Rozenblyum, A geometric approach to the cyclotomic trace.
I will describe a geometric construction of the trace map for stable oo-categories using factorization homology. A key ingredient is a new description of the category of cyclotomic spectra generalizing the description of Nikolaus-Scholze in the eventually connective case. This category is a convenient target for THH (viewed as factorization homology over the circle) and functoriality of factorization homology gives the cyclotomic trace map. This is joint work with David Ayala and Aaron Mazel-Gee.