Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Allen Yuan (now Kiran Luecke): Coherent characteristic classes and congruences

Event Type: Seminar/Symposium
Sponsor: UIUC math department
Location: Altgeld
Date: Jan 28, 2025 11:00 am
Views: 156
Originating Calendar: Topology Seminar; 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.

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