Research Seminars @ Illinois

View Full Calendar

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

Nikolai Konovalov (U Chicago): Synthetic Kriz theorem

Event Type: Seminar/Symposium
Sponsor: UIUC Math Department
Location: 243 Altgeld
Date: Sep 23, 2025 11:00 am
Views: 86
Originating Calendar: Topology Seminar; The Kriz theorem provides an algebraic model for $p$-adic homotopy
theory in terms of cosimplicial $p$-Boolean algebras, i.e.
$\mathbb{F}_p$-algebras such that $x^p=x$ for any element $x$.
Unfortunately, the Koszul duality for $p$-Boolean algebras is unknown,
so a Lie model for $p$-homotopy theory remains unknown as well. However,
Itamar Mor recently constructed the category $Syn$, which degenerates
unstable homotopy theory to simplicial restricted Lie algebras. The
category $Syn$ categorifies the lower central series spectral sequence.

In my talk, I will present an algebraic model for the category $Syn$
which degenerates the Kriz theorem into the Koszul duality between
restricted Lie algebras and $\mathbb{F}_p$-algebras with trivial
Frobenius. If time permits, I will also explain how the synthetic Kriz
theorem reveals some interactions between different versions of the
unstable Adams spectral sequence.

link for robots only