Previous Conferences & Workshops

I will consider the asymptotic behavior of Laplacian eigenfunctions on a locally symmetric compact manifold as the volume approaches infinity. I will formulate a precise conjecture "à la Berry" and will describe some partial results obtained with...

Let M be a compact manifold with negative curvature. The Quantum Unique Ergodicity conjecture of Rudnick and Sarnak says that eigenfunctions of the Laplacian on M get equidistributed as the eigenvalue tends to infinity. A weaker version, called...

We explain the magic of the entire function $\Psi_p \in \mathbb{Z}[x] \cap \mathbb{Q}_p\{x\}$ defined by the functional equation \[x = \sum_{j=0}^{\infty} p^{-j}\Psi_p (p^{j} x)^{p^{j}}\] which satisfies $\Psi_p (\mathbb{Q}_p) \subset \mathbb{Z}_p$...

Let $E$ be a CM elliptic curve over a totally real number field $F$ and $p$ an odd ordinary prime. If the ${p^{\infty}\mbox{-}\mathrm{Selmer}}$ group of $E$ over $F$ has ${\mathbb{Z}_{p}\mbox{-}\mathrm{corank}}$ one, we show that the analytic rank...

We show that any two birational projective Calabi-Yau manifolds have isomorphic small quantum cohomology algebras after a certain change of Novikov rings. The key tool used is a version of an algebra called symplectic cohomology, which is...

I will describe recent work with Ngaiming Mok and Jacob Tsimerman giving analogues of "Ax-Schanuel" for Shimura varieties. I will sketch the role of "o-minimal structures" in the proof, in particular point counting and powerful algebraicity results...