April 11 
Alina Bucur (UCSD) TBA. 
April 18 
Hadi Hedayatzadeh (Caltech) Using
results of Drinfeld and Taguchi, we establish an equivalence of
categories between the category of "Drinfeld displays" (objects to be
introduced) and the category of πdivisible modules. We define tensor
products of πdivisible modules and using the above equivalence, we
prove that the tensor products of π divisible modules over locally
Noetherian base schemes exist and commute with base change. If time
permits, we will show how this will provide tensor products of
LubinTate groups and formal Drinfeld modules. 
April 25 
NO SEMINAR 
May 2 
Veronika Ertl (University of Utah) For a proper smooth variety over a perfect field of characteristic p,
crystalline cohomology is a good integral model for rigid cohomology and
crystalline Chern classes are integral classes which are rationally
compatible with the rigid ones. The overconvergent de RhamWitt complex
introduced by Davis, Langer and Zink provides an integral padic
cohomology theory for smooth varieties designed to be compatible with
rigid cohomology in the quasiprojective case.
The goal of this talk is to describe the construction of integral Chern
classes for smooth varieties rationally compatible with rigid Chern
classes using the overconvergent complex. 
34pm 
Rudy Perkins (Ohio State University) Building on the work which will appear in my thesis and certain formalism introduced in F. Pellarin's paper Values of certain Lseries in positive characteristic, I will introduce a family arising from the Carlitz module in the ring of twisted power series over the ring K
of rational functions in one indeterminate with coefficients in a
finite field. I will describe how this family gives rise to both the
explicit calculation of the rational functions appearing (inexplicitly)
in Pellarin's main result in the paper above and also to certain Krelations between Thakur's multizeta values originally introduced in his book Function Field Arithmetic. This is a joint work with F. Pellarin. 
May 9 
Cristian Popescu (UCSD) I
will discuss an explicit Iwasawa theoretic construction of Tate (exact)
sequences and give some of its applications to various conjectures on
special values of Artin Lfunctions. This is based on joint work with
Greither and Banaszak. 
May 16 
David Helm (The University of Texas at Austin) We describe joint work (with David BenZvi and David Nadler) that
constructs an equivalence between the derived category of smooth
representations of GL_{n}(Q_{p}) and a certain category of coherent sheaves
on the moduli stack of Langlands parameters for GL_{n}. The proof of this
equivalence is essentially a reinterpretation of Ktheoretic results of
Kazhdan and Lusztig via derived algebraic geometry. We will also discuss
(conjectural) extensions of this work to other quasisplit groups, and
to the modular representation theory of GL_{n}. 
34pm 
Liang Xiao (UC Irvine) I will report on an ongoing joint project with David Helm
and Yichao Tian. Let p be a prime unramified in a totally real field F. The GorenOort strata are defined by the vanishing locus of the
partial Hasse invariants; they furnish an analog of the stratification
of modular curves mod p by the ordinary locus and the supersingular
locus. We give an explicit global description of the GorenOort
stratification of the special fiber of the Hilbert modular variety for
F. An interesting application of this result is that, when p is inert
of even degree, certain generalizations of the strata considered by
GorenOort contribute nontrivially as Tate cycles to the cohomology
of the special fiber of the Hilbert modular varieties. Under some mild
conditions, they generate all the Tate cycles.

May 23 
Fucheng Tan (Michigan State University) I will explain how to prove the BreuilMezard conjecture for
split (nonscalar) residual representations by local methods. Combined
with the cases previously proved by Kisin and Paskunas, this completes
the proof of the conjecture for GL_{2}(Q_{p}). As an application, we can prove
the FontaineMazur conjecture in the cases that the global residual
representation restricts to the decomposition group at p as an extension
of the trivial character by the mod p cyclotomic character. These are
the cases complementary to Kisin's. This is a joint work with Yongquan Hu. 
May 30 
Shahed Sharif (CSU San Marcos) Let Z be a variety and A an elliptic curve over the function field
of Z. I. Dolgachev and M. Gross define the geometric
ShafarevichTate group of A over Z to classify the set of
isomorphism classes of principal homogeneous spaces for A which are
locally trivial in the étale topology. In joint work with Chad Schoen,
we describe how to compute the ShafarevichTate group when A is the
generic fiber of a class of elliptic threefolds and Z is the base. We
also obtain results on the Brauer groups of such threefolds. 
June 6 
NO SEMINAR 

