Vertex decomposition, introduced by Provan and Billera in 1980,
is an inductive strategy for breaking down and understanding
simplicial complexes. A simplicial complex that is vertex
decomposable is shellable, hence Cohen--Macaulay. Through
the...
We will discuss recent results towards the quantum unique
ergodicity conjecture of Rudnick and Sarnak, concerning the
distribution of Hecke--Maass forms on hyperbolic arithmetic
manifolds. The conjecture was resolved for congruence surfaces
by...
Since the revolutionary discovery of gravitational wave (GW)
emission from a binary black hole merger in 2015, the remarkable GW
detectors LIGO, Virgo and KAGRA have detected at least ninety
compact object mergers. These events are transforming...
Distinct Hamiltonian isotopy classes of monotone Lagrangian tori
in $\mathbb{C} P^2$ can be associated to Markov triples. With two
exceptions, each of these tori are symplectomorphic to exactly
three Hamiltonian isotopy classes of tori in the ball...
A d-dimensional framework is a pair (G,p⃗ ) consisting of a
finite simple graph G and an embedding p⃗ of its vertices in
ℝd. A framework is called rigid if every continuous motion of the
vertices in ℝd that starts at p⃗ , and preserves the lengths...
An evolving surface is a mean curvature flow if the normal
component of its velocity field is given by the mean curvature.
First introduced in the physics literature in the 1950s, the mean
curvature flow equation has been studied intensely by...
New results on quantum tunneling between deep potential wells,
in the presence of a strong constant magnetic field are presented.
This includes a family of double well potentials containing
examples for which the low-energy eigenvalue splitting...
We travel the years in order to understand the relationship
between Nilpotency and Riemannian geometry: including Gromov's
almost flat theorem for manifolds with bounded curvature and
Fukaya-Yamaguchi's almost nilpotency of spaces with lower...
In quantum complexity theory, QMA and QCMA represent two
different generalizations of NP. Both are defined as sets of
languages whose Yes instances can be efficiently checked by a
quantum verifier that is given a witness. With QMA the witness can
be...
Kaledin established a Cartier isomorphism for cyclic homology of
dg-categories over fields of characteristic p, generalizing a
classical construction in algebraic geometry. In joint work with
Paul Seidel, we showed that this isomorphism and related...
