String stars, or Horowitz-Polchinski solutions, are string
theory saddles with normalizable condensates of thermal-winding
strings. In the past, string stars were offered as a possible
description of stringy (Euclidean) black holes in
asymptotically...
The Breuil-Mezard Conjecture predicts the existence of
hypothetical "Breuil-Mezard cycles" that should govern congruences
between mod p automorphic forms on a reductive group G. Most of the
progress thus far has been concentrated on the case G = GL_2...
Translational tiling is a covering of a space (such as Euclidean
space) using translated copies of one building block, called a
"translational tile'', without any positive measure
overlaps.
Can we determine whether a given set is a translational...
The dynamics associated with mechanical Hamiltonian flows with
smooth potentials that include sharp fronts may be modeled, at the
singular limit, by Hamiltonian impact systems: a class of
generalized billiards by which the dynamics in the domain’s...
One of the major open problems in complexity theory is proving
super-logarithmic lower bounds on the depth of circuits. Karchmer,
Raz, and Wigderson (Computational Complexity 5(3/4), 1995)
suggested approaching this problem by proving that depth...
I will describe some new "coarse-graining" methods in
quantitative homogenization and how they can be used to give
rigorous versions of certain heuristic "renormalization group"
arguments in physics, with a focus on several examples.
A fractal uncertainty principle (FUP) roughly says that
a
function and its Fourier transform cannot both be concentrated on
a
fractal set. These were introduced to harmonic analysis in order
to
prove new results in quantum chaos: if eigenfunctions on...
Cohomology of classifying space/stack of a group G is the home
which resides all characteristic classes of G-bundles/torsors. In
this talk, we will try to explain some results on Hodge/de Rham
cohomology of BG where G is a p-power order commutative...
A weighted pseudorandom generator (WPRG) is a generalization of
a pseudorandom generator (PRG) in which, roughly speaking,
probabilities are replaced with weights that are permitted to be
positive or negative. In this talk, we present new explicit...
