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...
Let E be an elliptic curve defined over \Q. The \Q¯-points
of E form an abelian group on which the Galois group
G\Q=\Gal(\Q¯/\Q) acts. The usual Galois representation
associated to E captures the action of G\Q on the points of finite
order. ...
The classic algorithm AdaBoost allows to convert a weak learner,
that is an algorithm that produces a hypothesis which is slightly
better than chance, into a strong learner, achieving arbitrarily
high accuracy when given enough training data. We...
