# International Conference in Number Theory and Physics

IMPA, Rio de Janeiro, June, 15 – 26, 2015

This school and conference aims to bring together mathematicians (from number theory and algebraic geometry,…) and theoretical physicists (from Quantum Chaos, QFT and String Theory,…). The first week will be aimed at introductory minicourses and introductory lectures in several topics on Number Theory and Physics. And the second week will focus on research lectures and advanced level minicourses aimed at graduate students and researchers at all levels.

The main purpose of the school and conference is to bring together leading researchers in number theory and physics, to foster further mutually beneficial interaction between Number Theory and Physics.

The school will be made of a series of plenary lectures, short lectures and minicourses in different subjects on Number Theory and Physics. One of the aims of this school is to discuss the recent developments in a wide range of topics at the crossroads between Number Theory and Physics. The main topics to be covered in this conference are:

– Number Theory and Random Matrices
– Number Theory over Function Fields and Riemann Hypothesis for Curves
– Modular Forms, Mock Modular Forms and Generalizations
– String Theory, String dualities and automorphic forms
– Quantum Field Theory for Mathematicians and Number Theorists
– Quantum Chaos, Arithmetic Quantum Chaos and Number Theory
– Noncommutative Geometry in Number Theory and Physics
– Polylogarithms, Multiple Zeta Values and Pertubative Physics
– Mirror Symmetry, Calabi-Yau Manifolds and Zeta Functions
– Prime Numbers and recent developments
– AdS/CFT and arithmetic

Lecture

## Organizing Committee

Julio Andrade (IHÉS, France)
Emanuel Carneiro (IMPA, Brazil)
Jon Keating (University of Bristol, UK)
Hossein Movasati (IMPA, Brazil)
Peter Sarnak (IAS and Princeton University, USA)
Fernando Rodriguez Villegas (ICTP, Italy)
Felipe Voloch (University of Texas at Austin, USA)

## Scientific and Advisory Committee

Carolina Araujo (IMPA)
Michael Atiyah (University of Edinburgh)
Francis Brown (IHES)
Daniel Bump (Stanford University)
Alan Carey (Australian National University)
Brian Conrey (AIM and Bristol)
Edward Frenkel (Berkeley)
Sergei Gukov (Caltech)
Dirk Kreimer (Humboldt-Universitat)
Matilde Marcolli (Caltech)
Barry Mazur (Harvard)
Ken Ono (Emory University)
Xenia de la Ossa (Oxford)
Alfredo Miguel Ozorio de Almeida (CBPF)
Dinakar Ramakrishnan (Caltech)
Zeev Rudnick (Tel-Aviv)
Nina Snaith (Bristol)
Pierre Vanhove (IHES)
Michel Waldschmidt (Paris 6)
Edward Witten (IAS)
Shing-Tung Yau (Harvard)
Jean-Christophe Yoccoz (College de France)
Noriko Yui (Queen’s University)
Don Zagier (Max Planck Institute)
Lior Bary-Soroker (Tel-Aviv University – Israel)
Alina Bucur (University of California at San Diego – USA)
Kiran Kedlaya (University of California at San Diego – USA)

## Mini Courses

1st Week – School (June 15-19, 2015)

Course 1
Random Matrix Theory and Statistics of families of L-functions
(Prof. Brian Conrey – AIM and University of Bristol, USA)

Course 2
An Interpretation of the Birch Swinnerton-Dyer Conjecture
(Prof. Xenia de la Ossa – University of Oxford, UK)

Course 3
A Motivated Introduction to the Riemann Zeta-Function
(Prof. Steve Gonek – University of Rochester, USA)

Course 4
The Physics and Number Theory of the A-polynomial
(Prof. Ingmar Saberi – Caltech, USA)

Course 5
L-functions and Random Matrix Theory
(Prof. Jon Keating, FRS – University of Bristol, UK)

Course 6
Quantum Black Holes, Modular Forms and Mock Modular Forms
(Prof. Sameer Murthy – King’s College, UK)

## Invited Speakers

Lior Bary-Soroker (Tel-Aviv University – Israel)
On sums of two squares in function fields

Bruce Berndt (University of Illinois at Urbana-Champaign – USA)
Circle and Divisor Problems, Bessel Function Series, and Associated Riesz and Logarithmic Means

Sir Michael Berry (University of Bristol – UK)
Seeing and hearing the Riemann zeros

David Broadhurst (Open University – UK)
Periods in quantum field theory

Alina Bucur (University of California at San Diego – USA)
The distribution of points on cyclic trigonal curves over finite fields

Philip Candelas (University of Oxford – UK)
A Physicists Take on the Conjecture of Birch and Swinnerton-Dyer

Brian Conrey (AIM and University of Bristol)
Statistics of L-functions

Gunther Cornelissen (Utrecht University – Netherlands)
Reconstruction of walks in graphs

John Duncan (Case Western Reserve University – USA)
Umbral Moonshine Modules

Jordan Ellenberg (University of Wisconsin – USA)
Geometric aspects of arithmetic statistics over function fields

Solomon Friedberg (Boston College – USA)
Higher Theta Functions

Steve Gonek (University of Rochester)
Large values of the zeta-function at critical points

Jeffrey Hoffstein (Brown University – USA)
Second moment formulas for Rankin-Selberg convolutions and character twists of GL(2) L-series

Christopher Hughes (University of York – UK)
Zeros of linear combinations of L-functions

Jon Keating (University of Bristol – UK)
Arithmetic Statistics in Function Fields

Kiran Kedlaya (University of California at San Diego – USA)
Recent progress in computing zeta functions of varieties

Alex Kontorovich (Yale University – USA)
The Unreasonable Effectiveness of Thin Groups

Jeffrey Lagarias (University of Michigan – USA)
Multivariable zeta functions

Micah Milinovich (University of Mississippi – USA)
Fourier Analysis and the zeros of the Riemann zeta-function

Michael Rosen (Brown University – USA)
Generating the Maximal Abelian Extension of A Global Function Field

Michael Rubinstein (University of Waterloo – Canada)
Moments of zeta functions in the hyperelliptic ensemble

Emanuel Scheidegger (Universitt Freiburg – Germany)
Topological strings and modularity

German Sierra (Instituto de Física Teórica, UAM-CSIC – Spain)
Prime numbers and Riemann zeros go Quantum

Christopher D. Sinclair (University of Oregon – USA)
Mahler measure, random polynomials and 2D electrostatics

Nina Snaith (University of Bristol – UK)
Beyond the excised model: random matrix models and elliptic curves

Mark Srednicki (University of California – USA)
Quantum mechanics on the idèle class group

Nicolas Templier (Cornell University – USA)
Large values of automorphic forms and integrable systems

Yuri Tschinkel (NYU)
Height zeta functions

Herman Verlinde (Princeton University – USA)
Conformal bootstrap, universality and gravitational scattering

Fernando Rodriguez Villegas (ICTP – Italy)
On the geometry of character varities

Raimar Wulkenhaar (University of Münster – Germany)
A solvable quantum field theory in 4 dimensions

## Poster Sessions Schedule

June 16 – Tuesday – 1st. Week, at 11:15 – 11:40 and 15:30 – 16:00

Alan Miguel Velasquez Toribio (UFES)
Cosmology and quantum field theory: Dark energy

Badidja (Kasdi Merbah University of Ouargla)
The primes in the Lucas and Lehmer sequences

Bogdan Stoica (California Institute of Technology)
Tomography from entanglement and holographic entropy inequalities in the large N limit

Daiane Soares Veras (UnB) and Lucimeire Alves de Carvalho (Puc de Goiás)
Unidades Fundamentais em alguns corpos cúbicos

Emanuel Guariglia (E. R. Caianiello – University of Salerno)
Fractional derivative of Riemann Zeta Function: series expansions, Fourier Transform and generalizations

G. Sudhaamsh Mohan Reddy (Fac. Sc. and Tech. – Icfai Foundation for higher Education-India)
Estimates for Ld(1)/Ld(2) for a quadratic field Q(squ d)

Juan Guillermo Dueñas (Centro Brasileiro de Pesquisas Físicas)
Thermodynamics of the Bosonic Randomized Riemann Gas

Maria Fernanda Araujo de Resende (USP-IF)
Toric code with matter: some algebraic considerations

June 23 – Tuesday – 2nd. Week, at 11:00 – 11:30 and 16:00 – 16:30

Fahd Alshammari (King Saud University)
On the construction of infinite families of elliptic curves with high rank and a point of order 5

Maria Lewtchuk Espindola (UFPB)
Hamiltonização Direta – Uma Generalização da Hamitonização ALternativa

Ilmar Gahramanov (Humboldt Universität Zu Berlin)
Elliptic hypergeometric functions and Physics

Jakhlouti Mohamed Taieb (I.P.e.I. Monastir)
Uniform Distribution of the a-points of Dirichlet series

Jonny Fernando Barreto Castañeda (Centro de Investigacion y Estudios Avanzados del Ipn)
Study of non-singular solutions of an Homogeneous Systems of Equations with coefficients in a finite field

Lohans de Oliveira Miranda (UFPI) & Lossian Barbosa Bacelar Miranda (IFPI)
Law of the lever and the equilibrium of magic hypercubes

Tian An Wong (City University of New York)
Zeroes of L-functions in the trace formula

Bander Almutairi (King Saud University)
Constructing all Irreducible Supercuspidal Representations of U(F/F_0)(1,1)

June 24 – Wednesday – 2nd. Week, at 11:00 – 11:30 and 16:00 – 16:30

Manuel Baptista Branco (Universidade de Evora)
The Frobenius Problem for Thabit Numerical Semigroups

Percy Caceres Tintaya (Puc – RJ)
Riemann Hilbert Problem for the Riemann Zeta function

Sankha Banerjee (Birla Institute of Technology, India)
Proof of Khabibillin´s conjecture in terms of increasing function (Conjecture on integral inequality)

Sebastián Herrero Miranda (Puc do Chile)
A converse theorem for Jacobi-Maass forms and applications.

Instructions for Poster Presentation

Due to the size of the poster boards your poster may not exceed 90 cm in width and 120 cm in height (portrait format). Materials for mounting the posters will be available at the poster areas.

Local organizers will provide the necessary materials for the setup, but please remember that there will be no possibility to print out the posters at the conference site.

The title and Author(s) Name(s) must appear on the top of the final poster. The poster should have a balance between the text and illustrations. The illustrations should have a bigger area of the poster. Font size should be large enough to enable reading from a certain distance. It is suggested the following font size:

Title: Size 70 (1,5cm H)
Author(s) Name(s): Size 50 (1cm H)
Text: Size 28 (0,7cm H)

## Program

1st Week – School (June 15-19, 2015)

2nd Week – Conference (June 22-26, 2015)

## Registration and Financial Support

Prices for Registration

 Category Prices Professors (Ph.D´s) R$120,00 Students (Master and Ph.D) R$ 70,00 IMPA’s Students R\$ 40,00

List

## Sponsors:

Postal Address: Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina 110, Jardim Botânico
Rio de Janeiro, RJ, CEP 22460-320, Brasil
E-mail: eventos@impa.br