Explore advanced mathematical concepts in this comprehensive workshop series covering symmetric tensor categories and their applications in representation theory. Delve into the fundamental properties of tensor categories equipped with braided structures, examining prototypical examples such as finite dimensional representations of affine group schemes. Investigate Deligne's celebrated theorem establishing the equivalence between symmetric tensor categories of moderate growth and super representations of affine supergroup schemes in characteristic zero, while exploring how positive characteristic cases reveal additional symmetries and complexities. Study Verlinde categories as symmetric fusion categories with non-integral dimensions constructed from tilting categories of classical groups, and examine their significance in modern mathematical research. Learn about breakthrough developments providing substitutes for Deligne's theorem in positive characteristic, with applications spanning modular representations of finite groups and Lie superalgebras. Analyze algebraic structures within symmetric categories, including commutative algebras, affine group schemes, and Lie algebras, while exploring categories of super-exponential growth representing classical groups in non-integral rank. Engage with cutting-edge research presentations covering growth and tensor products, exceptional simple Lie superalgebras, vector Delannoy categories, representations in Verlinde categories, oligomorphic groups, braided monoidal categories via Soergel bimodules, Tannakian formalism for stacks, support varieties, stable module categories, symmetric fusion categories in positive characteristic, spin Brauer categories, support varieties for algebraic supergroups, Drinfeld centers, nil-Brauer categories, pre-Galois categories, interpolation categories for finite linear groups, polynomial superfunctors, and the extended Freudenthal magic square. Participate in collaborative discussions and poster sessions designed to foster exchange of ideas among researchers at various career stages working in Hopf algebras, tensor categories, Lie superalgebras, homological algebra, and representation theory.

Syllabus

Daniel Tubbenhauer - Growth and tensor products - IPAM at UCLA
Arun Kannan - Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix
Sophie Kriz - Vector Delannoy categories and further developments - IPAM at UCLA
Alexandra Utiralova - Representations of general linear groups in the Verlinde category
Andrew Snowden - Oligomorphic groups and tensor categories - IPAM at UCLA
Catharina Stroppel - A braided monoidal 2-category via Soergel bimodules - IPAM at UCLA
Kent Vashaw - A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories
Bregje Pauwels - Tannakian formalism for stacks - IPAM at UCLA
Sarah Witherspoon - Support varieties and the tensor product property - IPAM at UCLA
Julia Pevtsova - Stable module category for a finite group scheme over a commutative Noetherian ring
Agustina Czenky - Low rank symmetric fusion categories in positive characteristic - IPAM at UCLA
Alistair Savage - The spin Brauer category - IPAM at UCLA
Vera Serganova - On support variety for algebraic supergroups - IPAM at UCLA
Kevin Coulembier - Symmetric tensor categories of moderate growth - IPAM at UCLA
Eric Friedlander - G-modules: Stable Categories and Subcoalgebras - IPAM at UCLA
Noah Snyder - The Delannoy Category - IPAM at UCLA
Robert Laugwitz - Induced functors on Drinfeld centers via monoidal adjunctions - IPAM at UCLA
Victor Ostrik - Growth in tensor powers - IPAM at UCLA
Jonathan Brundan - The nil-Brauer category - IPAM at UCLA
Nate Harman - Pre-Galois Categories and Discrete Categories - IPAM at UCLA
Thorsten Heidersdorf - Interpolation categories for finite linear groups - IPAM at UCLA
Dmitri Nikshych - Tannakian radical and mantle of a braided fusion category - IPAM at UCLA
Jonathan Kujawa - Support varieties for Lie superalgebras - IPAM at UCLA
Christopher Drupieski - Polynomial superfunctors, applications to and from finite supergroup schemes
Alberto Elduque - The Extended Freudenthal Magic Square via tensor categories - IPAM at UCLA