This weekly seminar series is part of the Follow-Up Higher Homotopical Structures

Follow Up Higher Homotopical Structures: Weekly Seminar

Below you can find a schedule of seminar talks.

There will be coffee 15 minutes before each talk.

MAY 18TH, 2022 | The W-construction for cubical Feynman categories and moduli spaces

Ralph Kaufmann

Purdue University

ABSTRACT

We discuss a W-construction that is inspired by Boardman-Vogt in the setting of cubical Feynman categories (joint work with B. Ward). Homotopically this yields a cofibrant replacement in a category of functors to topological spaces. Concretely this is given by a cubical complex which in special cases have a combinatorial description. It turns out that particular combinatorics of graphs appear. As a first consequence this allows to construct moduli spaces of curves and various compactifications in an ontologically small setting (joint with C. Berger). An interesting double categorical version of graphs underlies the specific computations. If time permits, we will comment on relations to bi-algebras (joint with I. Gálvez-Carrillo and A. Tonks) and Koszulness (joint with Ward).

From 12:00 to 13:00

Institut de Matemàtica, Universitat de Barcelona (IMUB)

Gran Via de les Corts Catalanes, 585, 08007, Barcelona

MAY 26TH, 2022 | Infinity-operads as analytic monads

Rune Haugseng

NTNU Trondheim

ABSTRACT

I will explain that an infinity-operad in Lurie’s sense can be recovered from its monad for free algebras in spaces, and that this (almost) gives an equivalence between infinity-operads and a certain class of “analytic” monads. This builds on previous joint work with David Gepner and Joachim Kock where we developed the infinity-categorical theory of analytic monads and showed these are equivalent to dendroidal Segal spaces.

From 12:00 to 13:00

Aula C1/028, Centre de Recerca Matemàtica (CRM)

June 1st, 2022 | Coset posets of finite groups

Jesper Møller

University of Copenhagen

ABSTRACT

The coset poset of a finite group is the partially ordered set of cosets of all proper subgroups. Similarly, for a prime p, the p-coset poset is the partially ordered set of all proper p-subgroups. In both cases, the order relation is simply set inclusion. These posets are related to subgroup posets, but they are maybe less well-known. I will review what is known about coset posets and also report on some new results on the Euler characteristic of coset posets. There are fairly explicit results about Euler characteristic of p-coset posets of finite groups of Lie type in characteristic p. In other cases, there are more combinatorial, and much less explicit, expressions for the Euler characteristic.

From 12:00 to 13:00

Aula C1/028, Centre de Recerca Matemàtica (CRM)