# Princeton University

## Abelian varieties with maximal Galois action on their torsion points

Abstract:

Associated to an abelian variety A/K is a Galois representation which describes the action of the absolute Galois group of K on the torsion points of A. In this talk, we shall describe how large the image of this representation can be (in terms of a number field K and the dimension of A). We achieve this by considering abelian varieties in families and then using a special variant of Hilbert's irreducibility theorem. Some results of Serre on the mod ell Galois image will also be reviewed. (This is joint work with David Zureick-Brown)

## Proof of a 35 Year Old Conjecture for the Entropy of SU(2) Coherent States, and its Generalization.

## Towards Weak p-Adic Langlands for GL(n)

## Near-Linear Time Approximation Algorithm for Balanced Separator

The goal of the Balanced Separator problem is to find a balanced cut in a given graph G(V,E), while minimizing the number of edges that cross the cut. It is a fundamental problem with applications in clustering, image segmentation, community detection, and as a primitive for divide-and-conquer on graphs.

## Formation of Singularities in Fluid Interfaces

The interface between water and vacuum (governed by the "water wave equation"), and the interface between oil and water in sand (governed by the "Muskat equation") can develop singularities in finite time. Joint work with A. Castro, D. Cordoba, F. Gancedo, J. Gomez and M. Lopez.

## Lattices, Hecke Operators, and the Well-Rounded Retract

## The Search for Natural Quasicrystals

## Joint IAS-PU Symplectic Geometry Seminar: Symplectic Inverse Spectral Theory in the Semiclassical Regime for Toric Systems . . . and Beyond

## Orientability and Open Gromov-Witten Invariants

I will first discuss the orientability of the moduli spaces of J-holomorphic maps with Lagrangian boundary conditions. It is known that these spaces are not always orientable and I will explain what the obstruction depends on. Then, in the presence of an anti-symplectic involution on the target, I will give a construction of open Gromov-Witten disk invariants. This is a generalization to higher dimensions of the works of Cho and Solomon, and is related to the invariants defined by Welschinger