Algebraic Topology

Our research lies in homotopy theory and its interaction with related subjects, like algebraic geometry, combinatorics, differential topology and logic. Some of our research interests include:
  • Algebraic K-theory
  • Chromatic and telescopic homotopy theory
  • Derived algebraic geometry
  • Equivariant homotopy theory
  • Functor calculus
  • Higher category theory
  • Homotopy type theory
  • ∞-operads (especially through the lens of dendroidal sets)
  • Moduli of elliptic curves
  • Spectral Lie algebras
  • Topological modular forms
  • Unstable homotopy theory
Our members are part of the Dutch cluster on Geometry and Quantum Theory (GQT) and they collaborate with the algebraic topologists at Radboud University Nijmegen and Vrije Universiteit Amsterdam.

Our members

Gijs Heuts (webpage)
Interests: Algebraic topology, specifically Goodwillie calculus, chromatic homotopy theory, higher category theory and operads.
Lennart Meier (webpage)
Interests: Chromatic homotopy theory (stable and unstable), equivariant homotopy theory, topological modular forms, moduli of elliptic curves
Ieke Moerdijk (webpage)
Interests: Algebraic topology, applications of topology to mathematical logic.
Paige North (webpage)
Interests: Category theory, homotopy theory, higher category theory, logic, homotopy type theory, and connections of those subjects with computer science and engineering
Guy Boyde (webpage)
Interests: Unstable phenomena in homotopy theory, especially the asymptotic behaviour of torsion in unstable homotopy groups.
Christian Carrick (webpage)
Interests: Equivariant, chromatic, and motivic homotopy, computations with higher real K-theories
Léonard Guetta (webpage)
Interests: Higher category theory, category theory, homotopical algebra and homotopy type theory.
Josefien Kuijper (webpage)
Interests: Homotopical methods in algebraic geometry, algebraic K-theory and scissors congruence.
Vignesh Subramanian (webpage)
Interests: Homotopy theory (both stable and unstable), homotopical algebra and representation theory.
Miguel Barata (webpage)
Supervisor: Ieke Moerdijk
Interests: Homotopy theory, in particular dendroidal homotopy theory and Goodwillie-Weiss's manifold calculus.
Max Blans (webpage)
Supervisor: Gijs Heuts
Interests: Homotopy theory, specifically (unstable) chromatic homotopy theory and Goodwillie calculus.
Maite Carli
Supervisor: Gijs Heuts
Interests: Homotopy theory, more precisely chromatic and unstable homotopy theory.
Marco Nervo (webpage)
Supervisor: Gijs Heuts
Interests: Metastable, chromatic and telescopic homotopy theory, functor calculus, computations, synthetic spectra.
Sven van Nigtevecht (webpage)
Supervisor: Lennart Meier
Interests: Stable homotopy theory and higher algebra, particularly topological modular forms, synthetic spectra, and Brauer groups.
Ryan Quinn
Supervisor: Lennart Meier
Interests: Homotopy theory, in particular equivariant stable homotopy theory and equivariant elliptic cohomology.
Jaco Ruit (webpage)
Supervisor: Lennart Meier
Interests: Homotopy theory, particularly equivariant stable homotopy theory and higher category theory

Local events

Courses and minicourses. The group offers various courses aimed at master and PhD students. The last iteration of the MSc seminar was about K-Theory and complex-oriented cohomology theories. The last minicourse was on Synthetic spectra.
Reading seminars. The group organizes various reading seminars. The current ones are on Factorization homology (joint with Vrije Universiteit Amsterdam) and on Trace methods and computations.
TopICS. The Topology Intercity Seminar is a joint seminar organized together with the algebraic topologists from Radboud University Nijmegen and Vrije Universiteit Amsterdam. The current program is here.

National and international events

EAST. The European Autumn School in Topology is a yearly autum school, mainly aimed at PhD students. The 2024 edition took place during the week September 16-20, close to Utrecht.
Higher Geometric Structures along the Lower Rhine. The «Higher-Lower» is a recurring event jointly organised between the universities of Bonn, Cologne, Nijmegen and Utrecht. The next workshop will be in Nijmegen, 23-24 January 2025.
Kan Lectures. The Kan lectures are yearly lecture series by renowned mathematicians. The last speaker was John Jones, 26 and 27 September 2024.
Conferences and workshops. The group organizes various other conferences and workshops in Utrecht. The last one was about (∞,n)-Categories and their applications and took place during the week April 15-19 2024.

Former members

Jack Davies (webpage)
Supervisor: Lennart Meier
Interests: Spectral algebraic geometry, chromatic homotopy theory, (higher/model) category theory, and (global/equivariant) stable homotopy theory.
Peter Dawson
Supervisor: Ieke Moerdijk
Hadrian Heine
André Henriques (webpage)
Interests: Algebraic topology.
Magdalena Kedziorek
Brice le Grignou
Interests: Homotopy theory and operads.
Tobias Lenz (webpage)
Interests: Equivariant and global homotopy theory, with a particular focus on equivariant infinite loop space theory and the corresponding refinements of algebraic K-theory.
Joost Nuiten (webpage)
Supervisor: Ieke Moerdijk
Interests: Abstract homotopy theory.
Yuqing Shi (webpage)
Supervisor: Gijs Heuts
Interests: Homotopy theory, with a focus on Goodwillie calculus and its applications.
Niall Taggart (webpage)
Interests: Algebraic topology, specifically functor calculus, stable and equivariant homotopy theory, model categories and higher category theory.
Mingcong Zeng (webpage)
Interests: Chromatic homotopy theory from an equivariant perspective.

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