International Conference in Number Theory and Physics - Mini Course - Conrey - 01

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International Conference in Number Theory and Physics

Mini Course - Prof. Brian Conrey AIM and University of Bristol
Class 1

Random Matrix Theory and statistics of families of L-functions An important subject in number theory today goes by the name of \arithmetic statistics." This course will introduce the notion of a "family" of L-functions and will develop the random matrix tools needed to express detailed theorems and conjectures about the distribution of zeros and values of the L-functions in a family. It will make use of a good mix of techniques from random matrix theory and from analytic number theory to develop the modern theory of family statistics, including the \recipe" and the \ratios conjecture" - which are theorems in random matrix theory and conjectures in number theory. Examples from all three symmetry types - unitary, orthogonal, and symplectic will be considered in detail.


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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

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