Topology Seminar

Title: The geometry of the cyclotomic trace
Speaker: Aaron Mazel Gee
Speaker Info:
Brief Description:
Special Note:

The cyclotomic trace is a natural map running from algebraic K-theory to topological cyclic homology (TC). This trace map is important both conceptually and computationally, as it is known to be "locally constant" by the celebrated Dundas--Goodwillie--McCarthy theorem: its fiber remains unchanged under nilpotent extensions of connective associative ring spectra. However, the original construction of TC is quite subtle, and in particular it does not permit a precise interpretation of TC or of the cyclotomic trace at the level of derived algebraic geometry. In this talk, I will describe a new construction of TC that affords just such a precise geometric interpretation, which is based on nothing but universal properties (coming from Goodwillie calculus) and the geometry of 1-manifolds (via factorization homology). This represents joint work with David Ayala and Nick Rozenblyum.‚Äč
Date: Monday, February 20, 2017
Time: 4:10pm
Where: Lunt 104
Contact Person: Prof. John Francis
Contact email: jnkf@math.northwestern.edu
Contact Phone: 847-491-5544
Copyright © 1997-2024 Department of Mathematics, Northwestern University.