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Fourth Latin American School on Algebraic Geometry and its Applications (ELGA IV)

The Escuela Latinoamericana de Geometría Algebraica (ELGA) series of schools quickly became a major event for algebraic geometry in Latin America, serving as a meetng point for the whole community.  The goal of this fourth edition is again to bring together experts in algebraic geometry to present different topics of current research to advanced graduate students, post docs and early career researchers.  The school will offer five main courses by Jean-Pierro Demailly (Grenoble Alpes), Igor Dolgachev (Michigan), Angela Ortega (Humboldt), Vincent Pilloni (ENS Lyon), and Claire Voisin (Collège de France).  There will also be several survey lectures on a wide range of themes in algebraic geometry and its applications, as well as a series of research talks given by young researchers.

Image: Felipeutal, Wikimedia Commons

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Venue: Universidad de Talca, Chile

Summer School in Semiclassical Analysis

The aim of this summer school is to offer a complete course in semiclassical analysis to students and post docs unfamiliar with these tools, giving a thorough introduction with full technical detail in the core of the subject.  Alongside the main course, there will be courses offering background information for students with less preparation and courses on cutting-edge applications of semiclassical methods in a variety of areas of pure and applied mathematics.  During the first week a course in mathematical quantum mechanics will provide some historical context and physical intuition for the ideas of semiclassical analysis, while a concurrent course in Fourier analysis and distribution theory will ensure that all participants are proficient with these essential tools.  Weeks two and three will offer more sophisticated topics courses, featuring applications of semiclassical methods in scattering theory and eigenfunction asymptotics.

Image:  Madcoverboy at English Wikipedia

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Venue: Northwestern University

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. 

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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.

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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.

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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.

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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)

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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.

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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.  

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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.  

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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

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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.

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Venue: Vietnam Institute for Advance Study in Mathematics, Hanoi