Abstract: In the last five years Bridgeland stability has revolutionized
our understanding of the geometry of moduli spaces of sheaves on surfaces,
allowing us to compute ample and effective cones and describe different
birational models. In this talk, I will survey some of my joint work with
Daniele Arcara, Aaron Bertram, Jack Huizenga and Matthew Woolf on the
birational geometry of moduli spaces of sheaves on the plane. I will
describe the ample and effective cones of these moduli spaces,

The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:H^->G^ between their dual complex groups should naturally give rise to a map r*:Rep(H)->Rep(G) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.

Abstract: Let X be a regular scheme, projective and flat over Spec Z. We
give a conjectural formula in terms of motivic cohomology, singular
cohomology and de Rham cohomology for the special value of the
zeta-function of X at any rational integer. We will explain how this
reduces to the standard formula for the residue of the Dedekind
zeta-function at s = 1.
‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts.

Abstract: Calabi conjectured that the complex Monge-Ampère equation on compact Kaehler manifolds has a unique solution. This was solved by Yau in 1978. In this talk, we present a non-archimedean version on projective Berkovich spaces. In joint work with Burgos, Jell, Künnemann and Martin, we improve a result of Boucksom, Favre and Jonsson in the equicharacteristic 0 case. We give also a result in positive equicharacteristic using test ideals.

I discuss some class of function of several elliptic variables,
this functions generalize multiple polylogarithms of D. Zagier.
I show some applications of developed formalism.
This is a joint work with F. Brown.

Abstract: In the talk I will discuss classical problems concerning the distribution
of square-full numbers and their analogues over function fields. The
results described are in the context of the ring Fq[T ] of polynomials
over a finite field Fq of q elements, in the limit q → ∞.
I will also present some recent generalization of these kind of
classical problems.
‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts.

Abstract: I will start with a motivation of what algebraic (and model-theoretic) properties
an algebraically closed field of characteristic 1 is expected to have. Then I will explain
how these properties can be obtained by the well-known in model theory Hrushovski's
construction and then formulate very precise axioms that such a field must satisfy.
The axioms have a form of statements about existence of solutions to systems
of equations in terms of a 'multi-dimansional' valuation theory and the validity

Using the endoscopic classification
of automorphic forms for unitary groups,
I will prove conjecturally sharp upper
bounds for the growth of Betti numbers
in congruence towers of complex
hyperbolic manifolds. This is
joint work with Sug Woo Shin.
‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts.
הצטרף: https://plus.google.com/hangouts/_/calendar/ODdkc2JxNmlmbjNhZ2U0ODVvb3E3...

Many of the main conjectures in Iwasawa theory can be phrased as saying
that the first Chern class of an Iwasawa module is generated by a p-adic
L-series.
In this talk I will describe how higher Chern classes pertain to the higher
codimension behavior of Iwasawa modules. I'll then describe a template
for conjectures which would link such higher Chern classes to elements
in the K-theory of Iwasawa algebras which are constructed from tuples of
Katz p-adic L-series. I will finally describe an instance in which a result of

In his investigation of modular forms of half-integral weight, Shimura established, using Hecke theory, a family of relations between eigneforms of half-integral weight k+1/2 with a given level 4N and character chi and cusp forms of weight 2k and character chi^2.
The level being subsequently determined by Niwa to be at most 2N.

We prove cases of Rietsch mirror conjecture that the quantum
connection for projective homogeneous varieties is isomorphic to the
pushforward D-module attached to Berenstein-Kazhdan geometric crystals.
The idea is to recognize the quantum connection as Galois and the
geometric crystal as automorphic. In particular we link the purity of
Berenstein-Kazhdan crystals to the Ramanujan property of certain Hecke
eigensheaves.
The isomorphism of D-modules comes from global rigidity results where a

In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields.
I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial
setting.

In this talk we present a database of rational elliptic curves with
good reduction outside certain finite sets of primes, including the
set {2, 3, 5, 7, 11}, and all sets whose product is at most 1000.
In fact this is a biproduct of a larger project, in which we construct
practical algorithms to solve S-unit, Mordell, cubic Thue, cubic
Thue--Mahler, as well as generalized Ramanujan--Nagell equations, and
to compute S-integral points on rational elliptic curves with given
Mordell--Weil basis.