Abstract

In his recent lectures at IPM, Freydoun Rezakhanlou presented a reformulation of a well-known combinatorial problem about the permutation group as a "toy" problem in interacting particle systems or statistical physics and proposed a partial solution along the lines of the theory of random point processes and the Hamilton-Jacobi equation. In this lecture I begin with the same combinatorial problem, relate it to the notions of Young diagrams and tableaux and show how these combinatorial concepts together with considerations from group theory and analysis can lead to deep results. In the process I will also have the opportunity to explain how Young diagrams naturally emerge in some other areas of mathematics.



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