Chicago/Bogotá - UIC-UNAL joint seminar: Model Theory of Analytic Functions

Meeting weekly 2-3 PM (Chicago) 3-4 PM (Bogotá) - Friday in SEO 1227 (UIC) + Zoom (click here).

838 6947 9965

Passcode: nQ53LMd5

The goal of this weekly seminar held jointly between UIC (University of Illinois at Chicago) and UNAL (Universidad Nacional de Colombia) is to explore the connections between the two topics in the title. We will expound Zilber's general program to capture analytic information  about a canonical structure by an algebraic  $L_{\omega_1,\omega}$-description that is  categorical in power. The seminar will aim at fostering understanding of the viewpoints of model theory and function theory-number theory- algebraic topology- etc.

The first example of Zilber's program is the Bays-Zilber proof of the $L_{\omega_1,\omega}$-categoricity of the universal cover of $(\CC,\times)$ by $(\CC,+)$.  Later work in the program considers covers of specific (e.g. elliptic) complex curves on the one hand and covers of moduli spaces on the other.  This inquiry intersects with the study of Fuchsian groups transcendence result on solutions of Schwartzian equations. Relevant bibliography will be distributed. Projected speakers include Baldwin, Freitag, and Nagloo (UIC) and Villaveces and Cruz (UNAL).  For further info contact Baldwin (jbaldwin@uic.edu) or Villaveces (avillavecesn@unal.edu.co).

• First session: September 17: John Baldwin (UIC)- Categoricity of Canonical Structures and Fuchsian Groups (1)

• Second session: September 23: John Baldwin (UIC)- Categoricity of Canonical Structures and Fuchsian Groups (2)

• Third session: September 30: Andrés Villaveces (UNAL) - The Harris/Zilber theory of j: Understanding Types (1)

• Fourth session: October 14: Andrés Villaveces (UNAL) - The Harris/Zilber theory of j: Understanding Types (2)

• Fifth session: October 28: Jim Freitag (UIC) - More on the theory of j (1)

• Fifth session: November 4: Jim Freitag (UIC) - More on the theory of j (2)

• Sixth session: November 11: Jim Freitag (UIC) - More on the theory of j (3)

• Seventh session: November 18: John Baldwin and Andrés Villaveces - What is the general strategy of the proof from a model theoretical perspective? VIDEO here.