
THEMATIC PROGRAMS 

February 5, 2023  
Thematic
Program on Asymptotic Geometric Analysis July  December 2010
Coxeter Lecture Series

Lecture 1: Abstract
duality, the Legendre transform and a new duality transform.
Defining abstract duality as an order reversing involution, the only such transform on the class of convex functions is the Legendre transform. Restricting, however, the class to nonnegative convex functions which are pinned down to equal zero at the origin, an essentially different duality transform appears. We will describe it, prove uniqueness results, and point out geometric interpretations and consequences, for example concerning the support and the Minkowski functional for logconcave functions. Based on joint work with V. Milman Lecture 2: Order isomorphisms and the fundamental theorem
of affine geometry. Lecture 3: Multiplicative transforms and characterization
of the Fourier transform. 
For additional information contact thematic(PUT_AT_SIGN_HERE)fields.utoronto.ca