Seminars in geometry/topology

Topology Seminar Wednesday 17 August, 14:15 - 15:15, Room F2 Gamle Fysikk

Thomas Nikolaus (University of Münster): K-Theory of Z/p^k and prismatic cohomology

Abstract: We will explain the concept of a prism and of prismatic cohomology following Bhatt- Scholze. We will explain how to extend this notion to a more general setting and how to characterize it by a universal property (relative to so-called generaralized prisms, which are a higher categorical version of prisms). If time permits we explain how to use this to compute K- theory of rings of the form Z/p^n. This is joint work with B. Antieau and A. Krause.

Topology Seminar Wednesday 07 September, 14:15-15:15, 656 Sentralbygg 2

Andrea Gagna (The Czech Academy of Science): Fibrations of higher categories

Abstract: Generalizing classical work of Grothendieck, Lurie showed that (co)cartesian fibrations of simplicial sets over a base ∞-category B are in complete correspondence with functors from B to the ∞-category of small ∞-categories. This correspondence plays a crucial role in higher categories. In this talk I will introduce the notion of (∞, 2)-fibration, that is meant to encode a functor from a small (∞, 2)-category to the (∞, 2)-category of small (∞, 2)-categories, in the spirit of the Grothendieck–Lurie correspondence. I will provide some basic example of such fibrations, list some nice properties they enjoy and motivate their need in derived algebraic geometry.

Topology Seminar Monday 19 September, 14:15-15:15, Room 734 Sentralbygg 2

Drew Heard (NTNU): Cosupport in tensor-triangulated geometry

Abstract: We will give an introduction to the theory of cosupport in tensor-triangulated geometry, dual to the Balmer–Favi notion of support. This gives a method of classifying the colocalizing coideals of a tensor-triangulated category in terms of subsets of its spectrum of prime ideals. We will explain how this recovers and unifies a number of classification theorems in the literature, and give some new examples. This is joint work with Tobias Barthel, Natalia Castellana, and Beren Sanders.

Topology Seminar Monday 10 October, 14:15-15:15, F3 Gamle Fysikk

Martin Frankland (Regina): Multiparameter persistence modules in the large scale

Abstract: A persistence module with \(m\) discrete parameters is a diagram of vector spaces indexed by the poset \(\mathbb{N}^m\). If we are only interested in the large scale behavior of such a diagram, then we can consider two diagrams equivalent if they agree outside of a "negligeable" region. In the 2-dimensional case, we classify the indecomposable diagrams up to finitely supported diagrams. In higher dimension, we partially classify the indecomposable diagrams up to suitably finite diagrams.

Along the way, we classify the tensor closed Serre subcategories of the category of finitely generated \(m\)-parameter persistence modules: they are in bijection with the simplicial complexes on \(m\) vertices. This is joint work with Don Stanley.

Topology Seminar Monday 31 October, 14:15-15:15, F3 Gamle Fysikk

Nima Rasekh (Max Planck): Higher Algebra in non-classical Mathematics

Abstract: In the recent decade we have witnessed a focus on algebraic topological concepts in a variety of mathematical foundations. Examples of this development include homotopy group computations, Blakers-Massey theorem and constructing truncations. However, little progress has been made towards understanding higher algebra in such settings. In this talk I want to discuss various challenges that have hindered the expected development. If time permits I will further explain how broadening our understanding of operads can provide a possible path towards rectifying this situation.

Topology Seminar Wednesday 16 November, 14:15-15:15, B1 Berg

Fernando Abellán García (NTNU): Marked colimits and higher cofinality.

Abstract: In this talk, I will introduce a general class of colimits of (infinity,2)-categories known as marked colimits. After giving some examples we will discuss the notion of cofinality in this context and explain how the conditions of Quillen's Theorem A can be categorified to produce the main result of my thesis: A characterization of cofinal functors of (infinity,2)-categories.

Note the change in date and location. B1 can be found here: https://link.mazemap.com/KSkB63yc

Topology Seminar Monday 28 November, 14:15-15:15, F3 Gamle Fysikk

Torgeir Aambø (NTNU): Algebraicity in monochromatic homotopy theory

Abstract: Chromatic homotopy theory views the category of spectra as certain nicely behaved chromatic layers glued together along formal neighbourhoods — described respectively using Morava E-theory and Morava K-theory. Using Franke’s algebraicity theorem we know that these chromatic layers can be approximated using algebraic information. In this talk we will try to explain these approximations, as well as describe some progress on constructing similar approximations for the formal neighbourhoods.