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Upcoming Summer Graduate Schools

  1. Commutative Algebra and Related Topics

    Organizers: LEAD Shihoko Ishii (Tokyo Woman's Christian University), Kazuhiko Kurano (Meiji University), Ken-ichi Yoshida (Nihon University)

    The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research. 

    Updated on Aug 18, 2016 04:12 PM PDT
  2. Subfactors: planar algebras, quantum symmetries, and random matrices

    Organizers: LEAD Scott Morrison (Australian National University), Emily Peters (Loyola University), Noah Snyder (Columbia University)

    Subfactor theory is a subject from operator algebras, with many surprising connections to other areas of mathematics. This summer school will be devoted to understanding the representation theory of subfactors, with a particular emphasis on connections to quantum symmetries, fusion categories, planar algebras, and random matrices

    Updated on Aug 12, 2016 09:16 AM PDT
  3. Soergel Bimodules

    Organizers: LEAD Benjamin Elias (University of Oregon), Geordie Williamson (Max-Planck-Institut für Mathematik)

    We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra. We will give a comprehensive introduction to the "tool box" of modern (higher) representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory.

    Updated on Aug 18, 2016 04:30 PM PDT
  4. Séminaire de Mathématiques Supérieures 2017: Contemporary Dynamical Systems

    Organizers: Sylvain Crovisier (Université de Paris VI (Pierre et Marie Curie)-Université de Paris XI (Paris-Sud)), LEAD Konstantin Khanin (University of Toronto), Andrés Navas Flores (University of Santiago de Chile), Christiane Rousseau (Université de Montréal), Marcelo Viana (Institute of Pure and Applied Mathematics (IMPA)), Amie Wilkinson (University of Chicago)

    The theory of dynamical systems has witnessed very significant developments in the last decades, includi​n​g the work of two 2014 Fields medalists, Artur Avila and Maryam Mirzakhani. ​The school will concentrate on the recent significant developments in the field of dynamical systems and present some of the present main streams of research. Two central themes will be those of partial hyperbolicity on one side, and rigidity, group actions and renormalization on the other side.​ ​Other themes will ​include homogeneous dynamics and geometry and dynamics on infinitely flat surfaces (both providing connections to the work of Maryam Mirzakhani), topological dynamics, thermodynamical formalism, singularities and bifurcations in analytic dynamical systems.  

    Updated on Aug 17, 2016 03:34 PM PDT
  5. Positivity Questions in Geometric Combinatorics

    Organizers: Eran Nevo (Hebrew University), Raman Sanyal (Freie Universität Berlin)

    McMullen’s g-Conjecture from 1970 is a shining example of mathematical foresight that combined all results available at that time to conjure a complete characterization of face numbers of convex simple/simplicial polytopes. The key statement in its verification is that certain combinatorial numbers associated to geometric (or topological) objects are non-negative. The aim of this workshop is to introduce graduate students to selected contemporary topics in geometric combinatorics with an emphasis on positivity questions. It is fascinating that the dual notions of simple and simplicial polytopes lead to different but equally powerful algebraic frameworks to treat such questions. A key feature of the lectures will be the simultaneous development of these algebraic frameworks from complementary perspectives: combinatorial-topological and convex-geometric.  General concepts (such as Lefschetz elements, Hodge–Riemann–Minkowski inequalities) will be developed side-by-side, and analogies will be drawn to concepts in algebraic geometry, Fourier analysis, rigidity theory and measure theory. This allows for entry points for students with varying backgrounds.  The courses will be supplemented with guest lectures highlighting further connections to other fields.

    Updated on Aug 18, 2016 04:35 PM PDT
  6. Automorphic Forms and the Langlands Program

    Organizers: LEAD Kevin Buzzard (Imperial College, London)

    The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.

    Updated on Aug 18, 2016 04:44 PM PDT