Most work on Lagrangian fillings of Legendrian knots to date has
concentrated on orientable fillings, but instead I will present
some first steps in constructions of and (especially) obstructions
to the existence of (decomposable exact) non...
We study Chern-Simons theories at large N with either bosonic or
fermionic matter in the fundamental representation. The most
fundamental operators in these theories are mesonic line operators,
the simplest example being Wilson lines ending on...
Since the late 19th century, mathematicians have realized the
importance and generality of selection problems: given a collection
of sets, select an element in each set, possibly in a ``nice”
way. Of particular importance in computer science is
The existence of rational plane curves of a given degree with
prescribed singularities is a subtle and active area in algebraic
geometry. This problem turns out to be closely related to difficult
enumerative problems which arise in symplectic field...
I will discuss recent work with Maksym Radziwill in which we
show that for any fixed tempered cuspidal representation π of GL(4)
over the rationals, there exist infinitely many primitive
characters χ such that the twisted L-function L(s,π×χ) is
I will discuss how black holes can become nature's laboratories
for ultralight axions. When a boson's Compton wavelength is
comparable to the horizon size of a black hole, energy and angular
momentum from the black hole are converted into...
The Markoff equation x2+y2+z2=3xyz, which arose in his
spectacular thesis (1879), is ubiquitous in a tremendous variety of
contexts. After reviewing some of these, we will discuss
joint work with Bourgain and Sarnak establishing forms of
Quantum extremal surfaces and islands have led us to rethink the
very meaning of microscopic entropy in the presence of dynamical
gravity. I will present some work elucidating how the island/QES
prescription emerges in a simple doubly holographic...
Training a predictor to minimize a loss function fixed in
advance is the dominant paradigm in machine learning. However, loss
minimization by itself might not guarantee desiderata like fairness
and accuracy that one could reasonably expect from a...