## EVENT DETAILS AND ABSTRACT

**Special Seminar**
**Title:** Periodic cyclic complex as a homotopy crystal

**Speaker:** Boris Tsygan

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**: **First talk of Noncommutative geometry seminar**

**Abstract:**

The periodic cyclic complex of an associative algebra is a noncommutative generalization of the complex computing the singular cohomology of a finite dimensional algebraic variety over the complex numbers. The key property of the periodic cyclic complex in characteristic zero is its rigidity under deformations given by a theorem of Goodwillie. It turns out that a similar rigidity property holds for algebras over the integers. Namely, for two multiplications on the sale A that differ by a multiple of a prime p>2, the periodic cyclic complexes of corresponding algebras are isomorphic canonically up to all higher homotopies.

**Date:** Wednesday, October 17, 2018

**Time:** 4:00pm

**Where:** Lunt 103

**Contact Person:** Prof. Boris Tsygan

**Contact email:** b-tsygan@northwestern.edu

**Contact Phone:** 847-644-3317

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