Algebraic structures of Hochschild complexes – University of Copenhagen

Algebraic structures of Hochschild complexes

University of Copenhagen

October 12-16, 2015

Organized by Ryszard Nest & Massimiliano Ungheretti

There are several related but different perspectives on Hochschild complexes. They show up for example as

  • deformation complexes of algebras
  • differential forms in non-commutative geometry
  • algebraic models for loop space homology (string topology)
  • approximations to K-theory

The masterclass will present some aspects of the theory arising in these different contexts, featuring two lecture series.


Lecture series:


  • Jacek Brodzki (University of Southampton) - The periodic cyclic homology of crossed products of finite type algebras
  • Daniela Egas-Santander (FU Berlin) - On the homology of Sullivan diagrams
  • Niels Kowalzig (Univ. Sapienza di Roma) - Higher structures on modules over operads
  • Ryszard Nest (University of Copenhagen) - Some applications of operations on cyclic complexes
  • Nathalie Wahl (University of Copenhagen) - Universal operations on the Hochschild complex of algebras over props
  • Benjamin Ward (Simons center for geometry and physics) - Hyper-commutative and hyper-Lie structures on Hochschild complexes

Contributed talks:

  • Pieter Belmans (University of Antwerp) - Derived categories of noncommutative quadrics and Hilbert schemes of points
  • Eric Dolores Cuenca (Northwestern University) - Kontsevich Swiss cheese conjecture
  • Martin Doubek (Charles University, Prague) - Quantum open-closed homotopy algebras
  • Reiner Hermann (NTNU Trondheim) - The Lie bracket in Hochschild cohomology via the homotopy category of projective bimodules


The event took place at the Department of Mathematical Sciences, University of Copenhagen and was hosted by the Centre for Symmetry and Deformation. You can find information for short term visitors including directions to the mathematics department here.

Financial support:

Participants can apply for financial support to partly cover local expenses. If you wish to apply for support, please indicate this on the registration form and send a short CV to The support will be roughly DKK 500 per day, at most DKK 2500.


Participants are asked to arrange their own accommodation. We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandivania (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive---and still recommended---options are Hotel Nora and Ibsen's Hotel.

This masterclass is supported by the PhD-school of the Faculty of SCIENCE, Copenhagen University and the Centre for Symmetry and Deformation.