Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
Fusion 2-categories are a higher categorical analog of fusion categories that have gained a lot of attention in the last years because of their importance in many fields of math and physics, such as TQFTs, condensed matter physics and high energy physics. The classifiction of fusion (1-) categories is a very active research area and has provided new examples and led to the development of new invariants and tools to understand these categories.
In this talk, we will present a parametrization of multifusion 2-categories in terms of lower categorical data, involving braided fusion categories, group theory, and cohomological data. If time allows, we will also show some applications of this result. This is a joint work in with T. Décoppet, T. Johnson-Freyd, P. Huston, D. Nikshych, D. Penneys, D. Reutter, and M. Yu.
Across the multitude of definitions for a higher category, a dividing line can be found between two major camps of model. On one side lives the ‘algebraic’ models, like Bénabou’s bicategories, tricategories following Gurski and the models of Batanin and Leinster, Trimble and Penon. On the other end, one finds the ‘non-algebraic’ models, including more homotopy-theoretic ones like quasicategories, Segal n-categories, complete n-fold Segal spaces and more. The bridges between these models remain somewhat mysterious. Progress has been made in certain instances, as seen in the work of Tamsamani, Leinster, Lack and Paoli, Cottrell, Campbell, Nikolaus and others. Developing comparisons between these forms of higher category has relevance to topological quantum field theories in relating the work done on fully extended TQFTs using homotopy theoretic models of higher category, such as Lurie's proof-sketch of the Cobordism Hypothesis conducted using n-fold Segal spaces, and the large body of work on extended TQFTs using algebraic models of higher category, such as symmetric monoidal bicategories.
Nonetheless, the correspondence remains incomplete; indeed, for instance, there is no fully verified means in the literature to take an 'algebraic’ homotopy n-category of any known model of $(\infty, n)$-category for general n. One might see this as an extension of the fundamental n-groupoid of a homotopy type, a statement I will make precise. In this talk, I will explore current work in the problem of taking homotopy bicategories of non-algebraic $(\infty, 2)$-categories, including a construction of my own. If time permits, I will discuss the connections of this problem to topological quantum field theories.
