Nodal Lines of Random Waves

M. Sodin
Tel Aviv University
October 26, 2010

In the talk, I will describe recent attempts to understand the mysterious and beautiful geometry of nodal lines of random spherical harmonics and of random plane waves. If time permits, I will also discuss asymptotic statistical topology of other natural polynomial-like ensembles of random functions. The talk is based on a joint work with Fedja Nazarov.

Values of L-Functions and Modular Forms

Chris Skinner
Princeton University; Member, School of Mathematics
October 25, 2010

This will be an introduction to special value formulas for L-functions and especially the uses of modular forms in establishing some of them -- beginning with the values of the Riemann zeta function at negative integers and hopefully arriving at some more recent work on the Birch-Swinnerton-Dyer formula.

Splitting of Iwasawa Modules and Leopoldt Conjecture

Jean-Pierre Wintenberger
University of Strasbourg
October 20, 2010

Let p be an odd prime number and let F be a totally real field. Let F_cyc be the cyclotomic extension of F generated by the roots of unity of order a power of p . From the maximal abelian extension of F_cyc which is unramified (resp. unramified outside auxiliary primes), we get exact sequences of Iwasawa modules. We will discuss how splitting of these exact sequences are linked to Leopoldt conjecture for F and p . (JW with C. Khare)