# Seminars in geometry/topology

## February 25, 13:15 - 14:15, room 734, Sentralbygg 2

**Jarl Gunnar Taxerås Flaten (NTNU): Programming with Category Theory**

**Abstract:** Haskell is a programming language heavily inspired by category theory. We'll start by seeing how basic category theory is represented in this language, before having a deeper look at what monads are and their different uses here. Anyone with some familiarity with algebra is welcome—especially those who don't believe pure mathematics has real, practical uses!

## March 4, 13:15 - 14:15, room 734, Sentralbygg 2

**Viktoriya Ozornova (Ruhr-Universität Bochum): Homotopy theory for 2-categories**

**Abstract:** Grothendieck and Quillen introduced a notion of homotopy equivalences for categories using a by-now-standard tool called "nerve" of a category. This idea leads to various models of categories-up-to-homotopy. In a joint ongoing project with Martina Rovelli, we study variants of the Roberts-Street-nerve for 2-categories and notions of homotopy equivalences arising from this nerve, with an eye towards 2-categories-up-to-homotopy.

## April 1, 13:15 - 14:15, room 734, Sentralbygg 2

**Ambrus Pal (Imperial College London): An arithmetic Yau-Zaslow formula**

**Abstract:** We prove an arithmetic refinement of the Yau–Zaslow formula by replacing the classical Euler characteristic in Beauville’s argument by a variant of Levine’s motivic Euler characteristic. We derive several similar formulas for other related invariants, including Saito’s determinant of cohomology, and a generalisation of a formula of Kharlamov and Rasdeaconu on counting real rational curves on real K3 surfaces. Joint work with Frank Neumann.

## June 4 (!!!Tuesday!!!), 13:15 - 14:15, room 734, Sentralbygg 2

**Antoine Touzé (Université de Lille): Structure and applications of exponential functors**

**Abstract:** Exponential functors are functors from k-vector spaces to k-vector spaces which turn direct sums into tensor products, just as the exterior algebra does. In this talk, we will explain some structure results on these exponential functors, which show that these objects have a rather rigid structure. We will explain on a concrete example how our rigidity results can be used in practical computations of homological nature.

## June 17, 13:15 - 14:15, room 734, Sentralbygg 2

** Joachim Kock, Universitat Autònoma de Barcelona: Infinity operads as polynomial monads**

**Abstract:** I'll present a new model for ∞-operads, namely as analytic monads. In the ∞-world (unlike what happens in the classical case), analytic functors are polynomial, and therefore the theory can be developed within the setting of polynomial functors. I'll talk about some of the features of this theory, and explain a nerve theorem, which implies that the ∞-category of analytic monads is equivalent to the ∞-category of dendroidal Segal spaces of Cisinski and Moerdijk, one of the known equivalent models for ∞-operads. This is joint work with David Gepner and Rune Haugseng.