JHU Number Theory Seminar, Fall 2004

Abstract of Talks

Sep. 15, 4:30pm--5:30pm

Ramin Takloo-Bighash, The pull back of the Bessel functional via theta correspondence
In this talk, we explain some recent work on applications of global methods based on the theta correspondence for the dual reductive pair (GO(2,2), GSp(4)) to the representation theory of GSp(4) over a real field.

Sep. 29, 4:30pm--5:30pm

Dihua Jiang, On nonvanishing of the central value of the Rankin-Selberg L-functions
We characterize the nonvanishing of the central value of the Rankin-Selberg L-functions in terms of periods over classical groups. Some previous lower rank cases and the relation to the Gross-Prasad conjecture will be discussed along the way. The proof uses the recent work of Langlands functorial transfers from the classical groups to the general linear groups and the related work by Cogdell, Kim, Piatetski-Shapiro, and Shahidi, by Ginzburg, Rallis and Sourdy, and by Jiang and Soudry.

Oct. 27, 4:30pm--5:30pm

Kimball Martin, Artin's conjecture in four dimensions
Artin conjectured that the L-functions of Galois representations are entire (excluding the zeta functions). This would follow from Langlands' conjecture that Galois representations can associated to automorphic forms. I will discuss what is known about the above conjectures for four-dimensional Galois representations with solvable image. I will use the exterior square map from GL(4) to GL(6) along with base change on GL(4) to deduce certain cases.

Nov. 3, 4:30pm--5:30pm

Lawrence Washington, Visibility of ideal classes
There are many analogies between number fields and elliptic curves. We'll discuss some of these and then concentrate on ideal class groups and Shafarevich-Tate groups. Recently, Cremona, Mazur, and others have investigated a phenomenon called visibility for Shafarevich-Tate groups of elliptic curves. We'll discuss numerical results for the analogue for number fields and the corresponding predictions for the elliptic curve case.

Nov. 17, 4:30pm--5:30pm

Michael Rubinstein, L-functions and random matrix: theorems, Conjectuers, Algorithms, and Experiments
I'll discuss the connection between L-functions and random matrix theory.