We find ourselves at a pivotal era in the study of cosmology and
galaxy formation. The dark energy + cold dark matter (ΛCDM)
paradigm is firmly established as the default cosmological model,
owing in large part to its incredible success in explaining...
Coboundary expansion and cosystolic expansion are
generalizations of edge expansion to hypergraphs. In this talk, we
will first explain how the generalizations work. Next we will
motivate the study of such hypergraphs by looking at their
applications...
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...
