Upcoming Seminars

TBA

Previous Seminars

Time：December 30, Monday, 14:00-15:00

Venue： Lecture Hall

Title:  Fundamental groups and Ricci curvature

Speaker： 朱星宇 Xingyu Zhu (SLMath/Michigan State University)

Abstract：Understanding the topological obstruction of curvature lower bounds is a central theme in geometry. For complete manifolds of nonnegative Ricci curvature, it is previously known that when the manifold is compact its fundamental group is virtually abelian and when non-compact, any finitely generated subgroup of the fundamental group is virtually nilpotent. Moreover any finitely generated virtually nilpotent group can be realized a fundamental group of some manifold of nonnegative Ricci curvature. A natural question arising in this context is, how to recognize the (virtually) abelian fundamental group among the (virtually) nilpotent ones. In this talk we present a result that under extra linear volume growth condition, the fundamental group will always be virtually abelian and if one further assumes that the Ricci curvature is strictly positive, then the fundamental group is finite. We  highlight that, in the proof, the calculus on non-smooth metric measure spaces with lower Ricci curvature bounds (RCD spaces) plays a crucial role. This is joint work with Dimitri Navarro and Jiayin Pan.

Time：July 10, Wednesday, 14:30-15:30

Venue： Lecture Hall

Title:  Volume of moduli spaces of differentials 

Speaker： 陈大卫 Dawei Chen (Boston College)

Abstract：Moduli spaces of differentials with prescribed orders of zeros on Riemann surfaces admit a natural volume form. In this talk, I will explain how to use intersection theory to compute the corresponding volume of moduli spaces of differentials. 

Time：July 8, Monday, 16:00-17:00

Venue： Lecture Hall

Title: Gromov's almost flat theorem and local Ricci bounded covering geometry

Speaker： 王季康 Jikang Wang (University of California, Berkeley)

Abstract：Gromov proved that if a compact n-manifold is almost flat, |sec|*diam^2 less than a given small constant number, then it has a finite cover diffeomorphic to a nilmanifold. HKRX and Rong generalized the Gromov's theorem to a compact maniflod with Ricci lower bound, small diameter and non-collapsing universal cover. We shall give a new proof for the Ricci one using the structure of approximate groups.

Time：July 8, Monday, 14:30-15:30

Venue： Lecture Hall

Title: Geometry of collapsed metric measure spaces with Ricci bounded below

Speaker： 张若冰 Ruobing Zhang (Princeton University)

Abstract：This talk is concered with some of my recent work in studying metric measure spaces with Ricci curvature bounded below in the collapsed setting.

Time：May 28, Tuesday, 16:00-17:00

Venue： Lecture Hall

Title: Irrationality of degenerations of Fano varieties

Speaker： 曲三太 Santai Qu (University of Science and Technology of China )

Abstract：In this talk, I will introduce a recent result about bounding degrees of irrationality of degenerations of klt Fano varieties of arbitrary dimensions. This proves the generically bounded case of a conjecture proposed by C. Birkar and K. Loginov for log Fano fibrations of dimensions greater than three. Our approach depends on a method to modify the klt Fano fibration to a toroidal morphism of toroidal embeddings with bounded general fibres. This is a joint work with Prof. C. Birkar.

Time：May 23, Thursday, 16:00-17:00

Venue： Lecture Hall

Title: On Kähler Ricci shrinker surfaces

Speaker： 李宇 Yu Li (University of Science and Technology of China )

Abstract：Using convergence theories for Ricci shrinkers, we prove that non-compact Kähler Ricci shrinker surfaces possess two distinct canonical neighborhoods outside a compact set, leading to uniformly bounded sectional curvature. Combining this estimate with prior works by Bamler, Conlon-Cifarelli-Deruelle, and Sun, we achieve a comprehensive classification of all Kähler Ricci shrinker surfaces. This work was done in collaboration with Bing Wang.

Time：March 14, Thursday, 16:00-17:00

Venue： Lecture Hall

Title: A ddbar lemma and its applications 

Speaker： 曹俊彦 Junyan Cao (Université Côte d’Azur)

Abstract：In this talk, I will explain a very general ddbar lemma, together with a decomposition theorem for currents with values in a (singular) Hermitian line bundle. As a corollary, we establish the Kähler version on an injectivity theorem due to O. Fujino in the projective case. It is a joint with Mihai Paun.

Time：March 11, Monday, 9:30-10:30

Venue： Lecture Hall

Title: A Symplectic Reduction by Stages approach to Gravitating Vortices problem

Speaker： 姚成建 Chengjian Yao (ShanghaiTech University) 

Abstract：The coupled system of Kähler-Yang-Mills equations is introduced as the zero-momentum map equation of the extended gauge group, which naturally extends the usual gauge group and the Hamiltonian diffeomorphism group. A lower dimensional reduction of the system, called the Gravitating Vortex equations, accidentally includes the Einstein-Bogomolnyi equation in mathematical physics as a special case. Based on the moment map interpretation and the symplectic reduction by stages approach, we solve certain existence and uniqueness problems of Gravitating Vortex equations. Part of the work is joint with Alvarez-Consul, Garcia-Fernandez, Garcia-Prada and Pingali.