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