Topology Seminar
Upcoming Talks
The seminar will meet at 4:30pm on Tuesdays in Eckhart room 203 unless otherwise noted. There will also be a pretalk at 3pm in the same room.
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Dondi Ellis (University of Michigan)
Motivic Analogues of the Cobordism Theories MO and MSO
I will begin by reviewing the foundations of equivariant and nonequivariant stable motivic homotopy theory, as well as the construction of unoriented cobordism MO and oriented cobordism MSO. In the nonequivariant stable motivic homotopy category, I will construct a kspectrum MGLO whose topological realization over the field k=\mathbbC is MO. I will give a complete description of the coefficient ring of MGLO up to knowledge of the coefficients of motivic H\mathbbZ/2. Next I will discuss the relation of MGLO to the \mathbbZ/2equivariant kspectrum MGLR. MGLR is a motivic analogue of Landweber's real oriented cobordism MR. Just as taking fixed points of MR at the prespectrum level gives MO, taking fixed points MGLR at the prespectrum level gives MGLO. Restricting attention to the field k=\mathbbC, I will briefly discuss new research relating to MGLR. Finally I will construct a kspectrum MGLSO whose topological realization over the field k=\mathbbC is MSO. I will describe MGLSO_{(2)} as a wedge sums of EilenbergMacLane spectra H\mathbbZ_{(2)} and H\mathbbZ/2.

Doug Ravenel (University of Rochester)
What is a Gspectrum?
This is a department colloquium; it will be from 34pm in Eckhart 206.
Spectra in the sense of stable homotopy theory have been a major object of study in algebraic topology for half a century. During that time the basic definition has undergone some major revisions, including a major breakthrough in 1993 due to Peter May and three coauthors. Remarkably, these shifting foundations have not affected any of the computations made using earlier definitions. In the talk I will describe how the use of category theory has led to major simplifications.
If you have any questions, please contact Inna Zakharevich or Agnes Beaudry.