High-Dimensional Geometric Analysis

Alexander Litvak (University of Alberta) , Vladyslav Yaskin (University of Alberta)

Jan 1, 2022 — Apr 30, 2022

About the course

Asymptotic Geometric Analysis (AGA) lies at the border between geometry and analysis stemming from the study of geometric properties of finite dimensional normed spaces, especially the characteristic behavior that emerges when the dimension is suitably large or tends to infinity. Time permitting we plan to cover Banach-Mazur distance between convex bodies; John’s theorem; Dvoretsky’s theorem; properties of sections and projections of convex bodies; $MM^*$-estimate; M-ellipsoids, volumetric, entropic, and probabilistic methods for finite-dimensional convex bodies. We will also discuss methods of Fourier analysis in convex geometry. The idea of this approach is to express certain geometric quantities (such as sections or projections of convex bodies) in terms of the Fourier transform and then apply methods of harmonic analysis to solve geometric problems. In particular, we will talk about the following topics: the Fourier transform and sections of convex bodies; the Busemann-Petty problem; the Fourier transform and projections of convex bodies; Shephard’s problem; extremal sections of $l_p$-balls.


This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
High-Dimensional Geometric Analysis
Jan 1, 2022 — Apr 30, 2022
Course Number
Math 617 - Topics in Functional Analysis
Section Number
Section Code


For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details