Online Differential Geometry Seminar (2025)

Time: Tuesday 21:00-22:00  (Beijing Time) 

Organizers:  Jialong Deng;  Akito Futaki  

Venue: ZOOM Meeting 

If you would like to attend the online seminar, kindly send Jialong an email.

Schedule

Upcoming talks

.Date:  4 Mar., 2025 （No talks)

.Date:  11 Mar., 2025

Speaker: Kartick Ghosh (Tata Institute of Fundamental Research, Mumbai) 

Title: Computing the α-Futaki character

Abstract: Alvarez-Consul–Garcia-Fernandez–Garcia-Prada introduced the Kahler-Yang-Mills equations (coupled equations for a Kahler metric and a metric on a holomorphic vector bundle ). They also introduced the α-Futaki character, an analog of the Futaki character, as an obstruction to the existence of solutions of the Kahler-Yang-Mills equations. In this talk, we will prove a formula for the α-Futaki character for certain ample line bundles over toric manifolds. We will then compute the α-Futaki character in some cases and compare it with the known existence result of Keller–Tønnesen-Friedman.

.Date:  18 Mar., 2025

Speaker: Yanir Rubinstein (University of Maryland)  

.Date:  25 Mar., 2025

Speaker: Bo Berndtsson (Chalmers University of Technology & Göteborgs universitet)

.Date:  1 Apr., 2025 （No talks)

.Date:  8 Apr., 2025 （No talks)

.Date: 15 Apr., 2025

Speaker: Eleonora Di Nezza (IMJ-PRG, Sorbonne Université ) 

.Date: 22 Apr., 2025

Speaker: Yoshinori Hashimoto (Osaka Metropolitan University）

.Date: 29 Apr., 2025

Speaker: Gerard Misiolek (University of Notre Dame) 

.Date: 6 May, 2025 

Speaker: Lei Ni (University of California, San Diego)

Date: 13 May,  2025 (Last talk of the Spring Semester)

Speaker:  Eveline Legendre (Université Claude Bernard Lyon 1)

.Date:  25 Feb., 2025

Speaker: Marco Mazzucchelli (ENS Lyon)   

Title: Closed geodesics and the first Betti number 

Abstract: In this talk, based on a joint work with Gonzalo Contreras, I will present the following result: on a closed Riemannian manifold of dimension at least two with non-trivial first Betti number, the existence of a minimal closed geodesic, in the sense of Aubry-Mather theory, implies the existence of a transverse homoclinic, and thus of a horseshoe, for the geodesic flow of a suitable -close Riemannian metric. As a corollary of this result and of existing literature, we infer that on any closed manifold of dimension at least two with non-trivial first Betti number, a  generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length.