Expository Lecture (July 7-11)

Venue

TBA

Schedule

TBA

Titles & Abstracts

TBA

Conference (July 14-18)

Venue

Conference Room on 3rd Floor of Material Research Building (Section B&C), East Campus of USTC

Schedule

TBA

Titles & Abstracts

Zhongshan An (University of Michigan)

Title: Einstein manifolds with boundary

Abstract: We will talk about existence of Einstein metrics on manifolds with boundary, while prescribing the induced conformal metric and mean curvature of the boundary. In dimension 3, this becomes the existence of conformal embeddings of surfaces into constant sectional curvature space forms, with prescribed mean curvature. We will show existence of such conformal embeddings near generic Einstein background. We will also discuss the existence question in higher dimensions, where things become more subtle and a stability boundary condition is used to construct metrics with nonpositive Einstein constant.

*Simon Brendle (Columbia University in the City of New York)

Title: Systolic inequalities and the Horowitz-Myers conjecture

Abstract: Let $n$ be an integer with $3 \leq n \leq 7$, and let $g$ be a Riemannian metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$. We establish an inequality relating the systole of the boundary to the infimum of the mean curvature on the boundary. As a consequence, we obtain a new positive energy theorem where equality holds for the Horowitz-Myers metrics. This is joint work with Pei-Ken Hung.

Shouhei Honda (The University of Tokyo)

Title: From almost smooth spaces to RCD spaces

Abstract: We provide various characterizations for a given almost smooth space to be an RCD space, in terms of a local volume doubling and a local Poincaré inequality. Applications include a characterization of Einstein 4-orbifolds. This talks is based on a joint work with Song Sun (Zhejiang University).

Yang Li (University of Cambridge)

Title: Large mass of limit  G₂ & Calabi-Yau monopoles

Abstract: TBA

Jiayin Pan (University of California, Santa Cruz)

Title: Ricci curvature and linear volume growth

Abstract: We will talk about old and new results on the topology of complete manifolds with nonnegative Ricci curvature and linear volume growth. The new results are based on a joint work with Dimitri Navarro and Xingyu Zhu.