Geometric triviality in differentially closed fields

Ronnie Nagloo, University of Illinois at Chicago

In this talk, we revisit the problem of describing the 'finer' structure of geometrically trivial strongly minimal sets in DCF0. In particular, I will explain how recent work joint with David Blázquez-Sanz, Guy Casale and James Freitag on Fuchsian groups (discrete subgroups of SL2(R)) and automorphic functions has lead to intriguing questions around the $\omega$-categoricity conjecture of Daniel Lascar. This conjecture was disproved in its full generality by James Freitag and Tom Scanlon using the modular group SL2(Z) and its automorphic uniformizer (the j-function). I will explain how their counter-example fits into the larger context of arithmetic Fuchsian groups and has allowed us to 'propose' refinements to the original conjecture.

MC 5479