Title: Deformations of Algebras

Abstract: Deformations of algebras play an important role in combinatorics, representation theory, and noncommutative algebra. For example, the graded affine Hecke algebras of Lusztig, symplectic reflection algebras of Etingof and Ginzburg, and braided Cherednik algebras are examples of deformations of quadratic algebras extended by actions of finite groups. Group actions on Lie algebras provide other examples (we deform the universal enveloping algebra extended by the group). Hochschild cohomology gives a method for investigating and predicting deformations. Over fields of positive characteristic, the group action itself may be deformed to give new deformations of algebras in a way that we do not see over the real or complex numbers.