Royal Holloway - Number Theory Seminar
The seminar takes place on Tuesday at 4pm in ABLT2 (Arts Building Lecture Theatre 2).
Here is a campus plan.
Autumn Term 2015:
September 29th: Pavlo Yatsyna (Royal Holloway)
Title: A trace bound for positive definite connected integer symmetric matrices
October 13th: Steven Galbraith (University of Auckland) (part of his LMS-funded Aitken Lectureship tour)
The lecture will be held in MBLT at 6pm. There will be tea before the talk in the maths common room (MC237) from 5:15.
Title: Linear Algebra with Errors, Coding Theory, Cryptography and Fourier Analysis on Finite Groups
Abstract: Solving systems of linear equations $Ax = b$ is easy, but how
can we solve such a system when given a "noisy" version of $b$? Over
the reals one can use the least squares method, but the problem is
harder when working over a finite field. Recently this subject has
become very important in cryptography, due to the introduction of new
cryptosystems with interesting properties.
The talk will survey work in this area. I will discuss connections with
coding theory and cryptography. I will also explain how Fourier
analysis in finite groups can be used to solve variants of this
problem, and will briefly describe some other applications of Fourier
analysis in cryptography. The talk will be accessible to a general
October 20th: Glyn Harman (Royal Holloway)
Title: Some problems involving primes in Beatty sequences
October 27th: Bernhard Koeck (University of Southampton)
Title: Euler characteristics and ε-constants of curves over finite fields - some wild stuff
Abstract: After introducing Artin L-functions of curves over finite
fields we relate the corresponding $\varepsilon$-constants to an
equivariant Euler characteristic of the underlying curve. The main
result generalises a theorem of Ted Chinburg from the tamely ramified
case to the weakly ramified case. (This is joint work with Helena
November 17th: Aleen Sheikh (Royal Holloway)
Title: The Davenport constant of finite abelian groups of rank three
December 1st: Cecilia Busuioc (Royal Holloway)
Title: Modular Curves and Explicit Class Field Theory
Abstract: In this talk, we will give a brief account of a result of
Fukaya and Kato on a deep connection between the geometry of modular
curves and the arithmetic of cyclotomic fields ( originally conjectured
by Sharifi). We will then give further insight into how one might
try to generalise these ideas for the study of ray class fields of
quadratic fields, of particular interest being a conjectural
construction of elliptic units for real quadratic fields proposed by
Darmon and Dasgupta.