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Seminar

DDC - Junior Seminar: Finite Grothendiekc ring September 29, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program: Decidability, definability and computability in number theory: Part 1 - Virtual Semester MSRI: Online/Virtual
Speaker(s) Esther Elbaz (Ben Gurion University of the Negev)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

The seminar will feature research talks by the six postdoctoral scholars appointed to the Fall 2020 DDC program, along with talks by students and other pre-tenure researchers associated with this program.  Since seminar attendees will have disparate backgrounds, we plan that these talks will not be too advanced, nor will they assume substantial background knowledge.  Our postdocs include number theorists, model theorists, and computable structure theorists, and talks can be expected to span all of these areas.

Video

Finite Grothendieck Rings

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Grothendieck rings were introduced in model theory in the early 2000s. They appear especially in motivic integration, where they are used to express formulas for certain counting functions in a uniform manner. There also is a dictionary of the combinatorial properties of a structure and of the algebraic properties of its Grothendieck ring.

It wasn't known until recently wether there exist finite Grothendieck ring.

In this talk, we will show that for any integer $N$, we can construct a structure whose Grothendieck ring is $\ mathbb {Z} / N \ mathbb {Z}$.