## Welcome to GAP seminar

This seminar aims at filling up the gap between graduate level math and research math, and enlarging the scope of graduate students as well as more advanced researchers. In each talk, the speaker will focus on a currently active research topic. He/she will spend one hour or so to introduce the background of the topic, including basic conceptions/examples, important known results and major problems etc. The last part of the talk will usually be more technical and is related to the speaker's own work. The subjects of future talks are mainly chosen from geometry(G), algebra, analysis(A), and mathematical physics(P).

## Upcoming Talks

## Past Talks

Archive of GAP Seminar: Fall 2013 | Spring2014 | Fall 2014 | Spring 2015 | Fall 2015 | Spring 2016 | Fall 2016 | Spring 2017 | Fall 2017 | Spring 2018 | Fall 2018

Date: 07/12, 16:00-17:30

Speaker: Yang Liu (Max Planck Institute for Mathematics, Bonn)

Title: Modular geometry on noncommutative tori

Abstract: A general question behind the project is to explore the notion of intrinsic curvature for noncommutative spaces given in terms of Connes's spectral triple paradigm. It has only recent began (2014) to be understood on noncommutative two tori in the paper of Connes and Moscovici. The notion of curvature (or general local invariants) is modeled on spectral geometry of Riemannian manifolds. The new input, purely due to the quantum feature, is the modular theory of weights for Von Neumann algebras. In this talk, I will focus on some intriguing spectral functions arising from the interplay between the two components. I will present a bending phenomenon in contrast to the commutative world. My recent progress relates the calculus for those spectral functions to hypergeometric functions and cyclic homology/cohomology.

Date: 06/21, 16:00-17:30

Speaker: 李铎（清华大学）

Title: Categorical characterization of quadrics

Abstract: We give a characterization of smooth quadrics in terms of the existence of full exceptional collections of certain type, which generalizes a result of C.Vial for projective spaces.

Date: 06/06, 16:00-17:30

Speaker: 郭帅（北京大学）

Title: An Introduction to Gromov-Witten theory and Mirror Symmetry

Abstract: In this talk, I will first briefly introduce the motivation of defining and studying Gromov-Witten invariants. Then I will explain the physics mirror symmetry conjectures related to the Gromov-Witten invariants of the quintic threefolds. Finally I will list the recent progresses related to these conjectures.

Date: 05/31, 16:00-17:30

Speaker: 徐国义（清华大学）

Title: The analysis and geometry of isometric embedding

Abstract: In 1950's, Nash-Kuiper built up the C^1 isometric embedding for any surface into $\mathbb{R}^3$, this can be viewed as analysis side of isometric embedding. On the other hand, there is obstruction for the existence of $C^2$ isometric embedding of surface into $\mathbb{R}^3$ known since Hilbert, which reflects the geometry flavor of isometric embedding. What's happening from $C^1$ to $C^2$ (from analysis to geometry)? We will present our partial progress along this direction. The talk will be accessible to audience with basic knowledge of analysis and differential geometry.

Date: 05/24, 16:00-17:30

Speaker: 来米加（上海交通大学）

Title: On Hang-Wang type rigidity theorem

Abstract: Let (M, g) be a compact manifold with boundary and Ric \geq n-1, Hang-Wang proved M is isometric to the standard hemisphere provided \partial M is isometric to standard S^{n-1} and convex. In this talk, we discuss some recent results of Hang-Wang type rigidity when the boundary is isometric to a product manifold with one factor isometric to S^{k-1}. A new ingredient of the proof is Obata type equation with Robin boundary condition.

Date: 05/10, 16:00-17:30

Speaker: 薛江维 (武汉大学)

Title: On counting certain principally polarized superspecial abelian surfaces over F_p

Abstract: We study the principally polarized superspecial abelian surfaces over the prime finite field F_p with Frobenius endomorphism π = ±sqrt{p}. We give a description of this set in terms of double coset spaces and obtain an explicit formula for its cardinality. This is a joint work with Prof. Chia-Fu Yu.

Date: 05/10, 14:30-16:00

Speaker: Alexander Cruz Morales (National University of Colombia)

Title: Quantum cohomology for isotropic Grassmannians

Abstract: We will discuss the big quantum cohomology ring of isotropic Grassmannians IG(2,2n). After introducing the basic notions we will show that these rings are regular. In particular, by “generic smoothness”, we will give a conceptual proof of generic semisimplicity of the big quantum cohomology for these Grassmannians. We will also relate certain decomposition of the ring with a exceptional collection of the derived category of IG(2,2n). This is based on joint work with A. Mellit, A. Kuznetsov, N. Perrin and M. Smirnov.

Date: 04/26, 16:00-17:30

Speaker: Li, Si (清华大学)

Title: Singularities: from L^2 Hodge theory to Seiberg-Witten geometry

Abstract: Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus, satisfying a general asymptotic condition. We establish a version of twisted L^2 Hodge theory for the pair (X,f) and prove the corresponding Hodge-to-de Rham degeneration property. It can be viewed as a generalization of Kyoji Saito's higher residue theory and primitive forms for isolated singularities. In the second part of the talk, I will explain a connection between primitive period maps and 4d N=2 Seiberg-Witten geometry.

Date: 04/19, 16:00-17:30

Speaker: Li, Zhan (南方科技大学)

Title: On iterated accumulation points of pseudo-effective thresholds

Abstract: Fujita proposed a conjecture which asserts that k-th accumulation points of pseudo-effective thresholds of n-dimensional log smooth varieties with respect to ample divisors are bounded by n-k. We will show an upper bound n-k+1. This work is partially joint with Jingjun Han.

Date: 04/16, 16:00-17:30

Speaker: Li, Qirui (Australian National University)

Title: The Monge mass transport problem

Abstract: The optimal transportation problem was introduced by Monge in 1781. Since then the problem has been extensively studied and general costs are allowed. But for Monge's orignal cost, very little is known about the regularity. In this talk, we discuss the regularity in Monge's problem, and in particular show that, in two dimensional case, the optimal mapping is continuous. The talk is based on joint works with F. Santambrogio and X.-J. Wang.

Date: 04/12, 16:00-17:30

Speaker: Li, Muxi (USTC)

Title: The Abel-Jacobi Map for Higher Chow Complexes and its Integral Version

Abstract: In 1980s, Spencer Bloch constructed a cycle-class map between Bloch's higher Chow groups and Deligne- Beilinson homology for smooth, complex quasiprojective varieties, which generalizes the classical Griffiths Abel-Jacobi map and the Beilinson regulator map. In 2004, Matt Kerr, James D. Lewis and Stefan Müller-Stach gave an explicit formula that agrees rationally with Bloch's abstract definition. A recent work adapted Kerr, Lewis and Müller-Stach's formula, proved the existence of an integral regulator on higher Chow complexes, and gave an explicit expression for it. This integral regulator can be applied to detect torsion phenomena in higher Chow groups.

Date: 04/04, 16:00-17:30

Speaker: Xinyi Yuan （University of California Berkeley）

Title: The averaged Colmez conjecture

Abstract: In this talk, I will introduce the averaged Colmez conjecture proved by Yuan-Zhang and Andreatta-Goran-Howard-Madapusi Pera. Some related terms in the talk are CM abelian varieties, Faltings height, Shimura varieties, and Artin L-functions.

Date: 03/29, 16:00-17:30

Speaker: Sheng, Li (四川大学)

Title: Extremal Metrics on Toric Manifolds and Some Applications of Affine Techniques

Abstract: Donaldson initiated a program to study the extremal metrics on toric manifolds and solved the problem for cscK metrics on toric surfaces. For toric manifolds, the equation is called the Abreu equation, which is similar to the affine maximal equation.
In joint papers with Li An-Min and Chen Bohui we apply the affine techniques to extend the existence result in dimension 2 to extremal metrics. We explain our main idea and methods. Next we talk some application of affine techniques to Bernstein problems.

Date: 03/27, 16:00-17:30 (Different Time!)

Speaker: Kang Zuo
(University of Mainz，USTC)

Title: Distribution on moduli spaces of minimal varieties

Abstract: I shall report some progress in a joint project with Steven Lu and Ruiran Sun in the study of a class of distributions on moduli spaces of minimal varieties. The ultimate goal is to show Borel hyperbolicity of those type moduli spaces.

Date: 03/21, 10:00-11:30 (Different Time!)

Speaker: Zhang, Hanxiong（中国矿业大学）

Title: Hurwitz numbers and the cut-and-join equation

Abstract: Hurwitz numbers are classical objects in enumerative geometry. In this introductory talk, I will review the geometric and algebraic definitions of Hurwitz numbers, and explain why these two definitions are equivalent. Then I will introduce the generating function of Hurwitz numbers using symmetric functions, which turns out to be a solution of the cut-and-join equation. Its link with integrable hierarchies via Boson-Fermion correspondence will also be gently addressed.

Date: 03/15, 16:00-17:30

Speaker: Chen, Yifan (北京航空航天大学)

Title: The 4-nodal cubic surface and certain surfaces of general type with geometric genus zero

Abstract: In this talk, after briefly describing the geometry of the 4-nodal cubic surface, I will introduce several families of surfaces of general type with geometric genus zero, which are all Galois covers of the 4-nodal cubic surface with the Klein group as the Galois group. I will also talk about the moduli problem of the Keum-Naie-Mendes Lopes-Pardini surfaces.

Date: 03/08, 16:00-17:30

Speaker: Li, Qin (南方科技大学)

Title: Toeplitz quantization, Fedosov quantization and Feynman graphs

Abstract: Toeplitz operators on K\"ahler manifolds are defined as the composition of multiplication by smooth functions and orthogonal projection to holomorphic sections of (tensor powers) of prequantum line bundles. In particular, the asymptotic behavior of these operators gives rise to deformation quantization on K\"ahler manifolds. In this talk, I will describe a localized version of Toeplitz operators using the technique of Feynman graph computations, and give an explicit equivalence between Toeplitz quantization and Fedosov quantization.