October 19: Felix Cherubini

[EMILY Riehl]

The HoTTEST seminar continues this Thursday at the usual (still summer!) time, 11:30am EDT = 15:30 UTC. 

Our speaker is Felix Cherubini, who will present “A foundation for synthetic algebraic geometry.”  The talk will be 60 minutes long, followed by
up to 30 minutes for questions.  The abstract is below.

The Zoom link is https://zoom.us/j/994874377

Further information, including the list of upcoming speakers, and videos and slides from past talks, is at:

https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html

Emily

(On behalf of the HoTTEST organizers: Carlo Angiuli, Dan Christensen, Chris Kapulkin, and Emily Riehl.)

 

Abstract: In this [1] joint work with Thierry Coquand and Matthias Hutzler, we develop a foundation for a synthetic treatment of algebraic geometry, which is much in the same spirit as synthetic differential geometry. The language we use for the synthetic reasoning is homotopy type theory together with a postulated ring and three axioms. Two of the axioms were already present in previous work of Blechschmidt and a weaker variant already in work of Kock.

Our third axiom, which we call "Zariski-local choice", postulates a local-triviality with respect to a topology called the Zariski-topology. Using this axiom, it is possible to compute cohomology groups which we define using internal Eilenbeg-MacLane spaces. In the talk, I will explain this central new feature of our setup and conclude with an overview of recent results in synthetic algebraic geometry.

[1] https://felix-cherubini.de/iag.pdf