Video Lectures

The ruled hypersurfaces are distinguished by being comprised of lines. When this characteristic exists as a consequence of vanishing principal curvatures, it yields possibilities for comparison with cylinders extending over lower-dimensional...

I will describe work in progress proposing and analyzing the bulk path integral of double scaled SYK in various bases.

In double-scaled SYK, the chord diagrams of Berkooz et al. give rise to a bulk algebra and geometry. The algebra is a "quantum deformation" of the JT gravitational algebra that includes a deformation of SL(2,R). The growth of operator size (in...

Spacetime wormholes can lead to surprises in black hole physics. We show that a very old black hole can tunnel to a white hole/firewall by emitting a large baby universe. We study the process for a perturbed thermofield double black hole in Jackiw...

One puzzling aspect of holography is that it conjectures a duality between a physical theory with a single rigid causal structure (the non-gravitational "boundary theory") and one whose causal structure is state-dependent (the gravitational "bulk...

Cauchy slice holography gives a duality between the wavefunction on a Cauchy slice and the partition function of a T2 deformed field theory.  I will review this correspondence and discuss its implications for the black hole information puzzle.  The...

A conjecture of Erdős states that for every large enough prime q, every reduced residue class modulo q is the product of two primes less than q. I will discuss my on-going work with Kaisa Matomäki establishing among other things a ternary variant of...

The online list labeling problem is a basic primitive in data structures. The goal is to store a dynamically-changing set of n items in an array of m slots, while keeping the elements in sorted order. To do so, some items may need to be moved over...