[Alta-Logic] Peripatetic Seminar Thursday September 28

[Kristine Bauer]

Next Thursday, Ben Williams from UBC will be visiting Calgary as part of the Peripatetic Seminar Lecture Series.  The details for his talk follow this message.  If you are interested in meeting Dr. Williams or joining us for dinner, please let me know.

Cheers,
Kristine

Date & Time:  Thursday, September 28 @ 11am
Place: MS 431

Speaker: Ben Williams
Title: Motivic homotopy groups and a conjecture of Suslin

Abstract: Fix an infinite field k. Associated to the group GL_n(F), one can form the +-construction of the classifying space BGL_n(F)^+. As n increases, both the homotopy groups and homology groups of this space stabilize; the homotopy groups give the higher algebraic K-theory of F, whereas the cokernel of the stabilization map in homology was proved by Suslin in the 1980s to give the Milnor K-theory of the field F, an older invariant of the field. There is a Hurewicz map relating homotopy to homology, and therefore a comparison map from algebraic K_n(F) to the Milnor K-group K^M_n(F). A longstanding conjecture of Suslin is that the image of this map is the subgroup (n-1)! K^M_n(F). By recasting this as a problem in motivic homotopy theory, we can borrow intuition and results from the calculation of the unstable homotopy groups of spheres and BU_n, and this allows us to settle the conjecture in the case n=5. This is joint work with Aravind Asok and Kirsten Wickelgren.
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