Structures which minimise area appear in numerous geometric
contexts often related to degeneration phenomena. In turn, in many
situations these structures also reflect the ambient geometry in
some way (they are ‘calibrated’) and so they may provide...
Since the beginning of the subject, it has been speculated that
Gromov-Witten invariants should admit refinements in complex
cobordism. I will propose a resolution of this question based on
joint work-in-progress with Abouzaid, building on recent...
About 20 years ago, Gurvits developed the notion of polynomial
capacity to give a simple proof of the famous van der Waerden lower
bound on the permanent of a doubly stochastic matrix. Since then,
similar techniques have led to various other...
We will discuss a graph that encodes the divisibility properties
of integers by primes. We will prove that this graph has a strong
local expander property almost everywhere. We then obtain several
consequences in number theory, beyond the...
Let G be a compact Lie group acting on a closed manifold M.
Partially motivated by work of Uhlenbeck (1976), we explore the
generic properties of Laplace eigenfunctions associated to
G-invariant metrics on M. We find that, in the case where 𝕋 is
a...
I will discuss escape of mass estimates for SL(d,ℝ)-horospheres
embedded in the space of affine lattices, which depend on the
Diophantine properties of the shortest affine lattice vector. These
estimates can be used, in conjunction with Ratner's...
In this talk, I will present a computation of the image of the
Hodge-Tate logarithm map (defined by Heuer) in the case of smooth
Stein varieties. When the variety is the affine space, Heuer has
proved that this image is equal to the group of closed...
Agreement testing (aka direct product testing), checks if
consistent local information reveals global structure. Beyond its
theoretical connections to probabilistic checkable proofs (PCPs),
constructing agreement testers is a fundamental...
A dictionary data structure maintains a set of at most n� keys
from the universe [U][�] under key insertions and deletions, such
that given a query x∈[U]�∈[�], it returns if x� is in the set. Some
variants also store values associated to the keys...
