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 mathematical audience.

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 Fischbacher-Weitz.)

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.