## Spring 2017 Schedule:

**February
**24: **
****
Mihran Papikian (****Pennsylvania State
University)**

Title:
Graph laplacians and Drinfeld modular curves

Abstract: The relationship
between combinatorial laplacians and automorphic
forms is an active area of current research with
applications to a variety of problems arising in
number theory, group theory, and coding theory. I
will discuss certain combinatorial laplacians
arising in the theory of Drinfeld modular curves,
and their applications to estimating congruences
between automorphic forms.

March 3: **
Joe Kramer-Miller (****University College London)**

Title:
Genus stability in ordinary p-adic towers of curves

Abstract: The topic of this talk
is genus growth in
$\backslash mathbb\; Z\_p$-towers
of curves in characteristic
$p$.
For example, by work of Katz and Mazur we know that
the genus of the
$p^n$-th
Igusa curve is given by a quadratic in
$p^n$.
This quadratic genus growth property is known as
genus stability. We show that any tower
arising from the monodromy of a family of ordinary
varieties is genus stable. This is the first
step towards the geometric Iwasawa theory program
devised by Daqing Wan.

March 10:
**Hisa-aki Kawamura (Hiroshima University)**

Title:
The semi-ordinary p-stabilization of Siegel
Eisenstein series for symplectic groups and unitary
groups

Abstract:
For each prime number p, we introduce a certain kind
of p-stabilization of holomorphic Siegel Eisenstein
series for the symplectic group GSp(2n) defined over
the field of rational numbers, and for the unitary
group U(n,n) defined over an imaginary quadratic
field such that the resulting automorphic forms are
assembled into the so-called "semi-ordinary" p-adic
analytic families, respectively. If time permits,
we’ll also show some applications of the above
result, for instance, to construct the lifting of
p-adic analytic families from GL(2) to GSp(2n) and
U(n,n).

April 21:
**Kimball Martin (University of Oklahoma)**

Title:
Atkin-Lehner signs and congruences mod 2

Abstract: In
the first part of the talk, I will explain some
things about the distribution of Atkin-Lehner signs
for modular forms fixed level and weight. In the
second part of the talk, I will explain how to prove
the existence of many congruences mod 2 within a
fixed space of modular forms, and how this is
related to the first part.

May 5: ** **** **** Catherine
Hsu (University of Oregon****)**

Title: Higher congruences between
newforms and Eisenstein series of

squarefree level

Abstract: Let $p\backslash geq\; 3$
be$$
prime. For squarefree level
$N>6$,
we use a commutative algebra result of Berger,
Klosin, and Kramer to bound the depth of
Eisenstein congruences modulo $p$
(from below) by the
$p$-adic
valuation of the numerator of $\backslash frac\{\backslash varphi(N)\}\{24\}$.
We then show that if $N$
has at least three prime factors and some
prime $p\backslash geq\; 5$
divides
$\backslash varphi(N)$,
the Eisenstein ideal is not locally principal.
We will conclude by illustrating these results
with explicit computations and give an
interesting commutative algebra application
related to Hilbert-Samuel multiplicities.

May 12: David Goldberg
(Purdue University)

Title: A survey of R-groups
and reducibility of induced representations for
reductive p-adic groups

Abstract: Parabolic
induction has played a crucial role in the
classification of reductive groups over local
fields. The techniques developed by
Knapp-Stein, Harish-Chandra, and others, for
reductive Lie groups was extended to the setting
of p-adic groups by Silberger. The
Langlands-Shahidi method shows that understanding
this aspect of the harmonic analysis on these
groups has deep arithmetic consequences,
particularly in terms of understanding local
L-functions. The theory of the Knapp-Stein
R-group, gives a combinatorial algorithm for
understanding the structure of induced
representations, and these R-groups (and their
construction on the dual side by Arthur et al)
have played a key role in trace formula methods.
We’ll give an overview of this program, including
the known results for quasi-split groups. We’ll
conclude by describing our joint work with Choiy
on inner forms, as well as developing work with
ban and Choiy on Spin groups.

May 19**: Tobias Berger
(University of Sheffield)**

Title:
Deformations
of Saito-Kurokawa type

Abstract:
I will report on work in progress with Kris Klosin
on the modularity of 4-dimensional p-adic
representations whose reductions modulo p are of
Saito-Kurokawa type. I will explain, in particular,
how this can be used in certain cases to verify
Brumer and Kramer's paramodular conjecture for
abelian surfaces over Q with a rational torsion
point of order p.