I will report on some recent work on multiple zeta values. I
will sketch the definition of motivic multiple zeta values, which
can be viewed as a prototype of a Galois theory for certain
transcendental numbers, and then explain how they were used...
The families of motives of the title arise from classical
one-variable hypergeometric functions. This talk will focus on the
calculation of their corresponding L-functions both in theory and
in practice. These L-functions provide a fairly wide...
A conjecture of Langlands-Rapoport predicts the structure of the
mod p points on a Shimura variety. The conjecture forms part of
Langlands' program to understand the zeta function of a Shimura
variety in terms of automorphic L-functions.
Let X a curve over F_q and G a semi-simple simply-connected
group. The initial observation is that the conjecture of Weil's
which says that the volume of the adelic quotient of G with respect
to the Tamagawa measure equals 1, is equivalent to the...
A fake projective plane is a smooth complex projective algebraic
surface whose Betti numbers are same as those of the complex
projective plane but which is not the complex projective plane. The
first fake projective plane was constructed by David...
A. Ghosh and P. Sarnak have recently initiated the study of
so-called real zeros of holomorphic Hecke cusp forms, that is zeros
on certain geodesic segments on which the cusp form (or a multiple
of it) takes real values. In the talk I'll first...
In this talk, I will present a formulation of the Gross-Zagier
formula over Shimura curves using automorphic representations with
algebraic coefficients. It is a joint work with Shou-wu Zhang and
Wei Zhang.
