MATH-IMS Joint Colloquium Series
(Pure Mathematics)

  • Organizers: Yi-Jen Lee and Martin Li
  • Hosts: Department of Mathematics & Institute of Mathematical Sciences, CUHK
  • Contact: Please email to yjlee@math.cuhk.edu.hk or martinli@math.cuhk.edu.hk for any inquiries. The recording of the talks are available upon request.

  • Remark: Due to current COVID-19 situation, we will be hosting the colloquium talks online via ZOOM until safe travels are permitted. You can access the talk via the ZOOM link below.


Upcoming talk

Date/Time/Venue Talks
Mar 11, 2021 (Thur)
4:00PM
Zoom link
Speaker: Alberto Abbondandolo (Ruhr Universität Bochum)
Title: Systolic questions in metric and symplectic geometry

Abstract: The prototypical question in metric systolic geometry is to bound the length of a shortest closed geodesic on a closed Riemannian manifold by the volume of the manifold. This question has been extensively studied for non simply connected manifolds, but in the recent years there has been some progress also for simply connected manifolds, on which closed geodesics cannot be found simply by minimizing the length. This progress involves extending systolic questions to Reeb flows, a class of dynamical systems generalising geodesic flows. On the one hand, this extension and the use of symplectic techniques provide some answers to classical questions within metric systolic geometry. On the other hand, new questions arise from the more general setting and relate seemingly distant fields such as the study of rigidity properties of symplectomorphisms and the integral geometry of convex bodies. I will give a non-technical panoramic view of some of these recent developments.


2020-21 Spring schedule


Date/Time/Venue Talks
Feb 4, 2021 (Thur)
4:00PM
Zoom link
Speaker: Fangyang Zheng (Chongqing Normal University)
Title: Kahler manifolds with positive orthogonal Ricci curvature

Abstract: The orthogonal Ricci curvature of a tangent direction in a Kahler manifold is the difference between the Ricci and the holomorphic sectional curvature of that direction. This curvature notion is closely related to Ricci and holomorphic sectional curvature. We are interested in understanding the class of compact Kahler manifolds with everywhere positive orthogonal Ricci curvature. In this talk, I will report on some recent progress on the topic.
Feb 18, 2021 (Thur)
4:00PM
Zoom link
Speaker: Vincent Colin (University of Nantes)
Title: Reeb dynamics in dimension 3 and broken book decompositions

Abstract: The study of the dynamics of vector fields in dimension 3 was at center of Poincaré's pioneering work on the 3-body problem. Vector fields arising from mechanics often have the extra property of preserving a contact structure and fall in the family of Reeb vector fields. I will describe how to extend the notion of a Poincaré's surface of section to the more general notion of a broken book decomposition and derive general dynamical properties. Amongst those, a nondegenerate Reeb vector field has either 2 or infinitely many periodic orbits. This is joint work with Patrick Dehornoy and Ana Rechtman.
Feb 25, 2021 (Thur)
4:00PM
Zoom link
Speaker: Gang Liu (East China Normal University)
Title: Gromov-Hausdorff convergence of Kahler manifolds

Abstract: We discuss some recent development of Gromov-Hausdorff convergence of Kahler manifolds with geometric applications.
Mar 4, 2021 (Thur)
4:30PM
Zoom link
Speaker: Hélène Esnault (Freie Universität Berlin)
Title: Local Systems in Geometry and Arithmetic

Abstract: Galois laid the foundations of Galois theory and Galois groups, Riemann and Poincaré the ones of algebraic topology and the fundamental group. Grothendieck showed the two worlds are analog and developed the notion of étale fundamental group. Where do we find (continuous) representations of those in mathematics? Essentially the only ones we have at disposal are those of geometric nature. I’ll discuss conjectures on the density of those in the parameter space of all representations, and some results giving a small evidence for it (based on joint work with Moritz Kerz and Michael Groechenig).
Mar 11, 2021 (Thur)
4:00PM
Zoom link
Speaker: Alberto Abbondandolo (Ruhr Universität Bochum)
Title: Systolic questions in metric and symplectic geometry

Abstract: The prototypical question in metric systolic geometry is to bound the length of a shortest closed geodesic on a closed Riemannian manifold by the volume of the manifold. This question has been extensively studied for non simply connected manifolds, but in the recent years there has been some progress also for simply connected manifolds, on which closed geodesics cannot be found simply by minimizing the length. This progress involves extending systolic questions to Reeb flows, a class of dynamical systems generalising geodesic flows. On the one hand, this extension and the use of symplectic techniques provide some answers to classical questions within metric systolic geometry. On the other hand, new questions arise from the more general setting and relate seemingly distant fields such as the study of rigidity properties of symplectomorphisms and the integral geometry of convex bodies. I will give a non-technical panoramic view of some of these recent developments.
Mar 18, 2021 (Thur)
11:00AM
Zoom link
Speaker: Thomas Haines (University of Maryland)
Title: TBA

Abstract: TBA
Mar 25, 2021 (Thur)
5:00PM
Zoom link
Speaker: Ruochuan Liu (BICMR, Peking University)
Title: TBA

Abstract: TBA
Mar 31, 2021 (Wed)
10:00AM
Zoom link
Speaker: Rachel Roberts (Washington University in Saint Louis)
Title: TBA

Abstract: TBA
Apr 8, 2021 (Thur)
4:00PM
Zoom link
Speaker: Patrice Le Calvez (Institut de Mathématiques de Jussieu - Paris Rive Gauche)
Title: TBA

Abstract: TBA
Apr 15, 2021 (Thur)
4:00PM
Zoom link
Speaker: Yiming Long (Chern Institute of Mathematics, Nankai University)
Title: Rabinowitz minimal periodic solution conjecture

Abstract: In 1978, Professor Paul Rabinowitz proved the existence of T-periodic solutions for autonomous Hamiltonian systems whose Hamiltonian function is super-quadratic at infinity and zero for any given T>0 by using a minimax variational method. Because the minimal period of this solution could be T/k for some positive integer k, he asked whether such a system possesses always a T-periodic solution with T as its minimal period. This is the famous Rabinowitz minimal periodic solution conjecture. In the last more than 40 years, many mathematicians have studied this conjecture and got many interesting results. But the conjecture is still open under the original conditions of Rabinowitz. In this lecture, I shall give a brief survey on the main results obtained and methods used in these studies so far, and hope to lead to more interests on this conjecture.
Apr 21, 2021 (Wed)
10:00AM
Zoom link
Speaker: Emily Riehl (Johns Hopkins University)
Title: TBA

Abstract: TBA
Apr 29, 2021 (Thur)
4:00PM
Zoom link
Speaker: Shun-Jen Cheng (Academic Sinica)
Title: TBA

Abstract: TBA
May 6, 2021 (Thur)
9:00PM
Zoom link
Speaker: Peter Constantin (Princeton University)
Title: TBA

Abstract: TBA


Past Colloquium



© Martin Li, Department of Mathematics, The Chinese University of Hong Kong