Speaker: Valerii Sopin (SIMIS)
Host: Veronica Pasquarella
Time: 14:00, Wednesday, Jun. 4, 2025
Location: R1210, SIMIS
Zoom Meeting ID: 88027894883 (Passcode 294343)
Abstract: The triplet vertex operator algebra for coprime integers is defined as the intersection of the kernel of two screening operators acting on a rank 1 lattice vertex operator algebra. We present a new construction of the triplet algebra using a tensor category of representations of the universal Virasoro VOA. The construction also uses the correspondence between vertex operator algebra extensions and commutative algebras in braided tensor categories due to Huang–Kirillov–Lepowsky. A byproduct of the construction is an obvious action of PSL_2 on the triplet algebra by automorphisms. In another words, the brand new construction of triplet algebras discovers a way toward W-algebras (the opposite direction to the Peter-Weyl theorem) and Geometric Langlands correspondence (via fusion rings). This talk is based on joint work with my Ph.D. advisor Robert McRae.
Introduction to the speaker: Valerii Sopin is currently a Postdoctoral Researcher at SIMIS. He completed his PhD in Mathematical Sciences in Tsinghua University in 2024, under the supervision of Professor Robert Mc Rae. His main area of research is representation theory and category theory.
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