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
 online

Scientific Organisers:

  • 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:
 
The algebraic theory of cobordism Talk 1 can be viewed here 
Slides of Talk 1 can be viewed here
 
The algebraic theory of cobordism Talk 2 can be viewed here
Slides of Talk 2 (with a few typos corrected) can be viewed here
 
Following this workshop, there will be a special issue of the Proceedings of the Royal Society of Edinburgh dedicated to Andrew Ranicki:
Proceedings A Special Edition
 
Photographs of Andrew Ranicki:

Arrangements

Registration has now closed and participants were emailed Zoom and Sococo joining instructions by ICMS on 17 June 2021.

The workshop will run online from 14.00-18.00 BST each day. There will be additional special events to be held at 20:00-21:00 BST each day (except Friday): a quiz on Monday (to be held in Sococo); a talk by Ian Hambleton on Tuesday; a poster session on Wednesday (to be held in Sococo) and a problem session on Thursday. There is a workshop registration fee of 10.00 GBP for PhDs and early career researchers and 30.00 GBP for all other participants. Please ensure payment is made by 25 June latest.

See programme below for links to talk abstracts, slides & recordings.

Programme

Monday 21 June
14:00-15:00: Thomas Nikolaus (Universität Münster)
Cohomology of orthogonal and symplectic groups over the integers
abstract can be viewed here
recording can be viewed here

15:30-16:30: Carmen Rovi (Universität Heidelberg)
Cut and paste invariants of manifolds via algebraic K-theory
abstract can be viewed here

17:00-18:00: Shmuel Weinberger (University of Chicago)
Algebraic theory of topology
abstract can be viewed here
recording can be viewed here

20.00-21.00: Quiz (to be held in Sococo)

Tuesday 22 June
14:00-15:00: Manuel Krannich (University of Cambridge)
The Disc-structure space
abstract can be viewed here
recording can be viewed here

15:30-16:30: Wolfgang Steimle (Universität Augsburg)
Stable moduli spaces of hermitian forms
abstract can be viewed here
recording can be viewed here

17:00-18:00: Thomas Goodwillie (Brown University)
Manifolds and spaces of graphs
abstract can be viewed here

20.00-21.00: Ian Hambleton (McMaster University)
The Legacy of Andrew Ranicki - a photo tour
recording can be viewed here

Wednesday 23 June
14:00-15:00: Nathalie Wahl (University of Copenhagen)
Invariance of string topology
abstract can be viewed here
recording can be viewed here

15:30-16:30: Yonatan Harpaz (University of Paris 13, CNRS)
Relative L-theory and cyclic homology
abstract can be viewed here
slides can be viewed here

17:00-18:00: Alexander Kupers (University of Toronto)
Diffeomorphisms of discs
abstract can be viewed here
recording can be viewed here

20.00-21.00: Poster session (to be held in Sococo)

Thursday 24 June
14:00-15:00: Andrew Senger (MIT)
Classification of Manifolds and Homotopy Theory
abstract can be viewed here
slides can be viewed here

15:30-16:30: Markus Land (University of Copenhagen)
The Shaneson-Ranicki splitting is a Bass-Heller-Swan type splitting for Poincare categories
abstract can be viewed here
recording can be viewed here

17:00-18:00: Jim Davis (Indiana University)  
Topological Rigidity and low-dimensional topology
abstract can be viewed here
recording can be viewed here

20.00-21.00: Problem session

Friday 25 June

14:00-15:00: Mark Powell (Durham University)
Stable diffeomorphism
abstract can be viewed here
recording can be viewed here

15:30-16:30: Jan Steinebrunner (University of Oxford)
The classifying space of the surface category and tropical moduli spaces
abstract can be viewed here
recording can be viewed here
slides can be viewed here

17:00-18:00: Wolfgang Lück (University of Bonn)
The Farrell-Jones Conjecture for the Hecke algebras of reductive p-adic groups
abstract can be viewed here
recording can be viewed here
slides can be viewed here