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February 6, 2018 | 2:00 p.m. - 3:00 p.m.
Category: Seminar
Location: Faculty/Administration #1146 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Carl McTague,   University of Rochester

Title: The Cayley Plane, String Bordism, and Higher Genus Arithmetic in Homotopy Theory 

Abstract: I will describe how the projective geometry of the octonions both deepens the affinity between projective spaces and bordism rings and points to new connections between higher genus arithmetic and homotopy theory. Specifically, I will report on ongoing work to identify the ring of string bordism invariants π_*MO〈8〉→ℚ which are multiplicative for fiber bundles with the ring of genus-2 Siegel modular forms for the Igusa theta group Γ₂(1,2) – a congruence subgroup of the genus-2 modular group Sp(4,ℤ) whose cusp structure (under the Satake compactification) corresponds to the union of Ochanine and Witten genera meeting with multiplicity 2 at the Â-genus, analogous to how the Ochanine genus itself has two cusps, identified with the Â-genus and signature.



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