Algebraic structures of Hochschild complexes

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.

Information:

• Abstracts
• Schedule including notes

Lecture series:

• Boris Tsygan (Northwestern University) - Noncommutative differential calculus
• Thomas Willwacher (University of Zurich) - Graph complexes

Lectures:

• 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