I will then discuss the application of this construction to the irreducibility of Severi varieties and the moduli space of curves. This is joint work with Karl Christ and Ilya Tyomkin.
Title: Moduli spaces of hyperKahler manifolds and cubics
Speaker: Zhiwei Zheng, YMSC, Tsinghua
Time: Mar. 29 (Wed.) 3:30-5:05 pm
Place: Jinchunyuan West Building, Second Floor, Conference Room 3
Abstract:
The study of moduli spaces of hyperKahler manifolds and low dimensional cubic hypersurfaces is an active direction in algebraic geometry. Thanks to kinds of Torelli theorem, many moduli spaces can be realized as locally symmetric varieties of unitary type or orthogonal type. Hodge theory, birational geometry and arithmetic geometry converge in this topic. In this talk I will give a general introduction to the theory and examples, and discuss the future directions.
