Date

Speaker

Title

April 8

Mike Roth
(Queen's University)

Roth's theorem for arbitrary varieties
If X is a variety of general type defined over a number field k, then the
BombieriLang conjecture predicts that the krational points of X are not
Zariski dense. The conjecture is a prediction that a global condition on the
canonical bundle (that it is ''generically positive'') implies a global condition
about rational points...(Show Abstract)

April 15

Stefano Morra
(Fields Inst./ Univ. of Toronto)

On mod p localglobal compatibility for GL_{3} in the ordinary case
Let ρ:G_{Qp}→GL_{3}(F_{p}) be a maximally nonsplit, ordinary Galois representation.
If ρ is FontaineLafaille and sufficiently generic, the φaction on the associated
FontaineLafaille module lets us detect a local Galois invariant.
On the other hand, let π be a smooth GL_{3}(Q_{p})representation (over F_{p}). If
π verifies appropriate conditions...(Show Abstract)

April 22

Arul Shankar
(Harvard)

The average 5Selmer rank of elliptic curves
We use geometryofnumbers techniques to show that the average size of the 5Selmer group of
elliptic curves is equal to 6. From this, we deduce an upper bound on the
average rank of elliptic curves.
Then, by constructing families of elliptic curves with equidistributed root
number we show that the average rank is
less than 1. This is joint work with Manjul Bhargava.

April 29

William Casselman
(Univ. British Columbia)

Symmetric powers and the Satake transform
A classic formula of Tamagawa, following work of Hecke, relates certain Langlands Lfunctions associated to GL(n,k) groups (k padic) and some simple properties of the Satake transform for these groups, but applied to functions in the Schwartz space of the matrix algebra M(n,k).
Recent conjectures of Ngo and others suggest...(Show Abstract)

May 6

Wei Zhang
(Columbia)

Selmer groups and the divisibility of Heegner points
This talk is about a proof of Kolyvagin's conjecture in 1991
on pindivisibility of (derived) Heegner points for an ordinary prime
p > 3 with some ramification conditions, with some application to the
arithmetic of elliptic curves.

May 13

Matthew Young
(Texas A&M)

Equidistribution of Eisenstein series
The behavior of eigenfunctions of the Laplacian is a
wellstudied topic in analysis, geometry, math physics, etc. In some
arithmetical settings, such as for the modular surface, then there are
also interesting connections to number theory. In particular, the
behavior of the Eisenstein series is related to properties of the Riemann
zeta function. I will discuss some recent work showing that the
Eisenstein series equidistributes on "thin" sets, with various notions of
thin.

May 20

Daniel Le
(UChicago)

Lattices in the algebraic vectors in the cohomology of U(3) Shimura
varieties
Little is known about the padic Langlands correspondence outside
of GL_{1} and GL_{2}(Q_{p}). Assuming that it satisfies padic
localglobal compatibility, one would expect the correspondence to occur in
the completed cohomology of Shimura varieties. Though it is not known that
the result is independent of the global situation, we show that under
hypotheses the lattice in the algebraic vectors of the completed cohomology
of U(3) Shimura varieties depends only on the local Galois representation
at p.

May 27

MarcHubert Nicole
(Marseille/UCLA)

An ladic JacquetLanglands correspondence for paramodular Siegel
threefolds
T. Ibukiyama proposed, in the early ‘80s, a conjecture à la
JacquetLanglandsEichlerShimizu for spaces of Siegel modular forms for the
paramodular group K(p), where p is a prime. A concrete geometric consequence of
Ibukiyama’s conjecture is that: 1 + the dimension of the space S_{3}(K(p)) of Siegel
modular forms of weight three is equal to the number of irreducible components of
the supersingular locus of the moduli space A_{2,1} of principally polarized
abelian surfaces mod p....(Show Abstract)

June 3

Masoud Kamgarpour
(Univ. of Queensland)

Preservation of depth in local geometric Langlands program
Local Langlands program aims to establish a relationship between representations of
the Galois group of a local field and irreducible representations of the dual group.
It is expected that, under mild conditions, this correspondence preserves depths of
representations. In this talk, I will explain the geometric analogue of this
expectation, in the framework of FrenkelGaitsgory's local geometric Langlands
correspondence....(Show Abstract)
