Aim & Scope

Distinguished differential geometer Professor Simon Brendle of Columbia University will visit the National Center for Theoretical Sciences (NCTS) and Academia Sinica. Professor Brendle is renowned for his groundbreaking contributions to several major conjectures and problems, including the Yamabe flow convergence, the differentiable sphere theorem, the Hsiang-Lawson conjecture. He has also made significant advances to the study of mean curvature and Ricci flow. His numerous honors include the European Mathematical Society Prize, the AMS Bôcher Prize, the Fermat Prize, and the prestigious 2024 Breakthrough Prize in Mathematics.

During his visit, Professor Brendle will deliver two lectures. The first, titled "Minimal Surfaces and the Isoperimetric Inequality," will explore recent advances in this area. His second lecture, "Systolic Inequalities and the Horowitz-Myers Conjecture," will delve into the connections between geometry and topology. These lectures promise to be highly beneficial to the geometric analysis community in Taiwan, offering insights into cutting-edge research and inspiring students in the field.

Invited Speaker

Prof. Simon Brendle (Columbia University)

Event Time

March 19 (Wed.), 3:00-3:30 Tea Time, 3:30-4:30 Lecture

March 20 (Thu.), 3:30-4:30 Lecture,  4:30-5:00 Tea Time

Lecture 1:

Date: March 19, 2025

Time: 3:30 PM - 4:30 PM

Title: Minimal surfaces and the isoperimetric inequality

Abstract: The isoperimetric inequality has a rich history in geometry. This lecture will discuss the generalization of this inequality to submanifolds in Euclidean space. A sharp isoperimetric inequality for minimal submanifolds of codimension at most 2 will be presented, answering a question posed by Carleman. The proof is inspired by, but does not utilize, optimal transport.  

Lecture 2:

Date: March 20, 2025

Time: 3:30 PM - 4:30 PM

Title: Systolic inequalities and the Horowitz-Myers conjecture

Abstract: Let n be an integer such that 3 ≤ n ≤ 7. Let g be a Riemannian metric on B² × Tⁿ⁻² with scalar curvature at least -n(n-1). This lecture will establish an inequality relating the systole of the boundary to the infimum of the mean curvature on the boundary. As a result, a new positive energy theorem will be presented, where equality holds for the Horowitz-Myers metrics. This is joint work with Pei-Ken Hung.

Agenda with Title & Abstract 【Download】

Registration 【LINK】