Let P: ... -> C_2 -> C_1 -> P^1 be a Z_p-cover of the projective line over a finite field of characteristic p which ramifies at exactly one rational point. In this talk, we study the p-adic Newton slopes of L-functions associated to characters of the Galois group of P. It turns out that for covers P such that the genus of C_n is a quadratic polynomial in p^n for n large, the Newton slopes are uniformly distributed in the interval [0,1]. Furthermore, for a large class of such covers P, these slopes behave in an even more regular way. This is joint work with Hui June Zhu.

Let us take a couple of 2x2 matrices A and B, and consider a long product of matrices, where each multiplier is either A or B, chosen randomly. What should we expect as a typical norm of such a product? This simple question leads to a rich theory of random matrix products. We will discuss some of the classical theorems (e.g. Furstenberg Theorem), as well as the very recent results. 

We will discuss the reading for this week. If you are not on the emailing list and would like the reading list, please email Alice Silverberg.

Peer observation of teaching is an excellent way to receive concrete, fact-based feedback on what it's like in your classroom.  This spring quarter the math department will run peer observation among 1st and 2nd year grad students, and this meeting will introduce that.  It is also open to more advanced grad students.  In particular, any student eventually needing a teaching-focused letter of recommendation (which is required for almost all postdocs) is strongly encouraged to attend this session.  Our set-up will be based on Danny Mann's talk in fall quarter.