May 22, Saturday

9:00 - 9:30 AM

Registration Session

9:30 - 10:30 AM

孙笑涛

Compactification of moduli of parabolic bundles by conformal blocks

10:30 - 11:00 AM

Break

11:00 – 12:00 AM

袁瑶

A review on Strange duality conjecture

Lunch Break

2:00 - 3:00 PM

刘敏

Rational curves on the moduli spaces of stable bundles

3:00 - 3:30 PM

Tea Break

3:30 - 4:30 PM

陈猛

On birational geometry of varieties which are canonically fibered by curves

4:30 - 5:00 PM

Break

5:00 - 6:00 PM

顾怡

Slope inequalities and a Miyaoka-Yau type inequality in positive characteristic

May 23 Sunday

9:00-10:00 AM

周明铄

A finite dimensional proof of Verlinde formula

10:00 - 10:30AM

Break

10:30-11:30AM

文学清

Parabolic Higgs bundles over projective line and quiver varieties

11:30-12:00 AM

Tea Break

12:00 - 1:00 PM

苏晓羽

Parabolic Hitchin System and Mirror Symmetry

孙笑涛

天津大学

袁瑶

首都师范大学

刘敏

青岛大学

陈猛

复旦大学

顾怡

苏州大学

周明铄

天津大学

文学清

丘成桐数学科学中心

苏晓羽

丘成桐数学科学中心

袁瑶

首都师范大学

Title: A review on Strange duality conjecture

Abstract:

Strange duality is a conjecture formulated in 1990s, which asserts a duality between the global section spaces of determinant line bundles over two moduli spaces   of semistable sheaves over a smooth projective scheme $X$.When $X$ is a curve, this conjecture has been proved around 2007.  When $X$ is a surface, there is so far no general set-up for this conjecture; but under some assumption the conjecture can be extended.  There is not much known   for surfaces on the conjecture.  On the other hand, there is an analog of the duality in quiver representation theory which can be easily seen from the result of Derksen-Weyman on the semi-invariants. In this talk, I will   first introduce the formulation of the conjecture, then survey shortly the   proof for curves with comparison to the case in quiver representation theory, and also I will mention an application of the duality in quiver representation to some special cases on the projective plan, finally I will explain why the duality is essentially a corollary to some property in the intersection theory of some relative Quot-scheme.

刘敏

青岛大学

Title:Rational curves on the moduli spaces of stable bundles

Abstract:

In this talk, we give an account of rational curves on the moduli spaces of stable bundles over a smooth curve.

陈猛

复旦大学

Title:On birational geometry of varieties which are canonically fibered by curves

Abstract:

Let $n\geq 2$ be any integer. For minimal projective $n$-folds of general type which are canonically fibered by curves, we prove that the canonical stability index has the optimal upper bound $r_{n,n-1}=\frac{1}{3}(5n+{\rm   mod}(n,3)+3)$, and that the canonical volume has the optimal lower bound $v_{n,n-1}=\frac{6}{2n+{\rm mod}(n,3)}$.

顾怡

苏州大学

Title:  Slope inequalities and a Miyaoka-Yau type inequality in positive characteristic

Abstract:

In 1987, by a very clever use of the stability of vector bundles on curves, Xiao proved the so-called Xiao’s slope inequality for surface fibrations over C. In this talk, we will discuss its counterpart in positive characteristic and as an application we will prove a Miyaoka-Yau type inequality for surfaces of general type in positive characteristic. This is a joint work with Prof. Xiatao Sun and Mingshuo Zhou.

周明铄

天津大学

Title:A finite dimensional proof of Verlinde formula

Abstract:

In this talk, we will give a review about the algebraic geometric proof of Verlinde formula. Some related problems about moduli space of vector bundles over a curve will also be discussed.

文学清

丘成桐数学科学中心

Title:   Parabolic Higgs bundles over projective line and quiver varieties

Abstract:

We set up an isomorphism between the moduli spaces of parabolic Higgs bundles on the projective line and certain quiver variety. As consequences, we can show that there is an algebraically completely integrable system structure on the quiver variety. Moreover, we give a geometrical solution to the nilpotent case of the Deligne-Simpson problem, which enable us construct the solutions explicitly.

苏晓羽

丘成桐数学科学中心

Title: Parabolic Hitchin System and Mirror Symmetry

Abstract:

In this talk we will talk about our recent program to show the mirror symmetry conjecture holds (in both sense of SYZ and TMS) for moduli of Higgs bundles over parabolic curves. We will first review the concept of mirror symmetry and in particular in the since of Strominger-Yau-Zaslow and Hausel-Thaddeus. Then we will talk about our way to check the SYZ and topological mirror symmetry partners property for moduli of Higgs bundles over a parabolic curve.