We usually meet on Tuesdays at 2:30pm in room 319 of the Chase Building. The current organizers are Christopher Dean and Luuk Stehouwer. Information about summer/winter 2025 seminars can be found here.
On a generalization of dagger compact categories
The notion of a dagger compact category combines duals with an involutive dagger functor and provides a categorical setting for operator algebra and quantum theory. The key example of a dagger compact category is that of finite-dimensional Hilbert spaces. On the other hand, the symmetric monoidal category of finite-dimensional super Hilbert spaces is not dagger compact, yet naturally arises in quantum physics when fermions are present. In this talk I will provide a natural generalization of dagger compact categories to arbitrary rigid symmetric monoidal $n$-categories. The goal of this talk is not to overwhelm you with higher categories, but to spell out the definition in the case $n=1$ in full detail. The result will be a mild generalization of a dagger compact category that covers super Hilbert spaces as a special case.DL-closures and 2-3 closures applied to the ring $C^1(R)$.
In joint work with Barr and Kennison it was shown that commutative semiprime rings have a DL-closure and a 2-3 closure and that the ring of continuously differentiable real-valued functons is not closed in either sense. Our work is devoted to trying to describe the two closures of this ring. The methods are analytic often using basic ideas from calculus. A useful example sent by Alan Dow is presented.
Joint work with W. D. Burgess