# About the F1 World Seminar

This is an online seminar organized by Jaiung Jun, Oliver Lorscheid, Yuri Manin, Matt Szczesny, Koen Thas and Matt Young

The central theme of the seminar is the mathematics of F1, the “field with one element,” and its connections to other areas of mathematics, including arithmetic, geometry, representation theory and combinatorics. Topics covered by the seminar include, but are not limited to:

• Foundational theory (monoid schemes, relative schemes, F1-schemes, Lambda-schemes, generalized schemes, blue schemes);
• Arithmetic (relations to motives and Arakelov geometry, relations to modular forms, ideas around the Riemann Hypothesis);
• Tropical geometry and matroids;
• K-theory of F1-schemes;
• Representation theory (quivers, Hall algebras, degenerations of quantum groups);
• Combinatorics (finite field geometry).

WHEN and HOW?

We typically meet on alternating Wednesdays from 9:00 AM – 10:00 AM Eastern Standard Time. There will be room for mathematical discussion after each lecture.

A detailed schedule can be found here.

# Schedule Spring 2022

January 19, 2022: Alexander Smirnov, Steklov Institute

The 10th Discriminant and Tensor Powers of $\mathbb{Z}$

We plan to discuss very shortly certain achievements and disappointments of the $\mathbb{F}_1$-approach. In addition, we will consider a possibility to apply noncommutative tensor powers of $\mathbb{Z}$ to the Riemann Hypothesis. Recording

February 2, 2022Alain Connes, IHES

$\mathbb{F}_1$, $q$ and $\zeta$

This work is joint work with C. Consani. I will start from the role of the limit $q \rightarrow 1$ in the classical number theory formulas of Hasse-Weil when dealing with Riemann’s zeta function, and will then explore the various geometric paradigms corresponding to the limit. First the paradigm of characteristic one, which is tropical and then the paradigm of the sphere spectrum which is based on Segal’s gamma ringsand leads to a new algebraic geometry

February 16, 2022: Alex Sistko, Manhattan College

March 2, 2022: Chris Eur, Harvard University

March 16, 2022: Oren Ben-Bassat, University of Haifa

March 30, 2022: Kalina Mincheva, Tulane University

April 13, 2022: TBA