Location

中国科学技术大学 管理楼 1518 (下图中 A 点)

Handbook

Download

Program

Titles and Abstracts

王宏玉 扬州大学

Title: From Kodaira Conjecture to Donaldson question

Abstract: In this talk, we show that any tamed closed almost complex four-manifold with self-dual second Betti number one, there exists a new sympletcic form compatible with the given almost complex structure, Then, we give an affirmative answer to Donaldson question for tamed closed almost complex four-manifolds with self-dual second Betti number one. Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira Conjecture.

李逸 上海交通大学

Title: A geometric flow and Hopf’s conjecture

Abstract: In this talk, I will discuss a geometric flow recently introduced by Kefeng Liu and I on vector fields. This flow has its nature both in geometry and PDEs, in particular, in connecting with the long-standing two conjectures of Hopf and a problem of Yau.

李慧 苏州大学

Title: The fundamental group of G-manifolds

Abstract: Assume a compact connected Lie group acting on a symplectic manifold. We will discuss the fundamental group of the symplectic manifold, and that of the orbit space; when the Lie group action is Hamiltonian, we also discuss the fundamental groups of all the symplectic quotients.

刘博 Humboldt University

Title: Geometric model for differential K-theory

Abstract: In this talk, by using family index theorem, eta form and higher spectral flow, we will construct a new geometric model for differential K-theory on closed manifolds and define the push-forward map. Furthermore, we will extend this model and the corresponding properties to the orbifold case.

卢文 华中科技大学

Title: Optimal convergence speed of Bergman metrics on symplectic manifolds

Abstract: It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high p-tensor powers of the prequantum line bundle. We show that the Fubini-Study metrics induced by these embeddings converges at speed rate \(1/p^2\) to the symplectic form. This is a joint work with Professors Xiaonan Ma and George Marinescu.

麻小南 法国巴黎七大

Title: Toeplitz operator and vanishing theorem

Abstract: We will explain a criteria on the vanishing of the de Rham cohomology group associated with a family of flat vector bundles, this is a real analogy of the vanishing theorem of Kodaira-Serre. The theory on the Toeplitz operators plays an important role.

朱家林 复旦大学上海数学中心

Title: Gluing formula of analytic torsion and Scattering matrix

Abstract: In this talk I will introduce our joint work with Martin Puchol, Yeping Zhang on the gluing formula of analytic torsion. We give an analytic proof of the gluing formula of Brüning-Ma of analytic torsion by using the adiabatic method and scattering matrix.

冯仁杰 北京国际数学中心

Title: Extrema of random holomorphic fields

Abstract: In the first part of the talk, I will define the random holomorphic fields and exhibit several well-known results. In the second part, two of my results on the extrema of random fields will be given: the distribution of critical values and the mean value of the supremum of \(L^2\)-normalized fields. I will also discuss several open problems.

俞建青 中国科学技术大学

Title: Higher Spectral Flow for Dirac Operators with Local Boundary Conditions

Abstract: We consider a gauge invariant one parameter family of families of fiberwise twisted Dirac type operators on a fiberation with the typical fiber an even dimensional compact manifold with boundary, i.e., a family \({D _u}, u\in [0,1]\) with \(D_1=gD_0g^{-1}\) for a suitable unitary automorphism \(g\) of the twisted bundle. Suppose all the operators \(D_u\) are imposed with a certain local elliptic boundary condition \(F\) and \(D _{ u , F }\) is the self-adjoint extension of \(D_u\). We establish a formula for the higher spectral flow of \({D _{u,F}}\), \(u\in[0,1]\). Our result generalizes a recent result of Gorokhovsky and Lesch to the families case. If time permits, I will also touch briefly on the equivariant higher spectral flow, which is the potential joint work with Fei Han.

杨晓奎 中国科学院数学与系统科学研究院

Title: The Kahler-Ricci flow and collapsing limits

Abstract: We discuss the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This strengthens previous work of Song-Tian and others. This is joint work with Ben Weinkove and Valentino Tosatti.