2026 Workshop

Algebraic Surgery  

with Thomas Nikolaus and Fabian Hebestreit

22nd June - 26th June 2026

Kolding, Denmark

About

The eighth European Talbot workshop will take place in Denmark during the summer of 2026. The goal is to bring together a group of 35-40 master students, graduate students and post-docs to work on a focused topic under the guidance of two senior mentors.

Most of the talks will be given by the participants, with enough free time in the afternoon and evenings for further discussions and interaction. The character of the workshop is expository in nature, starting with the basic ideas and leading to a survey of the most recent developments in the field. Since all participants are staying together at a group house, jointly responsible for cooking and cleaning, we hope to create an informal and inspiring atmosphere.

Topic

The goal of this workshop is to introduce the framework and main results of algebraic and geometric surgery. Geometric surgery is a fundamental technique in manifold theory, providing a systematic method for modifying manifolds. Algebraic surgery emerged from this perspective by translating geometric constructions into an algebraic setting, where manifolds are replaced by chain complexes (for instance, singular cochains). This shift allows one to study the algebraic obstructions underlying geometric surgery in a precise and computable way.

Our treatment of algebraic surgery will take place in the setting of Poincaré categories—stable ∞-categories equipped with additional duality structures, following the work of Ranicki and Lurie. Within this framework, one can define Grothendieck–Witt groups and L-groups. These invariants not only capture the obstructions arising in surgery theory, but also play a central role in the study of symmetric and quadratic forms, particularly in number theory and in the study of their automorphism groups (such as symplectic groups over the integers).

A key result in this area is the relationship between L-theory and Grothendieck–Witt theory, which enables explicit computations of Grothendieck–Witt groups. In particular, this leads to a solution of a long-standing open problem in the case of the integers. These developments build on recent work by Calmès, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, and Steimle.

On the geometric side, we will discuss the surgery exact sequence and its relationship to algebraic results using this language, including the π–π theorem and the Weiss–Williams index theorem. We will also cover Ranicki’s total surgery obstruction, as well as the construction and analysis of the Kervaire invariant within the algebraic framework.

Concretely, the workshop will cover the following topics:

• Poincaré categories and their basic properties

• Grothendieck–Witt theory, L-theory, and the relation to algebraic K-theory

• Algebraic surgery, the Homotopy Limit Problem (HLP), and the computation of GW(ℤ)

• The geometric surgery exact sequence

• Ranicki’s total surgery obstruction and the structure space of a manifold

• Tate L-theory and Browder’s theorem

Application

If you would like to participate, please fill in the application form before Monday April 13, 2026.

Funding

The local expenses for all participants will be covered by the workshop, including costs for accommodation and meals. We strongly encourage participants to look for travel funding themselves. We thank the K-theory foundation for partially funding this workshop.

Contact

For questions or suggestions, please send an email to the organisers at europeantalbot@gmail.com.

This workshop is organised by Maite Carli, Marie-Camille Delarue, João Fernandes, Lucy Grossman, Fabio Neugebauer, and Maxime Wybouw.