Abstract: I will survey (in)coherence of lattices in semisimple
Lie groups, with a view toward open problems and connections with
the geometry of locally symmetric spaces. Particular focus will be
placed on rank one lattices, where I will discuss...
I will present a proof with some substantial details of the
Multiplicity One Conjecture in Min-max theory, raised by Marques
and Neves. It says that in a closed manifold of dimension between 3
and 7 with a bumpy metric, the min-max minimal...
Abstract: There seems to be an analogy between the classes of
fundamental groups of compact 3-manifolds and of one-relator
groups. (Indeed, many 3-manifold groups are also one-relator
groups.) For instance, Dehn’s Lemma for 3-manifolds (proved
by...
In this talk, we will be concerned with the existence of a third
embedded minimal hypersurface spanning a closed submanifold B
contained in the boundary of a compact Riemannian manifold with
convex boundary, when it is known a priori the existence...
Abstract: This will be a broad talk about coherence of groups,
and how it relates to conjectures about hyperbolic groups with
planar boundaries. A group is coherent if every finitely generated
subgroup is finitely presented. This is a property...
Are factors of sparse polynomials sparse? This is a really basic
question and we are still quite far from understanding it in
general. In this talk, I will discuss a recent result showing that
this is in some sense true for multivariate polynomials...
Kazhdan–Lusztig (KL) polynomials for Coxeter groups were
introduced in the 1970s, providing deep relationships among
representation theory, geometry, and combinatorics. In 2016, Elias,
Proudfoot, and Wakefield defined analogous polynomials in
the...
In the early 1930's, the Ergodic theorems of von Neumann and
Birkhoff put Boltzmann's Ergodic Hypothesis in mathematical terms,
and the natural question was born: is ergodicity the "general case"
among conservative dynamical systems? Oxtoby and Ulam...
Constraint satisfaction problems (CSPs) are a central topic of
study in computer science. A fundamental question about CSPs is as
follows. Given a CSP where each constraint has the form of some
predicate P and almost all of the constraints can be...
We consider a reaction-diffusion equation with a nonlocal
reaction term. This PDE arises as a model in evolutionary ecology.
We study the regularity properties and asymptotic behavior of its
solutions.
