Topology Seminar
Upcoming Talks
The seminar will meet at 4:00pm on Tuesdays in Eckhart room 203 unless otherwise noted. There will also be a pretalk at 2:30pm in the same room.
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Jonathan Rubin (UCLA)
Combinatorial and geometric N_{∞} operads
Let G be a finite group. A N_{∞} Goperad is an equivariant generalization of an E_{∞} operad. Such operads govern the natural algebraic structure on spectra over incomplete universes and on localizations of genuine commutative ring Gspectra. Since Blumberg and Hillâ€™s pioneering work, it has been known that the homotopy theory of N_{∞} operads is essentially algebraic. They proved that the homotopy type of a N_{∞} operad is completely determined by a single combinatorial invariant, and subsequent work has revealed that the homotopy theory of N_{∞} operads may be modeled entirely with discrete operads in the category of Gsets. On the other hand, there are natural classes of geometrically defined N_{∞} operads, which generalize the classical linear isometries and infinite little discs operads. Such operads encode real representationtheoretic properties of G, in addition to purely algebraic data. In this talk, I will explain how to reduce the homotopy theory of N_{∞} operads to combinatorics, and then I will discuss how the peculiarities of equivariant linear isometries and infinite little discs operads are encoded in algebra.

Anna Marie Bohmann (Vanderbilt)
A multiplicative comparison of Segal and Waldhausen Ktheory
In influential work of the 70s and 80s, Segal and Waldhausen each construct a version of Ktheory that produces spectra from certain types of categories. These constructions agree, in the sense that appropriately equivalent categories yield weakly equivalent spectra. In the 2000s, work of ElmendorfMandell and BlumbergMandell produced more structured versions of Segal and Waldhausen Ktheory, respectively. These versions are "multiplicative," in the sense that appropriate notions of pairings of categories yield multiplicationtype structure on their resulting spectra. In this talk, I will discuss joint work with Osorno in which we show that these constructions agree as multiplicative versions of Ktheory. Consequently, we get comparisons of rings spectra built from these two constructions. Furthermore, the same result also allows for comparisons of related constructions of spectrallyenriched categories.
If you have any questions, please contact Dylan Wilson or Zev Chonoles.