Viewing archives for CMI-LMS Research School

Microlocal Analysis and Applications

Lecture Courses:

1 ) Alexander Strohmaier (University of Leeds) & Jared Wunsch (Northwestern University)
Basic ideas in microlocal analysis 

2 ) Stéphane Nonnenmacher (Université Paris-Sud, Orsay) & Andrew Hassell (Australian National University)
Spectral and scattering theory

3 ) Viviane Baladi (CNRS, Institut de Mathématiques de Jussieu,  UPMC) & Colin Guillarmou (CNRS, Université Paris-Sud, Orsay)
Pollicott-Ruelle resonances, mixing in dynamical systems, and x-ray transforms

Each course will be 4 to 5 hours long, with 1 to 2 hours tutorials.

Distinguished Lectures:

Mark Pollicott (University of Warwick)
Hyperbolic dynamical systems

Gunther Uhlmann (University of Washington, Seattle)
Inverse problems

Nicolas Burq (Université Paris-Sud, Orsay)
Spectral theory and scattering theory

These lectures will be one hour each.

CMI-LMS Research Schools aim to introduce the brightest young mathematicians in the world to active and important areas of research through lectures by international leaders, as well as to help establish these participants as future leaders in their own research communities.

Details

Venue: Cardiff University

New Trends in Representation Theory

The focus is on recent advances that have emerged in representation theory through cluster theory: n-representation theory, integrable systems and friezes, and silting and infinite dimensional representations. These areas of mathematics are enriched by their interactions with other areas of mathematics such as category theory, dynamical systems and mathematical physics.

Details

Venue: University of Leicester

New Trends in Analytic Number Theory

Analytic number theory is the branch of mathematics in which ideas and methods of real and complex analysis are brought to bear on problems about integer numbers.  In particular, analytic techniques have led to major advances in number theory and helped to solve several important and difficult questions about integers.  In the last few years, analytic number theory has flourished and we have seen an upsurge of activity worldwide related to analytic number theory, prime number theory, and solutions to equations.

This CMI-LMS research school will focus on three major advances that have emerged in the last few years:  prime number theory, number theory in function fields, and the Hardy and Littlewood Circle Method and Diophantine Geometry.  Several recent results in these areas represent new trends in analytic number theory and the lecture courses aim to offer a gentle introduction to these exciting developments. 

Pretentiousness in Analytic Number Theory
Lecturer:  Andrew Granville (UCL)

Topics in Classical Analytic Number Theory
Lecturer: Steve Gonek (Rochester)

Number Theory in Function Fields
Lecturers: Jon Keating (Bristol) and Zeev Rudnick (Tel Aviv)

Hardy and Littlewood Circle Methods and Vinogradov’s Mean Value Theorem
Lecturer: Trevor Wooley (Bristol)

To complement the mini-courses, there will be guest lectures from Chris Hughes (York), James Maynard (Oxford), Damaris Schindler (Utrecht) and Caroline Turnage-Butterbaugh (Duke).

Details

Venue: University of Exeter

Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects

The focus of this CMI-LMS research school is on three major advances that have emerged lately in the interface between homotopy theory and arithemic:  cohomological methods in intersection theory, with emphasis on motivic sheaves; homotopical obstruction theory for rational points and zero cycles; and arithmetic curve counts using motivic homotopy theory.  The emergence of homotopical methods in arithmetic represents one of the most important and exciting trends in number theory, and the lectures will give a gentle introduction to this highly technical area. 

The three main lecture course topics are:

Cohomological methods in intersection theory
Lecturer: Denis-Charles Cisinski (Regensburg)
Assistant: Chris Lazda (Amsterdam)

Homotopical manifestations of rational points and algebraic cycles
Lecturer: Tomer Schlank (HUJ)
Assistant: Ambrus Pal (Imperial)

Arithmetic enrichments of curve counts
Lecturer: Kirsten Wickelgren (Georgia Tech)
Assistant: Frank Neumann (Leicester)

The lecture courses will be supplemented by tutorial sessions and guest lectures by Paul Arne Østvær (Oslo), Jon Pridham (Edinburgh) and Vesna Stojanovska (Illinois at Urbana-Champaign)

Image:  Wikimedia Commons, Man vyi

CMI Enhancement and Partnership Program

Details

Venue: Imperial College London