Geometric triviality in differentially closed fields

Joel Nagloo (University of Illinois Chicago)

19-Aug-2021, 18:00-19:00 (3 years ago)

Abstract: 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 Fuchsian groups (discrete subgroup of $SL_2(\mathbb{R})$) 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 $SL_2(\mathbb{Z})$ 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.

logic

Audience: researchers in the topic


Online logic seminar

Series comments: Description: Seminar on all areas of logic

Organizer: Wesley Calvert*
*contact for this listing

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