# Seminars in geometry/topology

## Topology Seminar 6 October, 14:15 - 15:15, Zoom & Sentralbygg 2, Room 656

**Luciana Basualdo Bonatto (University of Oxford, UK): Decoupling monoids of configurations on surfaces **

**Abstract:**
The monoid of oriented surfaces with one boundary component has featured prominently in the works of Miller and Tillmann, and has been essential to understanding the Mumford conjecture. On another direction, Segal's monoid of configurations in euclidean space originated a branch of scanning results. In this talk, we are going to discuss a combination of these and look at the monoid of configurations on oriented surfaces. More than being a model for the monoid of punctured surfaces, this allows us to look at configurations with labels and even with collision rules. We will show that the group completion of this monoid does not detect that the points in the configurations are constrained to the surface: it simply sees surfaces and particles in the infinite euclidean space. In other words, the particles get decoupled and this group completion splits as a product of the well known spaces originated from the surface and Segal's monoids.

## Topology Seminar 11 October (Monday), 14:15 - 15:15

**Drew Heard (NTNU): Classifying subcategories of tensor-triangulated categories **

**Abstract:** We will give an introduction to some of the basic ideas of the theory of tensor-triangulated geometry (tt-geometry), as developed by Balmer and others. We will discuss the problem of tt-classification; that is, attempting to classify objects in a category up to the tensor-triangulated structure available.

## Topology Seminar 27 October, 14:15 - 15:15, Sentralbygg 2 Room 734 & Zoom

**Simon Rea (University of Southampton, UK): Homotopy types of PU(p)-gauge groups**

**Abstract:**
Akira Kono proved in 1991 that there are precisely six homotopy types of gauge groups
of principal SU(2)-bundles over \(S^4\). Over the past three decades, several analogous results
have been obtained. We will examine the underlying strategy and methods that these results
have in common. We will then focus on how PU(n)-gauge groups over spheres are related
to the more well-studied SU(n)-gauge groups over spheres.

## Topology Seminar 10 November, 14:15 - 15:15, Sentralbygg 2 Room 656 & Zoom

**Magdalena Kedziorek (Radboud University, Netherlands): Equivariant commutativity**

**Abstract:** In this talk I will discuss different flavours of commutativity in the world of topological objects equipped with G-actions, where G is a finite group. I will also indicate how these flavours simplify when we investigate cohomology theories with rational coefficients. I will finish with a very special example of complex K-theory - this is joint work with A.M. Bohmann, C.Hazel, J.Ishak and C.May.

## Topology Seminar 17 November, 14:15 - 15:15, Sentralbygg 2 Room 734 & Zoom

**Sebastian Martensen (NTNU): Things to make and do in n-angulated categories**

**Abstract:** The stable homotopy category has many nice properties, some of which originally inspired the axiomatic of triangulated categories. In these general triangulated categories, however, we can only work from the axioms, so this prompts us to think about what can actually be said of these categories in general. In 2012, Geiss, Keller, and Oppermann introduced a generalisation of triangulated categories, namely the so-called n-angulated categories, and today we are working to see what this axiomatic allows for; specifically, which results of triangulated categories transfer to this more general setting. In this talk, I will convey some of the thoughts and results that we have come across so far.

## Topology Seminar 24 November, 14:15 - 15:15, Sentralbygg 2 Room 734 & Zoom

**Paul Trygsland (NTNU): Combinatorial models for topological Reeb spaces**

**Abstract:**
I will share some ideas from my recent arXiv posting "Combinatorial models for topological Reeb spaces". Fix a real-valued function f from a topological space X to \(\mathbb{R}\). We propose to study homotopic properties provided by f utilising its sections. The sections of f assemble into a topological category, which we refer to as the section category. We can often recover the homotopy type of X as the classifying space of the section category, but this requires f to be sufficiently 'nice'. Counter-examples will be provided to motivate the class of 'nice' functions we choose to work with. I will briefly explain two applications: homology computations and Reeb graphs/topological Reeb spaces.

## Topology Seminar 1 December, 14:15 - 15:15, Sentralbygg 2 Room 734 & Zoom

**Eiolf Kaspersen (NTNU): From complex cobordism to singular cohomology**

**Abstract:**
I will give an overview of several methods which can be used to study the Thom homomorphism from the complex cobordism of a space to its singular cohomology. This will include a look at Brown-Peterson cohomology, complex bordism and the Atiyah-Hirzebruch spectral sequence, with the goal of proving that for a finite cell complex, the Thom homomorphism is an isomorphism in dimensions \(\leq 2\) and injective in dimensions \(\leq 4\).

## Topology Seminar 8 December, 13:15 - 14:15

**Sebastian Wolf (Regensburg): Condensed mathematics and exodromy**

**Abstract:**
We will give a brief introduction to the language of condensed/pyknotic mathematics, which provides a way of keeping track of topological structures in homotopical or homological settings. We will then explain how this language can be used in order to improve the exodromy (=monodromy for exit paths) theorems of Barwick, Glasman and Haine in algebraic geometry.

## Topology Seminar 15 December, 14:15 - 15:15, Zoom

**Trygve Poppe Oldervoll (NTNU): Nearby Lagrangians and generating functions**

**Abstract:** This talk will be about Arnold's Nearby Lagrangian conjecture
in symplectic topology. I will give an introduction to the subject, and then
motivate the technique of generating functions as a finite dimensional reduction of the underlying infinite dimensional variational principles.
I will discuss a certain variation on this technique which is employed in a recent paper by T.Kragh and M.Abouzaid, and show how this relates to
Bott periodicity in real K-theory.