Title: The geometry of the cyclotomic trace
Speaker: Aaron Mazel Gee
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Abstract:
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.Date: Monday, February 20, 2017