This award is concerned with the representations of reductive groups in prime characteristic and of related infinitesimal groups, as well as of quantum groups at a root of unity. The principal investigator will investigate construction of graded structures on representation categories of restricted Lie algebras and their quantum analogues; explicit bounds for the truth of Lusztig's conjecture and investigation of its failure for small primes; applications of deformation categories to get more precise information on endomorphism algebras and projective functors; and cohomology varieties for higher Frobenius kernels and their quantum analogues. A group is an algebraic structure with an operation defined on it. A group is called an algebraic group if its elements satisfy a polynomial identity. Algebraic groups are important for several different areas of mathematics, as well as physics.
