Viewing archives for Research School

Aspects of Geometric Group Theory

A group is a mathematical object encoding natural notions of symmetries and transformations. Geometric group theory is an area in mathematics devoted to the study of discrete groups by exploring connections between algebraic properties of such groups and topo- logical and geometric properties of spaces on which these groups act. As a distinct area, geometric group theory is relatively new, and became an identifiable branch of mathematics in the early 1990’s. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, Lie groups and homogeneous spaces, algebraic topology, computational group theory, and differential geometry. There are also substantial connections with complexity theory, mathematical logic, dynamical systems, probability theory, K-theory, and other areas of mathematics.

In this summer school the organizers will choose a few important trends in geometric group theory to teach to graduate students across mathematical fields, giving young people in several areas of mathematics such as algebra, geometry, dynamics, or topology some basics to either understand a few problems in geometric group theory, or use geometric group theory methods in their respective fields. 

CMI Enhancement and Partnership Program

Details

Venue: Institut des Hautes Études Scientifiques (IHÉS)

Thermodynamic Formalism: Applications to Probability, Geometry and Fractals

Thermodynamic formalism is an area of dynamical systems which originated in the 1960s and 1970s with the introduction of ideas of mathematical physics.  In the past few years it has undergone something of a renaissance with applications to many different areas, including Riemannian geometry, microlocal analysis, and analytic number theory.  This is an active area of research which has both intrinsic elegance and useful applications to neighbouring areas.

CMI Enhancement and Partnership Program

Details

Venue: CIRM. Luminy

17th School on Interactions between Dynamical Systems and Partial Differential Equations (JISD 2019)

This annual meeting of experts and young researchers in Dynamical Systems and PDEs is designed to encourage and enhance exchange of knowledge and methods.  Its goal is to advance the study of cutting edge problems and foster interaction among the participants.

CMI Enhancement and Partnership Program

Details

Venue: Centre de Recerca Matemàtica, Barcelona, Spain

Arithmetic Geometry in Carthage

This two week program on arithmetic geometry will focus on a number of areas of important progress over the past three or four years:  p-adic Hodge theory, p-adic Langland program, ramification of étale l-adic sheaves, special values of L functions and automorphic and motivic periods, and conjectures of Deligne, Beilinson, and Gan-Gross-Prasad.  The first week will be devoted to a summer school and the second to a conference.

CMI Enhancement and Partnership Program

Details

Venue: Tunisian Academy Beit al-Hikma, Tunis, Tunisia

PDEs in Mathematical Biology: Modelling and Analysis

This research school offers PhD students and early career researchers the opportunity to acquire detailed knowledge in the rapidly evolving field of modelling/analysis in the biological, ecological, and medical sciences. The school aims to sit at the threshold between modelling and advanced analysis.  The speakers will provide complementary skills and methodologies that cover basic modelling, computation, and advanced theory related to problems spanning areas from ecology to cancer growth.  

The five lecture courses will cover:

Spatio-temporal modelling in biology, by Dagmar Iber (ETH Zürich)
The emergence of spatial segregation patterns from animal movements and interactions, by Jonathan Potts (Sheffield)
Front propagation and singular limits, by Elaine Crooks (Swansea)
Asymptotic analysis in models of tissue growth, by Vincent Colmez (ENS Lyon)
Multiscale modeling of cell migration in fiber networks, by Luigi Presiosi (Politecnico di Torino)

CMI Enhancement and Partnership Program

Details

Venue: ICMS, Edinburgh

Coulomb Gas, Integrability and Painlevé Equations

The aim of this research school is to introduce a new generation of researchers to the various connections between Coulomb gases, determinantal point processes, integrable structures and their relations to special functions, in particular Painlevé equations.

CMI Enhancement and Partnership Program

Details

Venue: CIRM, Luminy

Arizona Winter School 2019

The Arizona Winter School is an intensive five-day-long school in which advanced graduate students work closely with senior faculty and postdoctoral fellows. In contrast to a typical conference at which individual researchers present their work in relative isolation, the AWS features a small number of extended courses on a set of closely related topics. The organizers work hard to ensure significant interaction among all participants. Each speaker is assigned a group of students who work with him or her and a postdoctoral assistant on a research project during the Winter School. These students present the results of their research in a lecture at the end of the meeting. Other students work with a postdoctoral assistant in a problem session related to one or more of the lecture series. Still other students work in study groups, carefully learning the material from one the lecture series together. To facilitate work on the projects, problems, and study groups, speakers, assistants, and students meet in evening working sessions.

The 2019 AWS will be held on the topic of Topology and Arithmetic, exploring the boundary of higher homotopy theory and artithmetic geometry.  

CMI Enhancement and Partnership Program

Details

Venue: University of Arizona

Arizona Winter School 2020

The Arizona Winter School is an intensive five-day-long school in which advanced graduate students work closely with senior faculty and postdoctoral fellows. In contrast to a typical conference at which individual researchers present their work in relative isolation, the AWS features a small number of extended courses on a set of closely related topics. The organizers work hard to ensure significant interaction among all participants. Each speaker is assigned a group of students who work with him or her and a postdoctoral assistant on a research project during the Winter School. These students present the results of their research in a lecture at the end of the meeting. Other students work with a postdoctoral assistant in a problem session related to one or more of the lecture series. Still other students work in study groups, carefully learning the material from one the lecture series together. To facilitate work on the projects, problems, and study groups, speakers, assistants, and students meet in evening working sessions.

The 2020 AWS will be held on the topic of Non-Abelian Chabauty.  

CMI Enhancement and Partnership Program

Details

Venue: University of Arizona

Enumerative Geometry, Physics and Representation Theory

The main theme of this summer school is enumerative geometry with particular emphasis on connections with mathematical physics and representation theory.  Lecturers will focus on some of the main ideas and themes in the field, including Gromov-Witten theory and the study of moduli spaces of curves, Donaldson-Thomas/Pandharipande-Thomas theory and the study of moduli spaces of sheaves on threefolds, and the mathematical study of Coulomb and Higgs branches of quantum field theories (particularly with a representaiton theoretic flavor).  The school  will also cover subjects that have only recently been connected to enumerative geometry, such as the representation theory of quivers, cohomological/K-theoretic Hall algebras and categorified link invariants.

Image: Wikimedia Commons

CMI Enhancement and Partnership Program

Details

Venue: Institut des Hautes Études Scientifiques (IHÉS)

VIASM-ICTP Summer School in Group Theory and Representation Theory

The goal of this school is to introduce graduate students, advanced undergraduate students, young researchers, and interested mathematicians to basics of group representation theory, linear algebraic groups, structure and representation theory of finite groups of Lie type, including an introduction to the Deligne-Lusztig theory. It will also introduce the audience to a number of applications of group representation theory to various areas of mathematics including number theory, algebraic geometry, and combinatorics.

Professor Martin Liebeck (Imperial) will give the Clay Lecture at this two-week graduate summer school.

CMI Enhancement and Partnership Program

Details

Venue: Vietnam Institute for Advance Study in Mathematics, Hanoi

Elliptic Curves Graduate School

The aim of the school is to give an overview of established results and current research on elliptic curves by covering the whole spectrum of techniques developed so far. There will be 6 courses of 3 hours each plus exercises sessions.

  • Analytic Methods – Alina Cojocaru
  • Arithmetic Statistics – Jennifer Park
  • Modularity-based Methods – Chao Li
  • Points and Heights – Joseph Silverman
  • Selmer Groups – Christian Wuthrich
  • Torsion Points – Jan Vonk

CMI Enhancement and Partnership Program

Details

Venue: Baskerville Hall

IHÉS Summer School on the Langlands Program

It has been almost 45 years since the influential 1977 summer school held in Corvallis, Oregon, brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.

Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.

The summer school will attempt to bring these exciting new directions together and explore their interactions.

CMI Enhancement and Partnership Program

Details

Venue: Institut des Hautes Études Scientifiques