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Number fields and function fields: coalescences, contrasts and emerging applications

Event

Starts:

May
292014

09:00

Ends:

May
302014

17:00

Location

Kavli Royal Society Centre, Chicheley Hall, Newport Pagnell, Buckinghamshire, MK16 9JJ

Overview

Theo Murphy international scientific meeting organised by Professor Jon Keating FRS, Professor Zeev Rudnick and Professor Trevor Wooley FRS

Event details

Connections between problems in number fields and in function fields are of central importance in Number Theory. The past decade has seen fundamental new developments emerge in this direction, attracting some of the leading mathematicians. Our goal is to explore the interplay between these ideas, and their implications for other areas of mathematical science, including mathematical physics and computational complexity.

Download the meeting programme

Biographies of the organisers and speakers will be made available shortly, as well as the two-day programme. Recorded audio of the presentations will be available on this page after the event.

Attending this event

This is a residential conference, which allows for increased discussion and networking.  It is free to attend, however participants need to cover their accommodation and catering costs if required.

Enquiries: Contact the events team

Event organisers

Select an organiser for more information

Schedule of talks

Session 1

5 talks Show detail Hide detail

Chair of Session 1

Professor Roger Heath-Brown FRS, University of Oxford, UK

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Robust estimates for exponential sums in function fields

Professor Trevor Wooley FRS, University of Bristol, UK

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Moments of L-functions and a one-sided central limit theorem

Professor Kannan Soundararajan, Stanford University, USA

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Some problems in analytic number theory for polynomials over a finite field

Zeev Rudnick, Tel Aviv University, Israel

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The inverse large sieve problem

Professor Ben Green, University of Oxford, UK

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Session 2

5 talks Show detail Hide detail

Chair of Session 2

Alina Bucur, University of California - San Diego, USA

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Using Galois theory in analytic number theory

Professor Lior Bary-soroker, Tel Aviv University, Israel

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Statistics for cyclic trigonal curves over finite fields

Professor Chantal David, Université de Montréal, Canada

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Sums of products of trace functions over finite fields

Professor Emmanuel Kowalski, ETH Zurich, Switzerland

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How many points on a random curve over a finite field?

Kiran S Kedlaya, University of California, San Diego

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Session 3

5 talks Show detail Hide detail

Chair of Session 3

Professor Bryan Birch FRS, Oxford University Mathematical Institute, UK

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Questions about moments

Professor Brian Conrey, AIM and University of Bristol, UK

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Equidistribution questions raised by Entin, Keating, and Rudnick

Professor Nick Katz, Princeton University, USA

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Elliptic curves and random matrices

Professor Nina Snaith, University of Bristol, UK

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The anatomy and pretentions of function fields

Dr Andrew Granville, Université de Montréal, Canada

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Session 4

4 talks Show detail Hide detail

Chair of Session 4

Paul Pollack, University of Georgia, USA

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Conjectures, theorems, and experiments concerning the moments of zeta functions associated to quadratic function fields

Professor Michael Rubinstein, University of Waterloo, Canada

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A physicists take on the conjecture of Birch and Swinnerton-Dyer

Professor Philip Candelas, University of Oxford, UK

Abstract

We will show that the BDS conjecture can be recast as the problem of estimating a "path integral” of a form that is at least superficially familiar to physicists.

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Arithmetic of Calabi-Yau manifolds

Dr Xenia de la Ossa, University of Oxford, UK

Abstract

This talk will discuss the arithmetic of Calabi-Yau 3-folds considered as a manifold over finite fields.  De la Ossa will be concerned with the computation of these numbers and their dependence on the complex structure parameters.  We will see that these numbers are given by expressions which involve the periods of the manifold. The talk will discuss the form of zeta function and the L-function of the Dwork pencil of quintic 3-folds with attention as to what happens at singularities.

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Number fields and function fields: coalescences, contrasts and emerging applications Kavli Royal Society Centre, Chicheley Hall Newport Pagnell Buckinghamshire MK16 9JJ