Abstract: Given an arbitrary symmetric quiver equipped with a potential, Davison and Meinhardt constructed a natural filtration on the Kontsevich–Soibelman cohomological Hall algebra (CoHA) by exploiting the hidden properness of the semisimplification morphism. The aim of this talk is to describe, in the case of trivial potential, an explicit realization of this filtration in terms of certain limiting conditions on the shuffle algebra. We will then explain how this perspective can be used to conjecturally characterize the BPS Lie algebra of the preprojective algebra, which is known to coincide with the positive half of a generalized Kac–Moody Lie algebra, in terms of wheel and limit conditions.

Lawvere theories are one of many ways to view algebraic theories (e.g. the theories of groups, rings, and real vector spaces) from a category theoretic point of view. In this talk, I will introduce Lawvere theories, then go on to talk about various interesting features they have. I aim to define and explain the concept of Lawvere theory in an accessible way, with only a first course in category theory as a prerequisite; I will after that invoke notions of monads, 2-categories, and Kan extensions. There won't be anything novel in this talk.

For a smooth surface S, the Hilbert scheme of points on S gives a smooth compactification of the configuration space of n distinct points on S. Its cohomology is by now well understood and exhibits deep connections with representation theory. Understanding its quantum cohomology, a deformation of ordinary cohomology involving curve counting invariants, has since received a lot of…

In the study of dualizability of tensor categories, Brochier-Jordan-Snyder observe that the tensor product of two (compact-)rigid monoidal categories may fail to be (compact-)rigid, and hence the collection of such categories fails to form a well-behaved higher category, in which fully extended topological field theories could take values. To remedy this, one weakens the definition of a tensor category and instead requires only rigidity of (compact) projective objects, known as cp-rigidity.

In this talk, I will present some initial structural results for module categories over finite cp-rigid categories, which we term pre-tensor categories, following Décoppet. This includes variants of the standard reconstruction results via algebra and bimodule objects, a description of exact module categories, and, perhaps most importantly, a characterization of pre-tensor categories which are Morita equivalent to (rigid, finite) tensor categories. Higher-categorical applications include a characterization of fully dualizable pre-tensor categories, and of Witt equivalence as equivalence internal to the Morita 4-category of braided tensor categories.

This talk is based on work in progress joint with Thibault Décoppet.

TBA

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Abstract: TBA