Mathematical Sciences Research Institute

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Summer Graduate School

Representation stability June 24, 2019 - July 05, 2019
Parent Program: --
Location: MSRI: Simons Auditorium, Atrium
Organizers Thomas Church (Stanford University), LEAD Andrew Snowden (University of Michigan), Jenny Wilson (Stanford University)
An illustration of an adaptation of Quillen's classical homological stability spectral sequence argument

This summer school will give an introduction to representation stability, the study of algebraic structural properties and stability phenomena exhibited by sequences of representations of finite or classical groups -- including sequences arising in connection to hyperplane arrangements, configuration spaces, mapping class groups, arithmetic groups, classical representation theory, Deligne categories, and twisted commutative algebras.  Representation stability incorporates tools from commutative algebra, category theory, representation theory, algebraic combinatorics, algebraic geometry, and algebraic topology. This workshop will assume minimal prerequisites, and students in varied disciplines are encouraged to apply. 

Suggested prerequisites:
Students should have at a minimum familiarity with one of the following broad topics, and ideally at least 2. (But more than that is not necessary, and we certainly do not expect any student to be familiar with all of them!)

  • Representations of fi nite groups over C and the classifi cation of Sn-irreps 2
  • Commutative algebra (Noetherian rings, tensor product, free resolutions)
  • Gröbner bases
  • Representation theory of GLnC
  • Homological algebra (Tor, Ext, derived functors)
  • Topology (homology and cohomology of spaces and/or groups)
  • Symmetric functions

For eligibility and how to apply, see the Summer Graduate Schools homepage

Keywords and Mathematics Subject Classification (MSC)
  • Representation stability

  • Representation theory

  • homological stability

  • functor categories

  • Gröbner methods

  • Noetherian

  • group cohomology

  • Schur-Weyl duality

  • twisted commutative algebra

  • FI-module

  • VI-module

  • VIC-module

  • pure braid groups

  • hyperplane arrangements

  • mapping class groups

  • Moduli space

  • Torelli groups

  • configuration spaces

  • congruence subgroups

  • Deligne categories

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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