2007 Chern Lectures

The 2007 Chern Lectures will be delivered by Vladimir Igorevich Arnold on April 2, 4 and 6, 2007.

Department of Mathematics, University of California, Berkeley, presents

The 2007 Chern Lectures
Vladimir Igorevich Arnold
Steklov Mathematical Institute
Moscow, Russia

Talk 1: Statistics and topology of Morse functions
April 2, 10 Evans, 4:00-5:00pm

On the 2-sphere, there is exactly 17746 topologically different Morse functions with 4 saddles. This result, based on the combinatorics of random graphs, was obtained only a couple of years ago (in the process of study of Hilbert's 16th problem in real algebraic geometry on the topological classification of polynomials).

Last year L. Nicolaescu (University of Notre Dame) proved (using methods going back to conformal field theory and the physics theory of mirror symmentry) a conjecture of Arnold that the number of Morse functions with T saddles on the 2-sphere grows as T to the power 2T.

The talk will be about this research and about its analogues in the theory of smooth fucntions on other manifolds, e.g. for functions on the torus, and for trigonometric polynomials with a fixed Newton polyhedron of a given affine Coxeter group.

Talk 2: Complexity of finite sequences of zeros and ones
April 4, 50 Birge, 4:00-5:00pm

Talk 3: Statistics of Young diagrams of random permutations, and of periodic orbits of dynamical systems
April 6, 10 Evans, 4:00-5:00pm

Reception in 1015 Evans Hall following the April 4 lecture.