Startseite

Abstracts for Number theory lunch seminar

Alternatively have a look at the program.

Points on Quadratic Twists of the Classical Modular Curve

Posted in
Speaker: 
Ekin Ozman
Zugehörigkeit: 
U of Wisconsin-Madison/MPI
Datum: 
Mit, 2011-05-11 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

In this talk, we will give results on be the quadratic twist of the
modular curve X_0(N) through the Atkin-Lehner involution w_N and a
quadratic extension K/Q. Given (N,d,p) we give necessary and
sufficient conditions for the existence of a Q_p-rational point on the
twisted curve when (N,d)=1. The main result yields a population of
curves which have local points everywhere but no points over Q; in
several cases we show that this obstruction to the Hasse Principle is
explained by the Brauer-Manin obstruction. If time permits, we will

Special values of automorphic L-functions for GL(2n)

Posted in
Speaker: 
Anantharam Raghuram
Zugehörigkeit: 
Oklahoma St. U/MPI
Datum: 
Mit, 2011-05-18 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

I will begin my talk with Shimura's theorem on the critical values of the standard L-function attached to a holomorphic Hilbert modular form. Then, I will recast Shimura's theorem into a more representation-theoretic context by talking about the critical values of L-functions attached to cohomological cuspidal automorphic
representations for GL(2) over a totally real number field F. The second part of my talk will be about my
recent joint work with Harald Grobner concerning the critical values of L-functions attached to

Galois representations associated to holomorphic limits of discrete series

Posted in
Speaker: 
Wushi Goldring
Zugehörigkeit: 
IHES
Datum: 
Mit, 2011-06-01 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We attach Galois representations to automorphic representations on unitary groups whose weight
(=component at infinity) is a holomorphic limit of discrete series. The main innovation is a new
construction of congruences, using the Hasse Invariant, which avoids q-expansions and so is
applicable in much greater generality than previous methods. Our result is a natural
generalization of the classical Deligne-Serre Theorem on weight one modular forms and
work of Taylor on GSp(4).

 

Point count statistics for families of curves over finite fields

Posted in
Speaker: 
Par Kurlberg
Zugehörigkeit: 
KTH, Stockholm
Datum: 
Mit, 2011-06-15 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We investigate the distribution of the number of $F_p$-points of curves in various families,
where $F_p$ is the finite field with $p$ elements.  If we consider a family of curves having
fixed genus $g$ and let $p$ tend to infinity the situation is fairly well understood -
the distribution of the point count fluctuations are given by generalized Sato-Tate distributions,
which in turn is closely related to random matrix theory.  On the other hand, if $p$ is fixed

Cohomology of Bianchi Groups and Arithmetic

Posted in
Speaker: 
Mehmet Haluk Sengun
Zugehörigkeit: 
U. Duisburg-Essen
Datum: 
Mit, 2011-06-15 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Bianchi groups are groups of the form SL(2,R) where R is the ring of an imaginary quadratic field.
'They arise naturally in the study of hyperbolic 3-manifolds and of certain generalizations of the classical modular forms (called Bianchi modular forms) for which they assume the role of the classical modular
group SL(2,Z).

After giving the necessary background, I will start with a  discussion of the problem of
understanding the behavior of the dimensions of the cohomology of Bianchi groups and
their congruence subgroups. 

Arthur's trace formula and residues of Dedekind zeta functions

Posted in
Speaker: 
Jasmin Matz
Zugehörigkeit: 
Düsseldorf
Datum: 
Mit, 2011-07-06 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Arthur's trace formula for a reductive group G is an important tool in
number theory. We shall introduce a large natural class of non-compactly
supported test functions for which there is an absolutely convergent
expansion of the spectral side of the trace formula by a recent result of
Finis-Lapid-Müller, and for the geometric side for GL(2) by work of
Finis-Lapid. This allows us to use particular test functions for GL(2) to
recover classical results on the asymptotic behaviour of mean values of
residues of Dedekind zeta functions of quadratic fields. We can find an

$L$-series of elliptic curves and Mahler measures

Posted in
Speaker: 
Wadim Zudilin
Zugehörigkeit: 
U of Newcastle, Australia/MPI
Datum: 
Mit, 2011-07-13 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

For a 2-variate Laurent polynomial $P(x,y)$ the (logarithmic)
Mahler measure is an arithmetic mean of $\log|P|$ on the
torus $|x|=|y|=1$ in $\mathbb C^2$. Famous conjectures due
to Boyd express the Mahler measures of polynomials
$P=x+1/x+y+1/y+c$, $(1+x)(1+y)(x+y)-cxy$, and $x^3+y^3+1-cxy$
in terms of the $L$-series $L(E,2)$ of the elliptic curve $E:P(x,y)=0$.
In my talk I will overview the results and methods of our recent
work with Mat Rogers towards Boyd's conjectural evaluations.
 

Modularity of residually reducible Galois representations

Posted in
Speaker: 
Kris Klosin
Datum: 
Mit, 2011-07-20 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We will present a new modularity result for residually reducible Galois
representations of imaginary quadratic fields. We will discuss the method
of the proof and its possible extension that would allow one to prove R=T
theorems in analogous higher-dimensional situations. This is joint work
with T. Berger.
 

Crystalline Galois representations in families and their applications

Posted in
Speaker: 
Hui June Zhu
Zugehörigkeit: 
SUNY at Buffalo / MPIM
Datum: 
Mit, 2011-07-27 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We will discuss our recent results in
constructing crystalline Galois representations in families
of G_K for unramified K over the p-adic rational numbers,
and in 2-dimensional cases their applications in
Iwasawa theory and Galois deformations.

Gamma products and eigenvectors of Cartan matrices.

Posted in
Speaker: 
Vadim Schechtman
Zugehörigkeit: 
Université Paul Sabatier
Datum: 
Mit, 2011-07-27 16:00 - 17:00
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We propose a formula expressing the Perron - Frobenius
eigenvector of a Cartan matrix
in terms of products of  Gamma values
extended over the positive roots of the
corresponding root system.

This is a joint work with V.Cohen-Aptel.

 

... back to parent event

© MPI f. Mathematik, Bonn Impressum
-A A +A