Asymptotic Geometric Analysis is concerned with geometric and linear properties of finite dimensional objects, normed spaces and convex bodies, especially with asymptotics of their various quantitative parameters as the dimension tends to infinity. Deep geometric, probabilistic and combinatorial methods developed here are used outside the field in many areas, related to the subject of the program.

One of the main tools of the theory are concept of concentration phenomenon and large deviation inequalities. The concentration of measure is, in fact, an isomorphic form of isoperimetric problems. It was first developed inside the asymptotic geometric analysis and then became pertinent to other branches of mathematics as an efficient tool and useful concept. Some new techniques of the theory are connected with measure transportation methods and with related PDE's. The concentration phenomenon is well-known to be closely linked with combinatorics (Ramsey theory), and such links have been recently better understood in the setting of infinite-dimensional transformation groups.

The achievements of Asymptotic Geometric Analysis demonstrate new and unexpected phenomena characteristic for high dimensions. These phenomena appear in a number of domains of mathematics and adjacent domains of science dealing with functions of infinitely growing numbers of variables.

Main Directions of Research:

* Asymptotic theory of Convexity and Normed spaces
* Concentration of measure and isoperimetric inequalities, optimal transportation approach
* Applications of the concept of concentration
* Connections with transformation groups and Ramsey theory
* Geometrization of Probability
* Random matrices
* Connection with Asymptotic Combinatorics and Complexity Theory

Distinguished and Coxeter Lecturers

September 14-16, 2010
Distinguished Lecture Series:
Avi Wigderson (Institute for Advanced Study, Princeton)
Randomness, Pseudorandomness and Derandomization

September 17, 20 & 21, 2010
Coxeter Lecture Series:
Shiri Artstein-Avidan (Tel-Aviv University)

Fri., Sept 17 --3:30 pm Abstract duality, the Legendre transform and a new duality transform.
Mon., Sept 20 --3:30 pm Order isomorphisms and the fundamental theorem of affine geometry
Tues., Sept 21--3:30 pm Multiplicative transforms and characterization of the Fourier transform

Graduate Course

Isoperimetric Inequalities and Applications to Asymptotic Geometric Analysis
Instructor: Emanuel Milman

Workshops

September 13-17, 2010
Workshop on Asymptotic Geometric Analysis and Convexity
Organizers: Monika Ludwig, Vitali Milman and Nicole Tomczak-Jaegermann

Note: This Workshop will be preceeded by a Concentration period on Convexity (September 8-10, 2010) and followed by a Concentration period on Asymptotic Geometric Analysis (September 20-22, 2010)

October 12-15, 2010
Workshop on the Concentration Phenomenon, Transformation Groups and Ramsey Theory
Organizers: Eli Glasner, V. Pestov and S. Todorcevic

November 1-5, 2010
Workshop on Geometric Probability and Optimal Transportation
Organizers: B. Klartag and R. McCann

Note: This Workshop will be preceeded by a concentration period on Partial Differential Equations and Geometric Analysis (October 25-29) and followed by a concentration period on Nonlinear Dynamics and Applications (November 8-10).

Seminars

Young Researchers Seminars - Tuesdays 4-6:30 pm
Program Visitors Seminars - Wednesdays 11-12 pm & Thursdays 3:30-4:30 pm

Postdoctoral Fellows

The Thematic Program on Asymptotic Geometric Analysis is pleased to welcome the following Postdoctoral Fellows to the Program:

Fields Ontario Postdoctoral Fellows:

Deping Ye (University of Missouri-Columbia)
Samuel Coskey (Rutgers)

Fields Postdoctoral Fellows:

David Alonso (Universidad de Zaragoza) Marsden PDF
Radoslaw Adamczak (University of Warsaw)
Nikolaos Dafnis (University of Athens)
Emanuel Milman (University of Toronto)
Quentin Merigot (INRIA Sophia-Antipolis)
Peter Pivovarov (University of Alberta)

Program Visitors

We will offer support towards a visitors' program, including visiting Ph.D. students. All scientific events are open to the mathematical sciences community. Visitors who are interested in office space or funding are requested to apply to participate in the program by filling out the application form (open in early 2010). Invited visitors are offered shared office space durng the time of their visit if there is space available.
Additional support is available (pending NSF funding) to support junior US visitors to this program. Fields scientific programs are devoted to research in the mathematical sciences, and enhanced graduate and post-doctoral training opportunities. Part of the mandate of the Institute is to broaden and enlarge the community, and to encourage the participation of women and members of visible minority groups in our scientific programs.

For additional information contact thematic(PUT_AT_SIGN_HERE)fields.utoronto.ca

THEMATIC PROGRAMS

Thematic Program on Asymptotic Geometric Analysis July - December 2010

Outline of Scientific Activities