TopICS

The Topology Intercity Seminar (TopICS) is joint between Utrecht Universiteit, Radboud Universiteit Nijmegen, and Vrije Universiteit Amsterdam. Below you can find the abstracts from the 2025/26 academic year. Steffen Sagave maintains a list covering other years – you can find it here. If you want to be notified about upcoming seminars, you can subscribe to the mailing list. 

Sessions:

TopICS, Friday 27th February 2026 

Location & time: Nijmegen Huygensgebouw, Room: HG00.616 from 13:30 to 17:30 on 27th February.

Speakers and Time:

Maxime Wybouw (RU) 

Time: 13:30 to 14:30

Title : Homotopy transfer and minimal models 

Abstract: A classic result by Kadeishvili establishes that the algebraic structure

of an associative dg algebra can be fully transferred to a "minimal" A∞​

structure on its homology. This is known as the homotopy transfer

theorem. In this talk, I'll discuss this theorem and some of its

generalisations, such as those that apply to commutative and derived

homotopy structures. A key tool for these extensions involves working

with diagrams of chain complexes indexed by finite sets and injections.

This approach allows us to generalise the transfer process to a wider

range of algebraic settings. 

Georg Lehner (Münster) 

Time: 15:00 to 16:00

Title: Algebraic K-theory of stably compact spaces

Abstract: Recent advances by Efimov, Lurie, Clausen, Nikolaus, and others have made it possible to extend algebraic K-theory, originally defined for small stable categories, to the broader class of so-called dualizable categories. These include categories of sheaves on locally compact Hausdorff spaces, which play a role analogous to C*-algebras of continuous functions. This perspective enables a transfer of techniques between operator-theoretic K-theory and algebraic K-theory and provides a promising new framework for understanding assembly conjectures such as the Farrell–Jones and Baum–Connes conjectures.

There is a larger class of spaces, called stably locally compact spaces, which includes locally compact Hausdorff spaces as well as spectra of rings, for which the associated categories of sheaves remain dualizable. The category of stably locally compact spaces is particularly well suited to analysis: analogues of Tychonoff’s theorem and the Urysohn lemma hold in this setting. We give a formula for the algebraic K-theory of stably locally compact spaces that not only generalizes the corresponding formula for locally compact Hausdorff spaces, but also recovers the additivity theorem and the vanishing of K-theory for sheaves with singular support as special cases.

Christoph Winges (Regensburg)

Time: 16:30 to 17:30

Title: Localisation theorems in algebraic K-theory

Abstract:  One of the key structural properties of algebraic K-theory is the existence of localisation sequences associated to certain exact sequences of input categories. Going beyond the case of stable categories, there is a number of seemingly disparate localisation results in the literature, including Quillen's localisation theorem for abelian categories, Schlichting's localisation theorem for exact categories, and (somewhat in disguise) Barwick's theorem of the heart. After surveying these results, I will explain how they are all consequences of a single more general localisation theorem. If time permits, I will also touch on the question to which extent my joint work with Ramzi and Sosnilo puts natural restrictions on further generalisations of this localisation theorem. 

TopICS, Friday 30th January 2026 

Location & time: VU, NU Gebouw, Floor 9, Maryam 13:30 – 17:30

Speakers and Time:

Guy Boyde (VU Amsterdam) 

Time: 13:30 to 14:30

Title : Planar loops and Temperley--Lieb algebras

Abstract: Temperley--Lieb algebras are a family of associative algebras which arose independently in statistical physics (where they solve various counting problems on planar lattices) and knot theory (where they appear in the original definition of the Jones polynomial). More recently, they became one of the first and most important examples of algebras exhibiting homological stability (in a sense I'll explain) in work of Rachael Boyd and Richard Hepworth. Little was known about the remaining homology (i.e. "beyond the stable range"), but we now know that it is describable, highly structured, and interesting in its own right (in a way that has something to do with the planar loops in the title). This is joint work with Rachael Boyd, Oscar Randal-Williams, and Robin Sroka.

Julie Rasmusen (University of Warwick)

Time: 15:00 to 16:00

Title and Abstract: THR of Poincaré ∞-categories

Abstract: In recent years, work by Calmés–Dotto–Harpaz–Hebestreit–Land–Moi–Nardin–Nikolaus–Steimle has moved the theory of Hermitian K-theory into the framework of stable ∞-categories. I will introduce the basic ideas and notions of this theory, but as it is often the case when working with K-theory in any form, this can be very hard to describe. I will therefore introduce a tool which might make our life a bit easier: Real Topological Hochschild Homology. I will explain the ingredients that goes into constructing in particular the geometric fixed points of this as a functor, generalising the formula for ring spectra with anti-involution of Dotto–Moi–Patchkoria–Reeh. 

Natalia Castellana (Universitat Autònoma de Barcelona)

Time: 16:30 to 17:30

Title: Conservative geometric functors via purity 

Abstract: A tensor-triangulated (tt) functor f between rigidly-compactly generated tt-categories is called geometric if it preserves small coproducts. Such functors serve as auxiliary tools for understanding geometric properties of the source via those of the target. A particularly desired property of a geometric functor is conservativity. This property has strong consequences at the level of triangular spectra.  We establish a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories. We apply it to two particular situations involving sequencial limits of ring spectra. This is joint work with Juan Omar Gómez.

TopICS Friday 21st November 2025

Location and Time: David de Wiedgebouw, Room DDW 0.42 from 13:30 to 17:30 on 21st November.

Marco Nervo (Utrecht Universiteit): 

Title: A model for the Goodwillie tower of the circle

Time: 13:30 to 14:30

Abstract:

Computing the homotopy groups of spheres is a central problem in homotopy theory, and remains extremely difficult in the unstable setting. Goodwillie calculus offers a way to approximate spheres by spaces that agree with them on homotopy groups within a certain range. By making functorial a fiber sequence due to Gray, I will describe how each k-th approximation of a sphere can be expressed in terms of the (k–1)-st approximations together with the k-th approximation of the circle. To complete this inductive picture, I will present an explicit model for the k-th approximation of the circle, building on the work of Behrens and Kuhn on the Whitehead conjecture. I will also give examples of computations and discuss possible directions for further development.

Connor Malin (MPIM Bonn): 

Title: Some $k$-nilpotent algebras arising in the Goodwillie calculus of spaces

Time: 15:00 to 16:00
 

Abstract: 

Given a pointed space $X$, Quillen demonstrated that the Lie algebra of primitive elements of the cocommutative Hopf algebra $C_\ast(\Omega X; \mathbb{Q})$ records the rational homotopy type of $X$. Using deformation theory of operads, we produce a cocommutative Hopf algebra for which the underlying algebra is $k$-nilpotent and describe when this allows us to recover the Goodwillie approximation $P_k(F)(X)$. By generalizing to iterated loop spaces, we are able to construct a $k$-nilpotent formal Lie algebra, in the sense of Shi, which encodes the same data. We conjecture that the grouplike elements and Maurer-Cartan elements, respectively, recover the so-called fake Goodwillie approximations $P_k^\mathrm{fake}(\mathrm{Id})(\Omega X),P_k^\mathrm{fake}(\mathrm{Id})(X)$.

William Balderrama (University of Bonn): 

Title: Unstable synthetic deformations

Time: 16:30 to 17:30

Abstract:

Homotopical structure can often be viewed as deforming algebraic structure. For example, the Postnikov tower of a connective ring spectrum R interpolates between the spectrum R and its 0th homotopy ring. Each map in this tower is a square-zero extension; this realizes R as a "nilpotent thickening" of π_0(R), and leads to a deformation theory for lifting algebraic things over π_0(R) to homotopical things over R.

I will talk about joint work with Piotr Pstrągowski that develops a nonabelian generalisation of this, where connective ring spectra are replaced by certain higher algebraic theories. This provides further insight into Blanc-Dwyer-Goerss' style decompositions of moduli spaces in homotopy theory. Time permitting, I will sketch how this allows us to define categories of synthetic spaces, categorifying the unstable Adams spectral sequence.

TopICS Friday 31st October 2025

Location and Time: Nijmegen Huygensgebouw, Room: HG00.303 from 13:30 to 17:30 on 31st October.

Steffen Sagave (Radboud Universiteit):  

Title: Logarithmic Topological Cyclic Homology.

Time: 13:30 to 14:30

Abstract: Forming the fraction field of an integral domain is a classical construction in algebra. The generalization of this notion to structured ring spectra is less obvious because inverting all non-zero homotopy classes often leads to a too drastic localization. For the connective complex topological K-theory spectrum and the connective Adams summand, computations by Ausoni and Rognes suggest that a fraction field may be realized as a logarithmic ring spectrum with logarithmic structure generated by a given prime and the Bott element. In this talk, I will introduce logarithmic ring spectra, their topological Hochschild homology, and their topological cyclic homology, and I will show how localization sequences for these theories help to identify a good candidate for a fraction field of topological K-theory spectra. 

This is report on joint work in progress with John Rognes and Christian Schlichtkrull. 

Luca Pol (MPIM Bonn):

Title: New Phenomena in the tt-geometry of global representations.

Time: 15:00 to 16:00

Abstract:  A global representation over a field is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups U. Global representations assemble into an abelian category AU which simultaneously generalizes classical representation theory and the category of VI-modules appearing in the representation theory of the general linear groups. The derived category of global representations D(U) is an example of a non-rigid compactly generated tensor-triangulated category, which is known to be equivalent to the category of rational global spectra for the family U. In this talk I would like to present some new phenomena that we encounter and explain some calculations of the Balmer spectrum in this setting. This is based on joint work with Miguel Barrero, Tobias Barthel, Neil Strickland and Jordan Williamson.

Kathryn Hess (EPFL): 

Title: From group actions to actegories.

Time: 16:30 to 17:30 

Abstract: The notions of group action and of module over a ring can be categorified to that of an actegory, consisting essentially of a functorial action of a monoidal category on a (2-)category.  I will describe several interesting examples of actegories and of morphisms between them, in particular arising from group actions, and also explain how to see (homotopy) colimits and limits as morphisms between two different actegory structures on the 2-category of categories.  I’ll conclude by explaining how this type of actegory morphism can be used to build a machine that produces monads or comonads, like those that are central to the construction of the discrete calculus of Bauer-Johnson-McCarthy.

Joint work with Kristine Bauer, Brenda Johnson, and Julie Rasmussen