## Some things you need to know about machine learning but didn't know whom to ask (the grad school version)

## Concentration inequalities for linear cocycles and their applications to problems in dynamics and mathematical physics

Given a measure preserving dynamical system, a real-valued observable determines a random process (by composing the observable with the iterates of the transformation). An important topic in ergodic theory is the study of the statistical properties of the corresponding sum process.

## Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound

I will show an explicit construction of a binary error correcting code with relative distance $\frac{1-\epsilon}{2}$ and relative rate $\epsilon^{2+o(1)}$. This comes close to the Gilbert-Varshamov bound that shows such codes with rate $\epsilon^2$ exist, and theLP lower bound that shows rate $\frac{\epsilon^2}{\log \frac{1}{\epsilon}}$ is necessary. Previous explicit constructions had rate about$\epsilon^3$, and this is the first explicit construction to get that close to the Gilbert-Varshamov bound.

This talk will have two parts, on Monday and Tuesday.

## Modular symbols and arithmetic

## Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound

I will show an explicit construction of a binary error correcting code with relative distance $\frac{1-\epsilon}{2}$ and relative rate $\epsilon^{2+o(1)}$. This comes close to the Gilbert-Varshamov bound that shows such codes with rate $\epsilon^2$ exist, and theLP lower bound that shows rate $\frac{\epsilon^2}{\log \frac{1}{\epsilon}}$ is necessary. Previous explicit constructions had rate about$\epsilon^3$, and this is the first explicit construction to get that close to the Gilbert-Varshamov bound.

This talk will have two parts, on Monday and Tuesday.

## Symmetries of hamiltonian actions of reductive groups

## Impeachment: The Constitutional Remedy of Last Resort

## Dust, Distortions and Shadows in the Universe's Oldest Light

## A Constant-factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation.