**Number Theory and Function Fields at the Crossroads 2016**

Focused Research Workshop

20 - 22 January 2016

University of Exeter

__Funded by:__**Heilbronn Institute for Mathematical Research**

Heilbronn 10th Anniversary Focused Research Grants

Heilbronn 10th Anniversary Focused Research Grants

**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. There will be a small number of main lectures delivered by more senior and established mathematicians, a number of short talks given by postdocs followed by discussion sessions. The expectation is that a number of new and exciting collaborations will be initiated due to the meeting.

**LOCATION**

University of Exeter

Upper Lounge

Reed Hall

Streatham Drive

Exeter

Devon

EX4 4QR

The venue for the meeting is the number 14 in the campus map.

PARTICIPANTS

PARTICIPANTS

Ardavan Afshar (University College London)

Julio Andrade (University of Exeter and University of Oxford)

Lior Bary-Soroker (Tel-Aviv University)

Tim Browning (University of Bristol)

Hung Bui (University of Manchester)

Nigel Byott (University of Exeter)

Dan Carmon (Tel-Aviv University)

Brian Conrey (AIM)

Chantal David (Concordia University)

Alexei Entin (Stanford University)

Alexandra Florea (Stanford University)

Ofir Gorodetsky (Tel-Aviv University)

Andrew Granville (University College London and Université de Montréal)

Adam Harper (University of Cambridge)

Chris Hughes (University of York)

Henri Johnston (University of Exeter)

Jon Keating (University of Bristol)

Oleksiy Klurman (University College London)

Min Lee (University of Bristol)

Gihan Marasingha (University of Exeter)

Adelina Manzateanu (University of Bristol)

Brad Rodgers (University of Michigan)

Edva Roditty-Gershon (University of Bristol)

Igor Wigman (King's College)

**SCHEDULE AND ABSTRACTS**

Here is a pdf file with the schedule of the talks.

**TALKS**

**Speaker Title**

Lior Bary-Soroker Statistics of arithmetic functions in function fields

Tim Browning Algebraic geometry over finite fields via counting

Dan Carmon Square-free values of polynomials with large coefficients

Brian Conrey Approaches to RH

Chantal David Statistics for cyclic covers over finite fields

Alexei Entin Hurwitz Spaces and Extensions of the Rational Function Field

Alexandra Florea Mean value of quadratic Dirichlet $L$-functions in function fields

Andrew Granville Sieving differences

Adam Harper Multiplicative functions in function fields

Chris Hughes Modelling large values of $L$-functions

Min Lee The Selberg Trace Formula as a Dirichlet series and applications

Brad Rodgers Explicit formulas and symmetric function theory

Edva Roditty-Gershon Arithmetic Statistics in Function Fields

**ORGANIZER**

Julio Andrade (University of Exeter and University of Oxford)

**TRAVEL, ACCOMMODATION AND PRACTICAL INFORMATION**

Click here for a campus map.

The workshop will start on the morning of Wednesday 20th January and we anticipate that most participants will arrive on the afternoon or evening of Tuesday 19th January. See the schedule above for further details.

The participants of this meeting are staying in two different accommodations:

1-) The Bendene

15-16 Richmond Rd, Exeter EX4 4JA

or

2-) The Jurys Inn Exeter Hotel

Western Way, Exeter EX1 2DB

The participants of the meeting should by now have received an email containing information about the accommodation. If not, please let me know.

From the Jurys Inn to the conference venue is a 25 minutes walking or you can take the bus D as it is shown on this link.

From The Bendene is a 18 minutes walking or you can take the bus D as it is shown on this link.

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.

In the second day of the meeting, we will have a conference dinner, where all the participants are invited to attend. The dinner will take place at Reed Hall at the Reed Woodbridge Suite from 19:30 - 23:00.