# Recently Added

## A nearly optimal lower bound on the approximate degree of AC$^0$

The approximate degree of a Boolean function $f$ is the least degree of a real polynomial that approximates $f$ pointwise to error at most $1/3$. For any constant $\delta > 0$, we exhibit an AC$^0$ function of approximate degree $\Omega(n^{1-\delta})$. This improves over the best previous lower bound of $\Omega(n^{2/3})$ due to Aaronson and Shi, and nearly matches the trivial upper bound of $n$ that holds for any function.

## The Dark Side of the Earth in the Sixteenth Century

## On the mathematical theory of black holes III

I will discuss a recent result in collaboration with J. Szeftel concerning the nonlinear stability of the Schwarzschild spacetime under axially symmetric, polarized perturbations.

## Transfer operators for (relative) functoriality "beyond endoscopy" II

"Beyond endoscopy", broadly interpreted, is the idea that functoriality should be realized as a comparison between stable trace formulas. The nature of this comparison, however, remains completely unclear.

## On the mathematical theory of black holes II

I will discuss in some detail the main difficulties of the problem of nonlinear stability of black holes and the recent advances on the related issue of linear stability.

## Numerical Simulations of Black Hole Accretion

## The Patternmakers: Season 2

## On the mathematical theory of black holes I

On the reality of black holes. I will give a quick introduction to the initial value problem in GR and overview of the problems of Rigidity, Stability and Collapse and how they fit with regard to the Final State Conjecture.