BIMSA > BIMSA Lecture BIMSA Lecture A Classification of Positive-Curvature Discrete Einstein Metrics on Trees
A Classification of Positive-Curvature Discrete Einstein Metrics on Trees
Organizer
Shuliang Bai
Speaker
Haoxuan Cheng
Time
Wednesday, May 20, 2026 2:00 PM - 3:00 PM
Venue
A3-4-101
Online
Zoom 637 734 0280 (BIMSA)
Abstract
This report focuses on positive-curvature discrete Einstein metrics on finite trees. It introduces the basic concepts of graph Ricci curvature and the Ricci matrix, explains how the positive-curvature condition is transformed into the negativity of the largest eigenvalue, and summarizes the classification of all positive-curvature trees. The main topics include the classification of caterpillars, the distinction between long-spine and short-spine cases, and the structure of the zero-curvature boundary.
Speaker Intro
Cheng Haoxuan is a Ph.D. student in Mathematics at Fudan University. His research focuses on discrete geometric analysis, with particular interests in geometric structures on graphs, discrete curvature theory, and related analytic problems. He has received the Class B Fellowship from the National High-Level Talent Training Center at Fudan University.