Manifolds and K-theory: the legacy of Andrew Ranicki

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Manifolds and K-theory: the legacy of Andrew Ranicki

 21 - 25 Jun 2021


  • Clark Barwick, University of Edinburgh
  • Diarmuid Crowley, University of Melbourne
  • Oscar Randal-Williams, University of Cambridge
  • Ulrike Tillmann, University of Oxford


Andrew Ranicki and his theory of algebraic surgery played a central role in linking manifold theory, algebraic K-theory, and its close cousin L-theory. These areas have seen great developments and advances in the last decade from distinct research communities. This workshop will bring together mathematicians working on the topology of high-dimensional manifolds and their automorphisms with those working on the algebraic K-theory (and its cousins hermitian K-theory and L-theory) of rings and ring spectra, in order to share recent progress in these areas and kindle a fresh interaction between them.
Directly within the theme of this workshop is the major recent work of Calmès, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, and Steimle on Grothendieck--Witt theory, which will play a role in several talks. Fabian Hebestreit has prepared introductory lectures to this circle of ideas which we hope will serve as good preparation for those participants not yet familiar with it. Please see links below to recordings of Fabian's lectures:


Recordings of all talks which were recorded can be viewed here

Monday 21 June
Thomas Nikolaus , Universität Münster Cohomology of orthogonal and symplectic groups over the integers
Carmen Rovi, Universität Heidelberg Cut and paste invariants of manifolds via algebraic K-theory
Shmuel Weinberger, University of Chicago Algebraic theory of topology
Quiz (to be held in Sococo)
Tuesday 22 June
Manuel Krannich, University of Cambridge The Disc-structure space
Wolfgang Steimle , Universität Augsburg Stable moduli spaces of hermitian forms
Thomas Goodwillie, Brown University Manifolds and spaces of graphs
Ian Hambleton, McMaster University The Legacy of Andrew Ranicki - a photo tour
Wednesday 23 June
Nathalie Wahl, University of Copenhagen Invariance of string topology
Yonatan Harpaz, University of Paris 13, CNRS) Relative L-theory and cyclic homology
Alexander Kupers, University of Toronto Diffeomorphisms of discs
Poster session (to be held in Sococo)
Andrew Senger , MIT Classification of Manifolds and Homotopy Theory
Markus Land, University of Copenhagen The Shaneson-Ranicki splitting is a Bass-Heller-Swan type splitting for Poincare categories
Jim Davis, Indiana University Topological Rigidity and low-dimensional topology
Problem session
Friday 25 June
Mark Powell, Durham University Stable diffeomorphism
Jan Steinebrunner, University of Oxford The classifying space of the surface category and tropical moduli spaces
Wolfgang Lück, University of Bonn The Farrell-Jones Conjecture for the Hecke algebras of reductive p-adic groups