# Mathematical Sciences Research Institute

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# Seminar

MT Postdoc Seminar: Strong minimality of the $j$-function March 24, 2014 (11:00 AM PDT - 12:00 PM PDT)
Parent Program: Model Theory, Arithmetic Geometry and Number Theory MSRI: Simons Auditorium
Speaker(s) James Freitag (University of California, Berkeley)
Description No Description

Video
In this talk, we will be working in with the theory of differentially closed fields of characteristic zero; essentially this theory says that every differential equation which might have a solution in some field extension already has a solution in the differentially closed field. After introducing this theory in a bit of detail, we will sketch a proof of the strong minimality of the differential equation satisfied by the classical $j$-function starting from Pila's modular Ax-Lindemann-Weierstrass theorem. This resolves an open question about the existence of a geometrically trivial strongly minimal set which is not $\aleph _0$-categorical. If time allows, we will discuss some finiteness applications for intersections of certain sets in modular curves. This is joint work with Tom Scanlon.