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Seminar

DDC Junior Seminar: 0-1 laws for finitely presented structures October 06, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Meng-Che Ho (MSRI - Mathematical Sciences Research Institute)
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

0-1 Laws For Finitely Presented Structures

Abstract/Media

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

Abstract:

Random groups are proposed by Gromov as a model to study the typical behavior of finitely presented groups. They share many properties of the free group, and Knight conjectured that random groups satisfy a strong zero-one law and have the same first-order theory as the free group. In joint work with Remi Coulon and Alan Logan, we obtain a partial result for this question. 

On the other hand, in joint work with Franklin and Knight, we study this zero-one law in other classes of structures. In particular, we consider random presentations in algebraic varieties in the sense of universal algebra. We will discuss some concrete examples and some general results.

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0-1 Laws For Finitely Presented Structures

H.264 Video 25153_28651_8548_0-1_Laws_for_Finitely_Presented_Structures.mp4