A Diophantine upper bound on the dimensions of certain spaces of
holonomic functions was the main ingredient in our proof with
Calegari and Tang of the 'unbounded denominators conjecture'
(presented by Tang in last year's number theory seminar)
This lecture will partly survey branching laws for real and
p-adic groups which often is related to period integrals of
automorphic representations, discuss some of the more recent
developments, focusing attention on homological aspects and
Half-integral weight modular forms are classical objects with
many important arithmetic applications. In terms of
automorphic representations, these correspond to objects on the
metaplectic double cover of SL(2). In this talk, I will
In this three-part lecture series, we will present a series of
works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic
mixing and enhanced dissipation properties of a passive tracer
subject to the motion of an ergodic Markovian flow of...
I will discuss recent work with Maksym Radziwill in which we
show that for any fixed tempered cuspidal representation π of GL(4)
over the rationals, there exist infinitely many primitive
characters χ such that the twisted L-function L(s,π×χ) is
We determine the average size of the 3-torsion in class groups
of G-extensions of a number field when G is any transitive 2-group
containing a transposition, for example, D4. It follows from
the Cohen--Lenstra--Martinet heuristics that the average...
The black hole information paradox — whether information escapes
an evaporating black hole or not — remains one of the greatest
unsolved mysteries of theoretical physics. The apparent conflict
between validity of semiclassical gravity at low...
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...
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...
Wiles’s proof of the modularity of (semistable) elliptic curves
over the rationals and Fermat’s Last Theorem relied on his
invention of a modularity lifting method. There were two strands to