Joint IAS/PU Number Theory

Let G be a real semi-simple Lie group with an irreducible unitary representation \pi. The non-temperedness of \pi is measured by the parameter p(\pi) which is defined as the infimum of p\geq 2 such that \pi has matrix coefficients in L^p(G). Sarnak...

We will discuss the problem of constructing and characterizing uniquely, integral models of Shimura varieties over some primes where non-smooth reduction is expected.

Some 25 years ago, as announced at a previous version of this seminar, Vaughan and the speaker obtained asymptotic upper and lower bounds for the number of non-trivial integral points on the Segre cubic $$x_1^3+...+x_6^3=x_1+...+x_6=0$$ with naive...

This talk is about qualitative properties of the underlying scheme of Rapoport-Zink formal moduli spaces of p-divisible groups, resp. Shtukas. We single out those cases when the dimension of this underlying scheme is zero, resp. those where the...

The stacky approach was originated by Bhatt and Lurie. (But the possible mistakes in my talk are mine.)

Let X be a scheme over F_p. Many years ago Grothendieck and Berthelot defined the notion of crystal on X; moreover, they defined the notion of...

In their seminal work from the 80’s, Lubotzky, Phillips and Sarnak gave explicit constructions of topological generators for PU(2) with optimal covering properties. In this talk I will describe some recent works that extend the construction of LPS...

We parametrise elements in the full Hecke algebra in a way such that the parametrisation represents a generic automorphic form. By convolving, we then arrive at pre-trace formulas which are modular in three variables. From here, various identities...