Short Courses on Representation Theory and Applications

(Satellite event of the 11th Conference of the International Linear Algebra Society)

July 15-16, 2004
Department of Mathematics
University of Coimbra
Coimbra, Portugal

Persi Diaconis (Stanford University)

Applications of Representation Theory

Arun Ram (University of Wisconsin, Madison)

Crystals for Representations


Room 2.4  Thursday
 July 15
 10:00 - 11:00 Persi Diaconis
11:00 - 11:30 break
11:30 - 12:30 Arun Ram
Room 2.4   Friday
 July 16
 9:00 - 10:00 Persi Diaconis
10:00 - 11:00 Arun Ram


PERSI DIACONIS (Stanford University)

While representation theory is often developed as cutting edge pure mathematics, it also has many applications. Some of these are to other areas of mathematics (EG Group Theory or number theory). In these lectures I will venture further a field, to applied probability and statistics.
Lecture 1: The Mathematics of Shuffling Cards. How many random transpositions does it take to mix up 52 cards? I will show how character theory gives sharp answers to such questions.
Lecture 2: Applications. As a follow up to the first talk, I will show how the results apply to virtually any generating set (comparison theory) and then to problems in statistical physics (Bernoulli-Laplace urn) biology (phylogenetic trees) and chemistry (coagulation-fragmentation).


ARUM RAM (University of Wisconsin Madison)

One of the most beautiful confluences of combinatorics and representation theory is the theory of crystals: combinatorial models for the internal structure of representations of semisimpleLie algebras and Lie groups. In the first talk I will introduce crystals combinatorially--no backgroundis needed for this, only a willingness to watch me draw pictures. In the second talk I will explain why the crystals are so powerful for representation theory. In other words, the first talk will be an introduction to the Littelmann path model, the tableaux model and the Lenart-Postnikov model, and the second talk will focus on applications: the Weyl character formula, the Demazure character formula, the Littlewood-Richardson rule, and the K-theory of the flag variety.

If you are interested in attending please send an email to . Enrolment is free.