ICTS

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 with connections to operads, infinity algebras, Morse theory, mathematical physics and more. In order to obtain a computationally feasible approach to Quillen’s Algebraic K-theory, Bökstedt, Hsiang and Madsen developed topological refinements of these algebraic invariants. The topological 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) is related to circle-equivariant homology of spaces admitting a circle action. On the other hand, these topological invariants led to many successful algebraic K-theory computations. This program will have experts give lectures on classical Hochschild and cyclic homology and its connection to free loop spaces on the one hand and also give lectures on topological Hochschild (& cyclic) homology, its computations and connections with algebraic K-theory. This will provide us with an unifying algebraic topological and homotopy theoretic perspective on the topics.

Eligibility Criteria:  The school is primarily meant for graduate students, post-doctoral fellows and faculty working in algebraic topology, K-theory and related fields. A small number of highly motivated senior undergraduates may also be considered. A basic understanding of (co)homology theories and homological algebra is essential for participating in the program. Acquaintance with spectral sequence, though not mandatory, will be useful.

Accommodation will be provided for outstation participants at our on campus guest house.

ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.