This is the calendar of the Illinois' Math Department Topology Seminar. Talks are generally on Tuesdays at 11am, followed by an (optional) lunch with the speaker.
In Fall 2024 and Spring 2025, the seminar room is Altgeld Hall 241 (unless specified otherwise).
The Whitney sum formula for the total Chern class implies that it is a map of H-spaces from BU to the space of units of HZ[t] (|t|=2). It was a question of G. Segal from the 70's whether this could be lifted to a map of spectra. V. Snaith quickly showed that was not possible. Later B. Lawson et al constructed a theory of ``algebraic cycles" which produced a spectral lift with a different target. In this talk I will outline a new construction, joint with S. Carmeli and L. Yanovski, which provides a spectral lift with target gl_1 HZ^{tS^1}, the units of the Tate construction. As a result of our construction we obtain a proof that the ``sharp" construction of Ando-French-Ganter preserves E_infty orientations. As a corollary we establish that``two-variable elliptic genera," and their conglomerate, the "Jacobi orientation," admit E_infty lifts. With this knowledge, one is motivated to run the Ando-Hopkins-Rezk obstruction on the Jacobi orientation, which produces power series that satisfy nontrivial congruence conditions that may be of number theoretic interest. I will present some computational beginnings of this program, joint with E. Peterson.
Department of Mathematics
College of Liberal Arts & Sciences
273 Altgeld Hall
1409 W. Green Street (MC-382)
Urbana, IL 61801
Telephone: 217-333-3350
Email: math@illinois.edu