(Online Seminar) Ricci Curvature and Differential Harnack Inequalities on Path Space
Speaker(s): Aaron Naber (Northwestern University)
Time: 09:30-10:30 October 28, 2020
Venue: Online
ABSTRACT
There has been an observation of late that many analytic estimates on manifolds M with lower Ricci curvature bounds have counterparts on the path space PM of the manifold when there are two sided bounds on Ricci curvature. We will begin reviewing some of these, in particular the estimates of [Nab],[Has-Nab] which generalize the Bakry-Emery-Ledoux estimates to path space. We will then discuss new results, which are joint with Haslhofer and Knofer, which generalize the Li-Yau differential harnack inequalities to the path space, under the assumption of two sided Ricci curvature bounds.
To accomplish this, we will introduce a family of Laplace operators on path space PM, built from finite dimensional traces of the Markovian hessian, which we will review. The differential harnacks will take the form of differential inequalities for these operators, and will recover the classical Li-Yau when applied the simplest functions on path space, namely the cylinder functions of one variable.
BRIEF BIO
Dr. Aaron Naber is currently Kenneth F. Burgess Professor in the department of Mathematics at Northwestern University. He received his undergraduate education at Pennsylvania State University, and then obtained Ph.D in Mathematics at Princeton under the supervision of Professor Gang Tian. Naber's research focuses on the study of geometrically motivated equations and their applications. This covers a broad scope of works in the areas of Ricci curvature, nonlinear harmonic maps, Yang-Mills, minimal varifolds, sectional curvature, Ricci solitons, mean curvature flow, Ricci flow, and general elliptic equations. For more information about him, please visit his webpage https://sites.math.northwestern.edu/~anaber/.
ZOOM INFO
ID: 615 3525 5117
Password: 505995
https://zoom.com.cn/j/61535255117?pwd=amVRMUtzVDJsTno0NTVjT2RPcXhDdz09
For more information about this seminar, please see below.
【Wednesday Online Seminar on Geometric Analysis】
This is the 20th talk of Wednesday Online Seminar on Geometric Analysis, which is an online seminar organized by Prof. Gang Tian, Prof. Jie Qing, Prof. Zhenlei Zhang, and Prof. Xiaohua Zhu.
Below is a list of invited speakers:
April 8, 2020 Wenshuai Jiang (Zhejiang University)
April 15, 2020 Chi Li (Purdue University)
April 22, 2020 Lu Wang (Caltech)
April 29, 2020 Jianchun Chu (Northwestern University)
May 6, 2020 Richard Bamler (UC Berkeley)
May 13, 2020 Xin Zhou (UC Santa Barbara)
May 20, 2020 Daniel Stern (University of Toronto)
May 27, 2020 Jeff Streets (UC Irvine)
June 3, 2020 Chenyang Xu (MIT)
June 10, 2020 Yi Lai (UC Berkeley)
June 17, 2020 Ben Andrews (Australian National University)
June 24, 2020 Shiguang Ma (Nankai University)
July 1, 2020 Yuchen Liu (Yale University)
July 7, 2020 Min-Chun Hong (The University of Queensland)
July 15, 2020 Jian Song (Rutgers University)
September 8, 2020 Martin Kerin (NUI Galway)
September 23, 2020 Richard Bamler (UC Berkeley)
October 14, 2020 Chao Li (Princeton University)
October 21, 2020 Yu Yuan (University of Washington)
October 28, 2020 Aaron Naber (Northwestern University)
November 4, 2020 Carlo Scarpa (SISSA)
November 11, 2020 Keaton Naff (Columbia University)
December 16, 2020 Lei Ni (UC San Diego)
