Professor Anne Shepler invites you to attend the Doctoral Defense of Colin Lawson

WHEN: Wednesday, March 22, 2023

1:00pm in GAB 464

"Hochschild Cohomology of Finite Cyclic Groups Acting on Polynomial Rings"

ABSTRACT:

Hochschild cohomology records information about the deformations of a given algebra. For a finite cyclic group acting on a polynomial ring, we consider the semidirect product algebra (or skew group algebra) over a field of arbitrary characteristic and investigate the Hochschild cohomology. Many families of algebras arise as deformations of skew group algebras, such as symplectic reflections algebras and rational Cherednik algebras. In this defense, we give an explicit description of the Hochschild cohomology governing the graded deformations of skew group algebras for finite cyclic groups acting on polynomial rings. For skew group algebras, a description of the Hochschild cohomology is known in the nonmodular setting (i.e., when the characteristic of the field and the order of the group are coprime). However, in the modular setting (i.e., when the characteristic of the field divides the order of the group), much less is known as techniques commonly used in the nonmodular setting are not available.

Cake and coffee will be served in GAB 472 following this event.