Midwest Computability Seminar

Midwest Computability Seminar

XXXII


The Midwest Computability Seminar is a joint venture between the University of Chicago, the University of Notre Dame, the University of Wisconsin-Madison, and the University of Illinois Chicago. It meets once or twice per semester at the University of Chicago, and is attended by faculty and students from these universities and others in the area. The seminar started in the fall of 2008.

This meeting of the Midwest Computability Seminar is being held in collaboration with the Midwest Model Theory Seminar.



VIDEOS:   Lempp    Scott    Topaz

SLIDES:    Lempp



DATE: Thursday, February 29th, 2024

PLACE: John Crerar Library Building 390, The University of Chicago.
5730 South Ellis Avenue, Chicago, IL 60637 (see maps.uchicago.edu).

This is the same room as our previous meeting in November.

REMOTE ATTENDANCE: https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09
Meeting ID: 997 5433 2165
Passcode: midwest


Speakers:

Schedule:

Abstracts:


Steffen Lempp

Title: Minimal covers in the Weihrauch degrees

Abstract: We study the existence of minimal covers and strong minimal covers in the Weihrauch degrees. We characterize when a problem f is a minimal cover or strong minimal cover of a problem h. We show that strong minimal covers only exist in the cone below id and that the Weihrauch lattice above id is dense. From this, we conclude that the degree of id is first-order definable in the Weihrauch degrees and that the first-order theory of the Weihrauch degrees is computably isomorphic to third-order arithmetic.
This is joint work with J. Miller, Pauly, M. Soskova and Valenti.


Ronnie Nagloo

Title: Model theory and differential equations

Abstract: This talk provides a survey of recent work around applications of model theory to the study differential equations. In particular, we will focus on the work over the past decade centered around using geometric stability to study concrete definable sets in Differentially Closed Fields (DCF).


Isabella Scott

Title: Effective constructions of existentially closed groups

Abstract: Existentially closed groups were introduced in 1951 as a group-theoretic analogue to algebraically closed fields. Since then, they have been further studied by Neumann, Macintyre, and Ziegler, who elucidated deep connections with model theory and computability theory. We review some of the literature on existentially closed groups and present new results that further refine these connections. In particular, we are able to pinpoint more precisely how complexity arises in existentially closed groups, and quantify how much is visible to the "local" structure. We will also discuss constructions giving two existentially closed groups that are "as different as possible".


Adam Topaz

Title: Formalizing Lawvere theories in dependent type theory

Abstract: Lawvere theories provide a categorical approach to doing Universal Algebra, and their algebras have the benefit of being easily interpreted in any category with the correct limits. This talk will discuss some work in progress toward encoding (multi-sorted) Lawvere theories in dependent type theory, using the Lean4 interactive proof assistant (ITP). Specifically, after an introduction to the mathematical theory itself, I'll talk about why one might be interested in formalizing these objects in an ITP, as well as some of the challenges around making this formalization useful in relation to preexisting algebraic hierarchies.


Previous Seminars:

If you haven't been receiving the announcements and would like to be included in the list, send an email to drh@math.uchicago.edu.