**LMS South West and South Wales Regional Meeting 2018**

and

2nd Workshop on Number Theory and Function Fields at the Crossroads

17 - 20 December 2018

University of Exeter

and

2nd Workshop on Number Theory and Function Fields at the Crossroads

__Funded by:__**London Mathematical Society**

University of Exeter

University of Exeter

**REGIONAL MEETING DAY**

In the first day of the workshop we will host the London Mathematical Society South West and South Wales Regional Meeting. It will be a day with lectures aimed at a general mathematical audience. The speaker for the day are:

Keith Ball (University of Warwick)

Min Lee (University of Bristol)

Jens Marklof (University of Bristol)

The programme for this day is as follows:

- 2.00 pm Opening of the meeting and the LMS Business Meeting

- 2.15 pm
**Prof. Keith Ball**(University of Warwick)

*Title.*Rational approximations to the zeta function

- 3.30 pm
**Dr. Min Lee**(University of Bristol)

*Title.*Applications of trace formulas for $GL(2)$

- 4.30 pm Tea/Coffee Break

- 5.00 pm
**Prof. Jens Marklof**(University of Bristol)

*Title.*Chaos and randomness modulo one: the interplay of number theory and dynamical systems

- 6.00 pm Wine reception

- 7.30 pm Society Dinner

**Registration:**Please register for your place by contacting the organisers: Dr Julio Andrade and Prof. Nigel Byott

**Travel Funding for Research Students and LMS Members:**There are funds available to contribute in part to the expenses of members of the London Mathematical Society or research students registered at UK universities to attend the meeting and workshop. Requests for support, including an estimate of expenses, as well as all queries about the two events may be addressed to the organisers: Dr Julio Andrade and Prof. Nigel Byott

**PROGRAM**

The analogies between function fields and number fields are fundamental in Number Theory. In the past few years there has been an explosion of activity in function fields related to number theory, specifically in arithmetic statistics, analytic number theory and additive number theory.

The upsurge of activity in function fields has attracted some of the leading mathematicians and number theorists to think and revisit questions related to function fields and number theory.

The goal of this research workshop is to explore some of the new advances in number theory and investigate further the interplay between number fields and function fields and its connections with mathematical physics and random matrix theory.

The main aim of the workshop is to discuss new ideas and recent trends in the subject and to formulate some new and ambitious problems, as well as brainstorm various ideas for solving them. The expectation is that a number of new and exciting collaborations will be initiated due to the meeting.

**LOCATION**

University of Exeter

Harrison Building

North Park Road

EX4 4QF

All the talks will take place at the Lecture Room 004 at the Ground Floor of the Harrison Building.

The venue for the meeting is the number 23 in the campus map.

**PARTICIPANTS**

Alharith A. Abdullah (University of Babylon)

Faez AL-Maamori (University of Babylon)

Julio Andrade (University of Exeter)

Emma Bailey (University of Bristol)

Keith Ball (University of Warwick)

Lior Bary-Soroker (Tel-Aviv University)

Julia Brandes (University Gothenburg)

Hung Bui (University of Manchester)

Nigel Byott (University of Exeter)

Dan Carmon (Tel-Aviv University)

Robin Chapman (University of Exeter)

Rhianwen Davies (University of Exeter)

Adam Harper (University of Warwick)

Scott Kirila (University of Rochester)

Henri Johnston (University of Exeter)

Min Lee (University of Bristol)

Steve Lester (Queens Mary)

Allysa Lumley (York University - Canada)

Joseph MacMillan (University of Exeter)

Jens Marklof (University of Bristol)

Gihan Marasingha (University of Exeter)

Asmaa Shamesaldeen (University of Exeter)

Kevin Smith (University of Exeter)

Pankaj Vishe (Durham University)

Igor Wigman (King's College)

**TALKS**

**Speaker Title**

Emma Bailey Moments of Moments

Keith Ball Rational approximations to the zeta function

Lior Bary-Soroker Is a random polynomial with plus minus 1 coefficients irreducible over the integers?

Julia Brandes Rational lines on cubic hypersurfaces

Hung Bui Quadratic twists of elliptic curves $L$-functions over function fields

Dan Carmon Square-free Values of Polynomials with Large Coefficients and the ABC Conjecture

Adam Harper Low moments of character sums

Scott Kirila Some Discrete Moments in the Selberg Class

Min Lee Applications of trace formulas for $GL(2)$

Steve Lester Sign changes of Fourier coefficients of half-integral weight forms

Allysa Lumley Distribution of Values of $L$-functions in the Hyperelliptic Ensemble

Jens Marklof Chaos and randomness modulo one: the interplay of number theory and dynamical systems

Pankaj Vishe Counting points over function fields and rational points on smooth hypersurfaces of low degree

Igor Wigman Points on nodal lines with given direction

**ORGANIZERS**

Julio Andrade (University of Exeter)

Nigel Byott (University of Exeter)

**TRAVEL, ACCOMMODATION AND PRACTICAL INFORMATION**

(to be updated)

(to be updated)

Click here for a campus map.

Here is some general advice on to travel to Streatham via bus, rail, or Exeter Airport. Onward travel from Exeter Airport is available by bus or taxi. The bus is cheap (a few pounds), but doesn't run that that late. The taxi costs about £25.

The two largest airports in the UK are Heathrow and Gatwick, and partipants from North America will probably have to fly to one of these (they also have flights to many European cities). By far the cheapest onward travel option in both cases is to take the bus to Exeter Bus and Coach station. From Gatwick, you can travel by train via either Reading or Clapham Junction (cheaper, but a bit slower) to Exeter St David's train station. From Heathrow, you can take either the Heathrow Express or Heathrow connect (a bit slower but much cheaper) to London Paddington train station and then take the train from Paddington to Exeter St. David's. Rail prices and timetables (including for onward travel from airports other than Exeter) can be found at National Rail Enquiries.