We discuss various (still open) questions on approximations of
finitely generated groups, focusing on finite-dimensional
approximations such as residual finiteness and soficity. We survey
our results on the existence, stability and quantification
of...
The Satisfiability problem is perhaps the most famous problem in
theoretical computer science, and significant effort has been
devoted to understanding randomly generated SAT instances. The
random k-SAT model (where a random k-CNF formula is chosen...
The study of hyperkaehler manifolds of lowest dimension (and of
gauge theory on them) leads to a chain of generalizations of the
notion of a quiver: quivers, bows, slings, and monowalls. This talk
focuses on bows, their representations, and...
Earlier this semester we heard a fascinating talk by James Stone
describing how the equations of compressible magnetohydrodynamics
(MHD) can help us understand the Cosmos. Today we will return to
Earth and describe a mathematical model, derived from...
In the Pandora's Box problem, the algorithm is provided with a
number of boxes with unknown (stochastic) rewards contained inside
them. The algorithm can open any box at some cost, discover the
reward inside, and based on these observations can...
Let g be a semisimple Lie algebra. The affine W-algebra
associated to g is a topological algebra which quantizes the
algebraic loop space of the Kostant slice. It is constructed as a
quantum Hamiltonian (alias quantum Drinfeld--Sokolov) reduction
of...
The study of totally positive matrices, i.e., matrices with
positive minors, dates back to 1930s. The theory was generalised by
Lusztig to arbitrary split reductive groups using canonical bases,
and has significant impacts on the theory of cluster...
Links of strata in singular spaces are fundamental invariants
which govern the topology of small neighbourhoods around points in
those strata. This talk will focus on inferring links of strata
from incomplete information in three completely...
Given a maximal torus T of a connected reductive group G over a
local field F, there does not exist a canonical embedding of the
L-group of T into the L-group of G. Generalizing work of Adams and
Vogan in the case F=R, we will construct a natural...
In joint work with Andy Manion, we required a generalization of
the tensor product of 2-representations in order to reconstruct the
2-dimensional part of Lipshitz-Oszvath-Szabo’s bordered
Heegaard-Floer theory. I will discuss this and possible...
