I will present recent work with Hairer, Rosati and Yi
establishing quantitative lower bounds for the top Lyapunov
exponent of linear PDEs driven by two-dimensional stochastic
Navier-Stokes equations on the torus. For both the
advection-diffusion...
In this talk, we will present a proof of contact big fiber
theorem, based on invariants read off from contact Hamiltonian
Floer homology. The theorem concludes that any contact involutive
map on a Liouville fillable contact manifold admits at least...
A locally testable code (LTC) is an error-correcting code
equipped with a tester T that, given an input string x, queries
only a small number of positions and rejects x with probability
proportional to its distance from the code. Classic examples
of...
Selmer groups are a cohomological tool used to reduce the task
of finding solutions of certain diophantine equations to easier
field and modular arithmetic. I'll explain how this works in down
to earth terms and give some concrete applications...
Private Information Retrieval (PIR) is a method for a user to
interact with t non-colluding servers and read some entry of a
database of size n without revealing to the servers anything about
which entry of the database was read. After a long line...
The double bubble plumbing, first studied by Smith and Wemyss,
is a Stein neighborhood of two Lagrangian 3-spheres intersecting
cleanly along an unknotted circle in some 6-dimensional symplectic
manifold. Depending on the identification of the...
How many algebraic integers of bounded height have a minimal
polynomial with a given Galois group? One approach to this problem
is via Malle's conjecture. In this talk we will discuss an
alternative approach using a construction with the Galois...
A real plane algebraic curve C is called expressive if its
defining polynomial has the smallest number of critical points
allowed by the topology of the set of real points of C. We give a
necessary and sufficient criterion for expressivity (subject...
We present a combinatorial approach to the
Deligne-Mumford-Knudsen compactification of the moduli space of n
distinct points on the projective line P1. The idea is to choose a
totally symmetric embedding of the orbits of generic points into a
high...
We show that various classical theorems of linear incidence
geometry, such as the theorems of Pappus, Desargues, Möbius, and so
on, can be interpreted as special cases of a general result that
involves a tiling of a closed oriented surface by...
