Date & Time: Wednesday, March 18, 2015, 15:00-16:00.
Venue: Ramanujan Hall
Speaker: Murali Srinivasan, IIT Bombay
Title: Counting Using Commutation Relations
Abstract: This talk, meant for a general audience, is intended to be an introduction to the beauties and pleasures of enumerative combinatorics. A basic, and by now classical, discovery in combinatorics, due to Fomin and Stanley (independently), is that the commutation relations satisfied by the up-down operators on certain graded posets (= partially ordered sets) occurring in nature can be used to count combinatorial structures on the level sets of these posets. We shall be concerned with the Weyl commutation relation and with a q-analog of the sl(2,C) commutation relation. The first leads to counting standard Young tableaux and the second leads to counting spanning trees. Asking for combinatorial proofs of the resulting formulae leads to the famous Robinson-Schensted-Knuth bijection in the first case and is open in the second case.
The talk really is elementary, requiring nothing more than MA 401, our first course in linear algebra. Everybody, from M. Sc. I year students up, is encouraged to attend. A beautiful source for the first part of the talk is the book Algebraic Combinatorics: Walks, Trees, Tableaux, and more by R. Stanley (free download on his home page).