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Categorical sl2 actions and RoCK blocks, at Sydney, Australia, Wednesday, February 15, 2023:
rock_blocks_and_klrw_algebras.pdf

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It's a well-known theorem of Scopes that if we consider the blocks of FpSm for all m geq 0 with a fixed defect group, they will break into a finite number of Morita equivalence classes. In fact, it was later shown by Chuang and Rouquier that all blocks with a fixed defect group are derived equivalent; from this perspective, one can think of Scopes' theorem as the observation that “most” of Chuang and Rouquier's derived equivalences are induced by Morita equivalences (i.e. are t-exact). I'll discuss how one can...

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The noncommutative Springer resolution of type A and KLRW algebras, at IMS, Singapore, Wednesday, January 11, 2023:
singapore-2023.pdf

Video of the talk

 

The theory of Coulomb branch algebras, based on work of Braverman, Finkel- berg and Nakajima, has shed new light on many interesting algebras in repre- sentation theory. One of the most notable is the universal enveloping algebra of gln. I’ll explain how this theory shows a close relationship between the characteristic p and characteristic 0 representation of gln and the cylindri- cal and planar KLRW algebras, in...

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Coulomb branches and representation theory, at Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification, Northeastern University, Boston, Sunday, June 12, 2022:
us-can-mex-2022.pdf
Coulomb branches of quiver gauge theories are a type of almost commutative algebra arising from 3d quantum field theory.  These include many popular algebras, like universal enveloping algebras, W-algebras and Cherednik algebras of type A.  Realizing these algebras as Coulomb branches emphasizes the role of a commutative subalgebra (generalizing the Gelfand-Tsetlin subalgebra of the universal enveloping algebra), and analyzing the representation theory of these algebras with respect to these commutative subalgebras naturally gives rise to flavoured KLRW algebras.  I'll try to... Read more about Coulomb branches and representation theory

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