MATHEMATICS COLLOQUIUM Thursday, November 12, 2009 Kerchof Hall 317, 4:00 pm Refreshments served at 3:30 pm in the lounge Title: Presentations of Symmetric Groups (joint work with R. Guralnick, W. Kantor, A. Lubotzky ) Abstract: We study presentations of symmetric groups Sym(n) from a quantitative point of view. Our main result provides somewhat unexpected answers to the following questions: how many relations are needed to define Sym(n), and how short can these relations be? I will describe the main idea which allows us to produce presentations with a bounded number of relations (independent on n). I will also explain several tricks which further allow us to shorten the lengths of the relations and decrease their number to less than 10.
SEMINARS
Algebra Seminar - B. Parshall, Wang and Ershov http://people.virginia.edu/~mve2x/Algebra_seminar
http://www.math.virginia.edu/~zg7c/deds.htm Topic:
Recent Integral Inequalities and Applications to PDEs
Mathematical Physics Seminar - John Imbrie http://www.math.virginia.edu/mathphys/ Topic: The Exact Solution of the Two-Dimensional Ising Model Abstract: Many different methods have been designed for deriving the exact solution of the 2D Ising model. I will review in details how the combinatoric approach gives us the Onsager's formula of the free energy and, time permitting, the Wu's formula of the spin-spin correlation. This method is important since, as I will discuss in the following week's talk, it allows us to find rigorous results on Ising-like models without an exact solution.
Operator Theory/Operator Algebras Seminar - David Sherman www.people.virginia.edu/~des5e/sotoa/sotoa.html Topic:
The Cauchy Integral Formula and Composition Operators
http://www.people.virginia.edu/~mah7cd/Topology/TopologySeminar.html Topic: TBA
Seminar Regular Times and Homepages Mathematics Colloquium (Thursdays at 4:00 in Ker 317, tea in Ker 314 at 3:30)
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