Algebra Seminar- Anna Haensch , Duquesne University
"Kneser-Hecke operators for quaternary codes”
4:00PM, Mon Oct 5 2015, Math 250
There is a well known correspondence between lattices and codes via the classical “construction A.” With this, the weight enumerator for codes corresponds to the theta series for lattices, where one counts the number of codewords by composition, and the other counts the number of vectors in a lattice of a certain length. In this talk, we will explore how some of the attendant machinery of theta series are born out in this correspondence. In particular, we will consider the Kneser-Hecke operator, a code theoretic analogue of the classical Hecke operator.
Analysis Seminar- Eren Mehmet Kiral (Texas A&M University)
The Voronoi formula and double Dirichlet series
4:00PM, Wed Oct 7 2015, Math 250
A Voronoi formula is an identity where on one side, there is a weighted sum of Fourier coefficients of an automorphic form twisted by additive characters, and on the other side one has a dual sum where the twist is perhaps by more complicated exponential sums. It is a very versatile tool in analytic studies of L-functions. In joint work with Fan Zhou we come up with a proof of the identity for L-functions of degree N. The proof involves an identity of a double Dirichlet series which in turn yields the desired equality for a single Dirichlet coefficient. The proof is robust and applies to L-functions which are not yet proven to come from automorphic forms, such as Rankin-Selberg L-functions.
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
In this talk, we will discuss the local Langlands conjecture for the non quasi-split inner form Sp(1,1) of Sp(4) over a p-adic field of characteristic zero, studying the restriction of the the local Langlands correspondence for the non quasi-split inner form GSp(1,1) of GSp(4), established earlier by Gan and Tantono.
After a quick tour of some backgrounds and related work, we will construct L-packets for Sp(1,1), study their internal structure, and explain a new phenomenon arising when two distinct members in an L-packet of GSp(1,1) are restricted to Sp(1,1).
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)
4:00PM, Mon Oct 19 2015, Math 250
Algebra Seminar-Mahdi Asgari (Oklahoma State University)
4:00PM, Mon Oct 26 2015, Math 250