Topic Seminars

 Topic seminars/Learning groups

Paula de Lima Sousa, Henry Klatt, Jacob Rhody, Jose Jeremias Valenzuela Morales (GWU): Computable Structure Theory

Abstract: 

We will be following the books of Antonio Montalban, available for free at his website.  The pace of the course will be adjusted based on the participants, and people are welcome to come and go as they please. 

This week:  Tuesday will be preliminary definitions and organizational, covering chapters 1 and 2 of book 1.  Thursday will be a gentle introduction to forcing in the context of computable structure theory, covering chapter 4 of book 1 and a little bit more.

Announcements: 

The meetings will be on Tuesdays and Thursdays at 2-3pm in the seminar room (Poppelsdorfer Allee 45), starting on September 30. 

Zoom link: https://gwu-edu.zoom.us/j/93928946895

Whatsapp group: https://chat.whatsapp.com/KvDtzv8efIsEm4h6ynLCKW

Sylvy Anscombe (U Paris - Cité): Tame valued fields: underlying theory and results

Abstract: 

A (very) short course of three lectures around the theory of tame valued fields, due to F-V Kuhlmann (and coauthors), both the algebraic underpinnings and the model theoretic consequences, with attention paid to questions of decidability, though focussed on equal characteristic.

Announcements: 

Lecture 1 (10am Wednesday 1st): introduction, first-order theory, examples, AKE principles

Lecture 2 (TBC Friday 3rd): The Generalized Stability Theorem

Lecture 3 (TBC Tuesday 7th): Henselian Rationality

Toghrul Karimov (MPI SWS): Some applications of o-minimality to computational problems in dynamical systems theory

Talk: Thursday Oct 9th 11am

Abstract: 

The famously open Skolem Problem is to decide, given a linear recurrence sequence (u_n)_n, whether u_n = 0 for some n. The formulation in terms of linear dynamical systems is: given a matrix M, an initial point s, and a hyperplane H, decide whether the orbit <s, Ms, M^2s, ...> reaches (equivalently, avoids) H. I will discuss, among other results, the following: given M, s as above, and a semi-algebraic set T, we can decide whether there exists epsilon > 0 such that all orbits <s', Ms', M^2s', ...> with |s'-s| < epsilon avoid T. The talk is based on the recent paper "Verification of linear dynamical systems via o-minimality of the real numbers".

Sebastian Eterovic (University of Vienna): o-minimality and point counting

Abstract: 

1) What is o-minimality, what are some important examples of o-minimal structures, and does it mean that something is definable.

2) The Pila-Wilkie point counting theorem. Since this is intended as a user friendly seminar, we would focus mostly on the statement of the theorem, and skip the (very long and very technical) proof.

3) Two detailed examples of o-minimality and point-counting in action: a proof of Ax's theorem for exponentiation, and a proof of the multiplicative version of the Manin-Mumford conjecture.

Announcements: 

The first talk will be on Thursday, September 25 at 2pm (Poppelsdorfer Allee 45) in the seminar room. 

The next series of talks are Monday September 29, Tuesday September 30, and Thursday October 2, all at 11am in the seminar room.