School of Mathematics

Taking the Hecke algebra to its limits

Raphael Steiner
Member, School of Mathematics
September 12, 2019
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 for higher moments may be derived. We give applications to the sup-norm and fourth-norm of holomorphic Hecke eigenforms as well as Hecke-Maass forms on and furthermore outline future work on higher moments of periods and quantum variance. This is joint work with Ilya Khayutin.

Symmetries of Cosmological Cauchy Horizons with Non-Closed Orbits

Jared Speck
June 13, 2019
I will describe my recent works, some joint with M.\,Disconzi and J.\,Luk, on the compressible Euler equations and their relativistic analog. The works concern solutions with non-vanishing vorticity and entropy, under any equation of state.
The starting point is our new formulations of the equations exhibiting miraculous geo-analytic structures, including