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...
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
function and its Fourier transform cannot both be concentrated on
fractal set. These were introduced to harmonic analysis in order
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...
In the study of Hamiltonian systems, integrable dynamics play a
crucial role. Integrability, however, appears to be a delicate
property that is not expected to persist under generic small
perturbations. Understanding the essence of this fragility...