Algebra and Number Theory Seminar Fall 2017

Fridays - 2:45 p.m.
McHenry Library Room 4130
For more information please contact Professor Robert Boltje or call the Mathematics Department at 831-459-2969

September 29, 2017

No seminar

October 6, 2017

No seminar

October 13, 2017

Robert Boltje, University of California, Santa Cruz

Picard Groups of Block Algebras

We will report on joint work with Markus Linckelmann and Radha Kessar. The Picard group of a ring R is the set of isomorphism classes of (R,R)-bimodules M such that tensoring with M over R is an equivalence from the category of R-modules to itself. In the case of block algebras of finite group algebras, we describe particular subgroups of the Picard groups of blocks that are defined by requirements on the vertex of M. Interestingly, there is no example known where the weakest of these requirements is not satisfied. We also determine the Picard group completely in the case that the block has cyclic defect group.

October 20, 2017

No seminar

October 27, 2017

Joe Ferrara, University of California, Santa Cruz

A p-adic Stark Conjecture for Hecke Characters of Quadratic Fields

In the 1970's Stark made precise conjectures about the leading term of the Taylor series expansion at s=0 of Artin L-functions, refining Dirichlet's class number formula. Around the same time Barsky, Cassou-Nogues, and Deligne and Ribet for totally real fields, along with Katz for CM fields defined p-adic L-functions of ray class characters. Since then Stark-type conjectures for these p-adic L-functions have been formulated, and progress has been made in some cases. The goal of this talk is to discuss a new definition of a p-adic L-function and Stark conjecture for a mixed signature character of a real quadratic field. After stating the definition and conjecture, theoretical and numerical evidence will be discussed.

November 3, 2017

Edmund Karasiewicz, University of California, Santa Cruz

Eisenstein Series and L-functions

Automorphic forms often contain arithmetic information; for example, powers of the Jacobi theta-function encode the number of ways an integer can be represented as a sum of squares. One method of packaging this arithmetic information is in the form of an L-function; the problem of extracting this arithmetic information has become a principal problem for number theorists. We will describe some techniques that utilize Eisenstein series, particular types of automorphic forms, to prove important properties of automorphic L-functions. A particular emphasis will be placed on Eisenstein series of GL(2), GL(3), and their double covers.

November 10, 2017

No Seminar

November 17, 2017

No Seminar

November 24, 2017

Holiday - No Seminar

December 1, 2017

No Seminar

December 8, 2017

No Seminar