Department of Mathematics

March 8-11, 2008

8:30-9:00 Snacks and Registration

9:00-9:30 Matt Young (Texas A&M University)

"Mean values with cubic characters"

9:50-10:20 Eduardo Duenez (UT-San Antonio)

"Low critical zeros of modular (and automorphic) L-functions"

Abstract: We discuss two two instances of the interplay between the statistics of
low-lying zeros of L-functions and properties of the associated modular
(or automorphic) forms. The first (with SJ Miller) explains the efect on
the zero statistics of Rankin-Selberg convolution of the L-functions. The
second (in progress with DK Huynh, JP Keating, SJ Miller, NC Snaith) hints
at a connection between central zero repulsion and excess rank in families
of elliptic curves. In both cases random matrix theory ideas play an
important motivational role

10:40-11:10 Daniel Garbin (CUNY Graduate Center)

"Spectral convergence of
elliptically degenerating Riemann surfaces"

11:30-12:00 Andrew Knightly (University of Maine)

"Averages of modular L-values via trace formula"

** Lunch ** 12:00-2:00

2:00-2:40 Cris Poor and Dave Yeun (Fordham University and Lakeforest College)

"Paramodular Cusp Forms and Abelian Surfaces"

3:00-3:20 Olav Richter (University of North Texas)

"Congruences of Jacobi forms"

3:40-4:10 Kimberly Hopkins (UT-Austin)

"Higher weight Heegner points"

4:30-5:30 Panel Discussion: Where is research on Automorphic Forms Heading?

8:30-9:00 Snacks

9:00-9:50 Kathrin Bringmann (University of Minnesota)

"Weak Maass forms, mock theta functions, and applications"

Abstract:
The modularity of the partition generating function has many
important consequences, for example asymptotics and congruences for p
(n).
Recently it became clear that the rank, a partition statistic
introduced by Dyson, is related to weak Maass forms,
a class of functions which are related to modular forms.
I want to speak about some of the applications and also discuss
higher weight analogues.

10:10-10:30 Jenny Fuselier (US Military Academy)

"Traces of Hecke operators in level 1 and hypergeometric functions over
F_p"

10:50-11:10 Matijia Kazalicki (UW-Madison)

"Zeros of certain Drinfeld modular functions"

11:20-12:00 Panel Discussion: How to start and maintain mathematical collaboration.

** Lunch Break ** 12:00-2:00

2:00-2:40 Richard Hill (University College London/University of Bristol)

"Emerton p-adic Banach spaces"

2:50-3:10 Xian-Jin Li (Brigham Young University)

"A transformation of Hankel type on the field of $p$-adic numbers"

3:30-4:00 Wissam Raji (Temple University)

"Eichler Cohomology of Generalized
Modular Forms"

4:15-4:55 Joel Mohler (Lehigh University)

"Multiple Dirchlet series over the rational function field"

5:10-5:30 Nathan Jones (University of Montreal)

"A refined version of the Lang-Trotter conjecture"

6:00- 9:00 Conference Pizza Party

8:30-9:00 Snacks

9:00-9:40 Tomoyoshi Ibukiyama (Osaka University)

"Dimensions of Siegel modular forms of small weight"

10:00-10:20 Nathan Ryan (Bucknell University)

"Expirements with genus 2 siegel modular forms"

10:40-11:10 Paul Jenkins (UCLA)

"Integral traces of singular values of Maass forms"

11:25-12:00 Rob Rhodes (UW-Madison)

"Differential Operators, Weak Maass Forms,
and Rationality"

** Monday Afternoon is Free **

8:30-9:00 Snacks

9:00-9:40 Mahesh Agrawal (McMaster University)

"p-adic L-functions for GSp(4)x GL(2)"

Abstract: Let p be an odd prime. In this talk we will construct a p-adic analog of
a degree eight L-function L(s, F×f) where F is an ordinary holomorphic
degree 2 Siegel eigen cusp form of level a power of p and f is an
ordinary eigen cusp form of level a power of p.
Our method makes use of the work of M. Furusawa which gives an integral
representation for this L-function. By suitably interpreting this integral
representation in the context of inner products of automorphic forms, we
show that it p-adically interpolates the L-values as the forms F and f
vary in ordinary families (with the weights varying p-adically). This
interpolation is carried out by constructing an Eisenstein measure on a
higher-rank unitary group and exploiting a pull-back formula of P. Garrett
and G. Shimura.

10:00-10:30 Tomonori Moriyama (Osaka University)

"Rankin-Selberg convolutions for $GSp(2)\times GL(2)$
: archimedean theory and applications"

10:50-11:10 Keith Oullete (UCLA)

"On the Fourier inversion formula for reductive groups"

We demonstrate a new proof of the Fourier inversion formula for the continuous spectrum
in L2(SL2(Z)\SL2(R)/SO2(R)). Although this proof assumes the meromorphic continuation of the Maass-
Eisenstein series, it avoids a contour shift that increases in complexity when generalizing to reductive groups
of higher rank.

11:30-12:00 Frank Thorne (UW-Madison)

"Bounded Gaps between Products of Primes with Applications to Elliptic Curves
and Ideal Class Groups"

Abstract: In recent work, Goldston, Pintz, and Yildirim proved that
$\liminf (p_{n + 1} - p_n) / \log p_n = 0$. (Here $p_n$ denotes
the nth prime.) In follow-up work with S. Graham, they also proved the
existence of bounded gaps between products of two primes.
Generalizing their work, we will present a similar bound for products of $r$
primes, for any $r \geq 2$, which covers the case when these primes are
restricted to any Chebotarev set. As a consequence, we will obtain "bounded
gaps" results concerning class numbers, Fourier coefficients of modular
forms, and ranks of elliptic curves.

** Lunch Break ** 12:00-2:00

2:00-2:30 Lloyd Kilford (University of Bristol)

"Approximating the action of the U_p operator on overconvergent
modular forms"

2:50-3:20 Ahmad El-Guindy (Texas A&M University)

"Rankin-Cohen brackets for classical and Drinfeld modular forms"

3:40-4:00 Ken McMurdy (Ramapo College)

"Explicit Verification of a Theorem of Shimura"

4:20-4:50 John Leo (UCLA)

"Fourier Coefficients of Triangle Functions"

Back to the workshop's home page

Last modified on Feb 27, 2008