# School of Mathematics

## Open Gromov-Witten theory of $(\mathbb{CP}^1,\mathbb{RP}^1)$ in all genera and Gromov-Witten Hurwitz correspondence

In joint work with Buryak, Pandharipande and Tessler (in preparation), we define equivariant stationary descendent integrals on the moduli of stable maps from surfaces with boundary to $(\mathbb{CP}^1,\mathbb{RP}^1)$. For stable maps of the disk, the definition is geometric and we prove a fixed-point formula involving contributions from all the corner strata. We use this fixed-point formula to give a closed formula for the integrals in this case.

## Locally symmetric spaces: $p$-adic aspects

## Nonuniqueness of weak solutions to the Navier-Stokes equation

## Lattices: from geometry to cryptography

## Shimura curves and new abc bounds

## Geometric complexity theory from a combinatorial viewpoint

## Automorphic forms and motivic cohomology III

In the lectures I will formulate a conjecture asserting that there is a hidden action of certain motivic cohomology groups on the cohomology of arithmetic groups. One can construct this action, tensored with $\mathbb C$, using differential forms. Also one can construct it, tensored with $\mathbb Q_p$, by using a derived version of the Hecke algebra (or a derived version of the Galois deformation rings).

## Locally testable and locally correctable codes approaching the Gilbert-Varshamov bound

## Everything you wanted to know about machine learning but didn't know whom to ask

This talk is going to be an extended and more technical version of my brief public lecture https://www.ias.edu/ideas/2017/arora-zemel-machine-learning

I will present some of the basic ideas of machine learning, focusing on the mathematical formulations. Then I will take audience questions.