## O-minimality and Ax-Schanuel properties

This lecture will describe the historical context and some key properties of o-minimality. It will then describe certain results in functional transcendence, generalizing the classical results on exponentiation due to Ax, and sketch how they can be proved.

## Small-Set Expansion on the Grassmann Graph.

This talk is mainly concerned with the investigation of small set expansion on the Grassmann Graphs, a study that was motivated by recent applications to Probabilistically Checkable Proofs and hardness of approximation.

## Point-counting and diophantine applications

This introductory lecture will describe results about counting rational points on certain non-algebraic sets and sketch how they can be used to attack certain problems in diophantine geometry and functional transcendence.

## Existence of infinitely many minimal hypersurfaces in closed manifolds

## New Results in Tests of Gravity with Radio Pulsars

We are living in a golden era for testing gravitational physics with precision experiments. This talk will present new results using a variety of tests with radio pulsars. These results will be placed in context of other experiments (including LIGO, EHT etc), and I will demonstrate how pulsars continue to provide unique constraints on gravity and fundamental physics in general, and how they complement other methods.

## Approximating the edit distance to within a constant factor in truly subquadratic time.

## New and old results in the classical theory of minimal and constant mean curvature surfaces in Euclidean 3-space R^3

## Index Theory and Flexibility in Positive Scalar Curve Geometry

## Stability of the Positive Mass Thm