iTHEMS Math Seminar by Dr. Shigenori Nakatsuka on January 28, 2022
Dr. Shigenori Nakatsuka from Kavli IPMU gave us a talk on dualities in W-superalgebras. In the first half of the talk he reviewed some basic concepts of vertex superalgebras, in particular W-superalgebras, and the Feigin--Frenkel duality, which states that the W-algebras in a certain class are isomorphic to the other W-algebras associated with the dual Lie algebras and the dual levels. In the latter half of the talk he introduced dualities beyond the Feigin--Frenkel duality including his recent work with Creutzig, Genra, and Sato. One of the remarkable results is the proof of the Feigin--Semikhatov conjecture, which gives a correspondence between the W-algebras associated with certain Lie algebras and the W-superalgebras associated with the corresponding Lie superalgebras. His talk was so stimulating that we could enjoy the mathematics of W-algebras.
Reported by Mizuki Oikawa