February 28
Joel Nagloo, CUNY
Geometric triviality in differentially closed fields revisited
In this talk we revisit the problem of describing the 'finer' structure of geometrically trivial strongly minimal sets in $DCF_0$. In particular, I will explain how recent work joint with Guy Casale and James Freitag on automorphic functions, has lead to intriguing questions around the $\omega$-categoricity conjecture. This conjecture was disproved in its full generality by James Freitag and Tom Scanlon using the modular $j$-function. I will explain how their counter-example fits into the larger context of arithmetic automorphic functions and has allowed us to 'propose' refinements to the original conjecture.