Upcoming Talks:
Title: Slope inequalities and a Miyaoka-Yau type inequality
Speaker: 周明铄，天津大学数学学院/应用数学中心
Time: 16:00-17:30 on Wednesday, April 24th, 2024
Venue: C654, Shuangqing Complex Building
Zoom Meeting ID: 271 534 5558
Passcode: YMSC
Abstract: After a review about Xiao’s approach of Slope inequalities and its generalization to positive characteristic, a Miyaoka-Yau type inequality for a minimal smooth surface of general type is given as an application. This is based on some work with Professor Yi Gu, Hao Sun and Xiaotao Sun.
Past Talks:
Title: Counting l-adic local systems on a curve over a finite field
Speaker: 余红杰，中国科学院晨兴数学中心
Time: 16:00-17:30 on Wednesday, April 17th, 2024
Venue: C654, Shuangqing Complex Building；Zoom Meeting ID: 271 534 5558 Passcode: YMSC
Abstract: In 1981, Drinfeld enumerated the number of irreducible l-adic local systems of rank two on a projective smooth curve fixed by the Frobenius endomorphism. Interestingly, this number looks like the number of points on a variety over a finite field. Deligne proposed conjectures to extend and comprehend Drinfeld's result. By the Langlands correspondence, it is equivalent to count certain cuspidal automorphic representations over a function field. In this talk,I will present some counting results where we connect counting to the number of stable Higgs bundles using Arthur's non-invariant trace formula.
Title: Existence of Stable Higgs-de Rham Flow for Principal Bundles
Speaker: 孙浩，华南理工大学
Time: 16:00-17:30 on Wednesday, April 10th, 2024
Venue: C654, Shuangqing Building
Abstract: Lan-Sheng-Zuo established the Hitchin-Simpson correspondence in characteristic p. In this correspondence, semistable graded Higgs bundles with vanishing chern classes are related to crystalline representations with the help of periodic Higgs-de Rham flow. In this talk, we will give the construction of Higgs-de Rham flows for principal bundles and discuss the existence of such flows under stable conditions.
Title: Local equations defining stable map moduli, arbitrary singularities, and resolution
Speaker: 胡毅，亚利桑那大学
Time: 16:00-17:30 on Wednesday, March 20th, 2024
Venue: C654, Shuangqing Building; Zoom Meeting ID: 4552601552 Passcode: YMSC
Abstract:
I will explain the matrix local equations defining the moduli spaces of stable maps of arbitrary genus, found jointly by Jun Li and the speaker. These equations already guided us to find explicit global resolutions for these moduli spaces in the cases when the genera are one and two. By Murphy’s law, stable map moduli possess arbitrary singularities. Turning to this, I will explain Lafforgue’s version of Mnev’s universality, how it leads to standard local equations for arbitrary singularity types, and how it should guide to resolve arbitrary singularities.
Bio：
胡毅，美国亚利桑那大学教授，大湾区大学（筹）访问教授，博士毕业于麻省理工学院，主要研究方为代数几何，在几何不变量、曲线与稳定映射的模空间、奇点解消等问题上做了一系列重要的工作，获得1996年美国数学会百年纪念奖。
Title: Specialization of Linear Differential Equations
Speaker: 冯如勇，中国科学院数学与系统科学研究院系统科学研究所
Time: 16:00-17:30 on Wednesday, March 13th, 2024
Venue: C654, Shuangqing Building； Zoom Meeting ID: 4552601552 Passcode: YMSC
Abstract:
In this talk, we will discuss recent advancements in the specialization of linear differential equations. Given a linear differential equation with parameters, our focus is on how the algebraic properties of its solutions change as these parameters vary over an affine variety. For example, we inquire about the values of parameters for which linear differential equations can have a basis of algebraic solutions, assuming the original equation lacks such a basis. By extending a result of Hrushovski, we demonstrate that the set of such values is indeed ``small" in a meaningful sense. As an application, we establish Matzat’s conjecture in its entirety: The absolute differential Galois group of a one-variable function field, equipped with a non-trivial derivation, is the free proalgebraic group. The talk is based on joint work with Michael Wibmer from the University of Leeds, UK.
Bio：
冯如勇, 中国科学院数学与系统科学研究院研究员、博士生导师，主要研究方向为：符号计算与微分差分伽罗华理论，特别是微分差分方程的符号求解、构造性线性微分（差分）方程伽罗华理论及其在特殊函数理论与组合数学等领域的应用。目前已在符号计算领域国际会议ISSAC,以及期刊Journal of Symbolic Computation, Advances in Applied Mathematics, Mathematics of Computation, Transactions of the AMS等发表论文20多篇。
