# AIS - Hochschild Homology (2023)

## Venue: IISER, Kolkata

## Dates: 4 Dec 2023 to 16 Dec 2023

**Convener(s)**

Name: |
Somnath Basu | Surojit Ghosh |

Mailing Address: |
Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246,West Bengal. |
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667. |

Email: |
somnath.basu at iiserkol.ac.in | surojit.ghosh at ma.iitr.ac.in |

Hochschild homology and cohomology of associative algebras is a classical topic which is pursued on its own as well as for its connection with algebraic topology, homotopy theory and K-theory. Cyclic homology is connected to noncommutative geometry and was initiated independently by Connes and Tsygan. In the world of free loop spaces, both of these become connected in a nice manner.

A further refinement of Hochschild homology is topological Hochschild homology while the topological cyclic homology does the same for ordinary cyclic homology. On the one hand, cyclic homology (if these are arising from spaces) are related to S1-equivariant homology of spaces admitting a circle action. The techniques devel- oped and used in these topics are useful. In the AIS, we plan to study Hochschild