UCSB Distinguished Lectures in the Mathematical Sciences

Each UCSB Distinguished Lecturer in the Mathematical Sciences will visit our campus for about a week, and deliver two or three lectures. All department members are encouraged to attend!

Upcoming lecturers include:

 

 

Tuesday, April 26, 2011, 3:30 p.m.

South Hall 6635

(Refreshments at 3:00 p.m.)


Jeff Cheeger

Courant Institute of Mathematical Sciences, New York University

Title: Quantitative Differentiation

Abstract: The lectures will deal with the notion of quantitative differentiation and its applications. The simplest instance concerns functions $f:[0,1]\to \mathbb{R}$ with $|f'|\leq 1$. The basic assertion, which appears in work of Peter Jones from 1988, can be paraphrased as stating that in a precise quantitative sense, "$f$ is as close as one likes to being linear at most locations and scales". In the first lecture, it will be explained how the above is actually a particular case of something considerably more general. An "axiomatic" formulation is given in an appendix to a joint paper with B. Kleiner and A. Naor. This paper is discussed in the second lecture. The specific quantitative differentiation result concerns Lipschitz maps from the Heisenberg group to $L_1$. It turns out that there is an application to theoretical computer science. In the third lecture we will explain a quantitative differentiation result in riemannian geometry, which leads to curvature estimates for Kähler-Einstein manifolds off sets of small volume.

 


 

Wednesday, April 27, 2011, 3:30 p.m.

South Hall Room 6635


Jeff Cheeger

Courant Institute of Mathematical Sciences, New York University

Title: Lipschitz maps to L1

Abstract: The lectures will deal with the notion of quantitative differentiation and its applications. The simplest instance concerns functions $f:[0,1]\to \mathbb{R}$ with $|f'|\leq 1$. The basic assertion, which appears in work of Peter Jones from 1988, can be paraphrased as stating that in a precise quantitative sense, "$f$ is as close as one likes to being linear at most locations and scales". In the first lecture, it will be explained how the above is actually a particular case of something considerably more general. An "axiomatic" formulation is given in an appendix to a joint paper with B. Kleiner and A. Naor. This paper is discussed in the second lecture. The specific quantitative differentiation result concerns Lipschitz maps from the Heisenberg group to $L_1$. It turns out that there is an application to theoretical computer science. In the third lecture we will explain a quantitative differentiation result in riemannian geometry, which leads to curvature estimates for Kähler-Einstein manifolds off sets of small volume.

 


 

Thursday, April 28, 2011, 3:30 p.m.

South Hall Room 6635


Jeff Cheeger

Courant Institute of Mathematical Sciences, New York University

Title: Curvature estimates for Kähler-Einstein manifolds

Abstract: The lectures will deal with the notion of quantitative differentiation and its applications. The simplest instance concerns functions $f:[0,1]\to \mathbb{R}$ with $|f'|\leq 1$. The basic assertion, which appears in work of Peter Jones from 1988, can be paraphrased as stating that in a precise quantitative sense, "$f$ is as close as one likes to being linear at most locations and scales". In the first lecture, it will be explained how the above is actually a particular case of something considerably more general. An "axiomatic" formulation is given in an appendix to a joint paper with B. Kleiner and A. Naor. This paper is discussed in the second lecture. The specific quantitative differentiation result concerns Lipschitz maps from the Heisenberg group to $L_1$. It turns out that there is an application to theoretical computer science. In the third lecture we will explain a quantitative differentiation result in riemannian geometry, which leads to curvature estimates for Kähler-Einstein manifolds off sets of small volume.

 


 

Previous Lecturers: