Title: L^p bounds for spectral projectors on hyperbolic surfacesAbstract: In this talk I will present L^p boundedness results for spectral projectors on hyperbolic surfaces, focusing on the case where the spectral window has small width. I will show that the negative curvature assumption leads to improvements over the universal bounds of C. Sogge, thus illustrating […]
Title: Selmer groups, p-adic L-functions and Euler Systems: A new Framework Abstract: Selmer groups are key invariants attached to p-adic Galois representations. The Bloch—Kato conjecture predicts a precise relationship between the size of certain Selmer groups and the leading term of the L-function of the Galois representation under consideration. In particular, when the L-function does […]
Title: Singularity formation in incompressible fluids. Abstract: I will discuss a recent example of singularity formation in the 3d Euler equation. This is based on work joint with Federico Pasqualotto.
Title: TBA
Title: Bipartite Euler SystemsAbstract: I will give an example-based introduction to bipartite Euler Systems, starting with the construction in the case of Heegner points by Bertolini--Darmon from the early 2000's. I'll discuss the main obstacles in extending such methods to other settings, and survey some of the new constructions we have seen in the last […]