The question of stability of approximate group homomorphisms was
first formulated by Ulam in the 1940s. One of the most famous
results in this area is Kazhdan's 1982 result on stability of
approximate unitary representations of an amenable group...
The duality long exact sequence relates linearised Legendrian
contact homology and cohomology and was originally constructed by
Sabloff in the case of Legendrian knots. We show how the duality
long exact sequence can be generalised to a relative...
Tidal disruption events (TDEs) provide an exciting opportunity
to study supermassive black holes (SMBHs) in quiescent galaxies and
the stellar populations and dynamics in galactic nuclei. They test
the limits of black hole accretion by regularly...
In this lecture I will present basic elements of the theory of
nonlocal games from quantum information theory and give some
examples. I will then introduce the idea of "compressing" the
complexity of nonlocal games, and show how the right form of...
Global climate change policy is not enough: environmental damage
emerges patch by patch. It is up close and personal as well
as planetary. Perhaps what we need is a “field guide” to the
feral, that is, to nonhuman responses to human building...
Erdős-style geometry is concerned with combinatorial questions
about simple geometric objects, such as counting incidences between
finite sets of points, lines, etc. These questions can be typically
viewed as asking for the possible number of...
Given n∈ℕ and ξ∈ℝ, let τ(n;ξ)=∑d|ndiξ. Hall and Tenenbaum asked
in their book \textit{Divisors} what is the value of
maxξ∈[1,2]|τ(n;ξ)| for a ``typical'' integer n. I will present work
in progress, carried out in collaboration with Louis-Pierre...
The three problems referred to in the title originate in the
theory of von Neumann algebras, C* algebras, and quantum
information theory respectively. Each of them has been a deep
long-standing open problem in its respective area. Surprisingly,
the...
Black holes are expected to exhibit universal 'random matrix'
behavior at late times, indicative of quantum chaos. The
approach to a late-time plateau in the spectral form factor
(SFF) is a probe of this behavior. In this talk we study the SFF
in...
