By an observation of Efimov and Scholze, Efimov's theorem on the
rigidity of localizing motives allows one to construct refinements
of topological Hochschild homology and its variants. In this talk,
I'll explain how this refinement works, sketch an...
The SAT (Boolean Satisfiability) problem asks whether a given
logical formula on n Boolean variables has an assignment of
true/false values to its variables that makes the formula
true. The P vs NP question is equivalent to asking whether
SAT has a...
Matrix-perturbation bounds quantify how the spectral
characteristics of a baseline matrix A change under additive noise
E. Classical results, including Weyl’s inequality for eigenvalues
and the Davis–Kahan theorem for eigenvectors and eigenspaces...
In this talk I will introduce a new notion of approximability
for metric spaces that can be seen as a categorification of a
concept introduced by Turing for metric groups and as a
generalization of total-boundedness. I will explain how
recent...
Rational curves are one of the main tools in symplectic geometry
and provide a bridge to algebraic geometry. Complex lines are a
more general class of curve that has the potential to connect
symplectic and complex analytic geometry. These curves are...
Link spectral invariants and their homogenizations have been
defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim
Trifa, we define a linear combination of such quasimorphism and
show that it vanishes on the stabilizer of the equator in...
A Hodge structure is a certain linear algebraic datum.
Importantly, the cohomology groups of any smooth projective
algebraic variety come equipped with Hodge structures which encode
the integrals of algebraic differential forms over
topological...
The theory of rigidity for lattices in higher rank semisimple
Lie groups is a powerful and exciting subject, combining methods
from algebra, number theory, geometry and dynamics. One of the most
celebrated results is Margulis' normal subgroup...
Around 1992, Aldous made the following bold conjecture. Let A be
any set of transpositions in the symmetric group Sym(N). Then
the spectral gap of the Cayley graph Cay(Sym(N),A)
is identical to that of a relatively tiny N-vertex graph
defined by A...
