Let N and p greater than or equal to 5 be primes such that p
divides N−1. In his landmark paper on the Eisenstein ideal, Mazur
proved the p-part of the BSD conjecture for the p-Eisenstein
quotient J(p) of J0(N) over Q. Using recent results and...
In this talk I will describe recent progress in applying tools
from collider physics to problems in classical general relativity.
This program has produced state-of-the-art calculations of the
conservative two-body Hamiltonian at the fourth order in...
The Nielsen-Thurston theory of surface homeomorphism can be
thought of as a surface analogue to the Jordan Canonical
Form. I will discuss my progress in developing a similar
decomposition for free group automorphisms. (Un)Fortunately, free
group...
Two recent and seemingly-unrelated techniques for proving mixing
bounds for Markov chains are:
(i) the framework of Spectral Independence, introduced by Anari,
Liu and Oveis Gharan, and its numerous extensions, which have given
rise to several...
Given a trivalent plane graph embedded in the Euclidean plane
(up to isotopy), Treumann and Zaslow constructed and studied a
certain associated Legendrian surface embedded in standard contact
R5, nowadays referred to as a Legendrian 2-weave. Using...
The fundamental equations of fluid dynamics exhibit
non-uniqueness. Is this a mathematical fluke, or do the equations
fail to uniquely predict the motion of fluids? In this colloquium,
we present recent mathematical and physical progress toward...
Over the last three decades, the online bipartite matching (OBM)
problem has emerged as a central problem in the area of Online
Algorithms. Perhaps even more important is its role in the area of
Matching-Based Market Design. The resurgence of this...
I will review two combinatorial constructions of integrable
systems: Goncharov-Kenyon construction based on counting perfect
matchings in bipartite graphs, and
Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on
counting paths in networks...
I will explain how various results in arithmetic statistics by
Bhargava, Gross, Shankar and others on 2-Selmer groups of Jacobians
of (hyper)elliptic curves can be organised and reproved using the
theory of graded Lie algebras, following earlier...
