**Algebra Seminar- Kwangho Choiy(Southern Illinois University Carbondale)**

The local Langlands conjecture for the p-adic inner form of Sp(4)

4:00PM, Mon Oct 12 2015, Math 250

**Analysis Seminar- Jingbo Xia (SUNY at Buffalo)**

Essential normality of submodules of the Drury-Arveson module

4:00PM, Wed Oct 14 2015, Math 250

**Algebra Seminar-James Cogdell (Ohio State University) Artin L-functions and local factors for GL(n).**

Artin introduced his non-abelian L-functions for representations of the Galois group in a series of papers in 1923--1931. He was able to define the local Euler factors for all primes and define the Artin conductor that appears in the functional equation, but the Artin root number remained mysterious. It was factored by Deligne in 1971 as part of his proof of the existence of the local epsilon-factors that appear in the functional equation of the Artin L-functions. One way to try to understand these L-functions and epsilon-factors is to find a corresponding analytic object, an automorphic form, whose L-function and epsilon-factors match the arithmetic ones. This is the content of the local Langlands correspondence. This correspondence should be robust and preserve various parallel operations on the arithmetic and analytic sides, such as taking exterior or symmetric square. In collaboration with F. Shahidi and T-L. Tsai, we have recently shown that indeed the local epsilon-factor that appear in the functional equation are preserved under these operations. The proof is an application of local/global techniques and the stability of these factors under highly ramified twists. In this talk I will attempt to explain a bit about Artin L-functions, the local Langlands correspondence, and the techniques we use in our proof.

4:00PM, Mon Oct 19 2015, Math 250

**Algebra Seminar-Mahdi Asgari (Oklahoma State University)**

4:00PM, Mon Oct 26 2015, Math 250

**Algebra Seminar- Dani Szpruch (Howard University)**

Speaker Dani Szpruch from Howard University.

4:00PM, Mon Nov 9 2015, Room 250

**Start of Fall Recess**

Wednesday, November 25, 2015