In recent years, a new “fine-grained” theory of computational
hardness has been developed, based on “fine-grained reductions”
that focus on exact running times for problems.
We follow the fashion of NP-hardness in a more delicate manner.
We...
I will discuss features of the static responses of black
holes in General Relativity. In particular, I will describe how
black hole static responses are defined in point particle effective
theory and will explain how the vanishing of black hole...
I will describe how the orbit method can be developed in a
quantitative form, along the lines of microlocal analysis, and
applied to local problems in representation theory and global
problems involving the analysis of automorphic forms. This
talk...
Understanding the complexity of the Minimum Circuit Size Problem
(MCSP) is a longstanding mystery in theoretical computer science.
Despite being a natural problem about circuits (given a Boolean
function's truth table, determine the size of the...
In a work with Jacques Fejoz, we consider the conformal dynamics
on a symplectic manifold , i.e. for which the symplectic form is
transformed colinearly to itself. In the non-symplectic case, we
study the problem of isotropy and uniqueness of...
I will discuss new constraints on the spectra of Maass forms on
compact hyperbolic 2-orbifolds. The constraints arise from
integrals of products of four functions in discrete series
representations realized in L2(Γ∖G), where Γ is a cocompact
lattice...
A landmark result of Ratner states that if G is a Lie group, Γ a
lattice in G and if ut is a one-parameter Ad-unipotent subgroup of
G, then for any x∈G/Γ the orbit ut.x is equidistributed in a
periodic orbit of some subgroup L less than G, and...
The talk will be devoted to explain how to construct weak
solutions to 3D Ideal MHD equations obtained by convex integration
(in the non smooth regime). We will show the existence of bounded
weak solutions dissipating energy and cross helicity but...
I will present a joint work with Lijie, in which we revise the
hardness vs randomness framework so that it can work in a
non-black-box fashion. That is, we construct derandomization
algorithms that do not rely on classical PRGs, and instead
"extract...
