Royal Holloway - Number Theory Seminar
The NT-seminar takes place on Wednesday at 4pm in Munro Fox Lecture Theatre
(unless stated otherwise).
Here is a campus plan.
October 2
Martin Widmer (Royal Holloway)
Bounds on the l-torsion part of class groups
Abstract:
I survey some recent results on upper bounds (pointwise and on average)
of the
l-torsion part of class groups of number fields.
October 9
Natasha Morrison (Cambridge)
Invertibility of Random Symmetric Matrices
October
16 Reynold Fregoli
(Royal Holloway)
Bounded Exponential Sums
October
23 Jonathan Chapman (Manchester)
The Ramsey number of the Brauer
configuration
Abstract:
In this talk we obtain quantitative bounds for Brauer's
generalisation of van der Waerden's theorem. Brauer's theorem states that, given any positive integers k
and r, there exists a positive integer N such that any colouring of the first N
positive integers with r colours produces a monochromatic arithmetic
progression of length k with the same colour as its common difference. By
modifying the work of Gowers on Szemerédi's theorem,
we show that N can be taken to be double exponential in the number of colours
and quintuple exponential in the length of the progression. This talk is based
on joint work with Sean Prendiville (Lancaster).
October
30 No NT-Seminar!
November
6 Kevin Buzzard (Imperial College)
Doing
modern mathematics in Lean
Abstract:
I will talk about the practical problems that one faces when trying to do MSc
and higher level algebra and number theory using a
computer theorem prover. A background in algebra / number theory will be
assumed for most of the talk.
November
13 Stephanie Chan (University
College London)
On the negative Pell equation
Abstract: Stevenhagen
conjectured that the density of d such that the negative Pell equation
x^2-dy^2=-1 is solvable over the integers is 58.1% (to the nearest tenth of a
percent), in the set of positive squarefree integers
having no prime factors congruent to 3 modulo 4. In joint work with Peter Koymans, Djordjo Milovic, and Carlo Pagano, we use a recent breakthrough of
Smith to prove that the infimum of this density is at least 53.8%, improving
previous results of Fouvry and Klüners,
by studying the distribution of the 8-rank of narrow class groups of quadratic
number fields.
November
20 No NT-Seminar!
November
27 No NT-Seminar!
December
4 No NT-Seminar!
December
11 Joni Teräväinen (Oxford)
Higher order uniformity of the Möbius
function
In recent work, Matomäki,
Radziwill and Tao showed that the Möbius function is discorrelated with linear exponential phases on almost all
intervals around $X$ of length $X^{\varepsilon}$. I will discuss joint work where we generalize this
result to ''higher order phase functions'', so as a special case the Möbius
function is shown not to correlate with polynomial phases on almost all
intervals of length $X^{\varepsilon}$. As an application, we show that the number of sign
patterns of length $k$ that the Liouville function takes grows superpolynomially in $k$.
Autumn
2018
Spring 2018
Autumn 2017
Spring 2017
Summer 2016
Spring 2016
Autumn 2015
Spring 2015
Autumn 2014