Charley Cummings

Generation of the derived module category

Given a ring, it can be difficult to know how complicated its representation theory is. One way to measure the complexity is to calculate a numerical invariant of the ring called the finitistic dimension. In the 60s it was conjectured that the finitistic dimension of a finite dimensional algebra is finite; a claim that remains unproven today. At first glance this conjecture looks like a question simply concerning the modules of a ring, however, in 2019, Rickard proved that this conjecture can be reformulated into a question about a generation property of the derived module category. In this talk we will consider this generation property and look at its interaction with various ring constructions including triangular matrix algebras.