# Mathematical Sciences Research Institute

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# Seminar

Strong Minimality and Algebraic Relations between Solutions for Poizat's Family of Equations July 27, 2022 (02:15 PM PDT - 03:00 PM PDT)
Parent Program: Definability, Decidability, and Computability in Number Theory, part 2 MSRI: Simons Auditorium, Online/Virtual
Speaker(s) David Marker (University of Illinois, Chicago)
Description No Description
Video

#### Strong Minimality And Algebraic Relations Between Solutions For Poizat's Family Of Equations

Abstract/Media

Poizat proved that the only infinite differential algebraic subvariety of $x^{\prime\prime}=xx^\prime$ is the field of constants. His proof was a complicated computational argument. We give an easy algebraic proof of this result and completely characterize for which complex rational functions $f(x)$ the differential equation $x^{\prime\prime}/x^\prime=f(x)$ is strongly minimal. An application is given to certain Lienard equations.

We go on to examine algebraic relations between solutions of these equations and to look at some of the non strongly minimal cases. This is joint work with Jim Freitag, Remi Jaoui and Ronnie Nagloo.

 Strong Minimality and Algebraic Relations between Solutions for Poizat's Family of Equations 387 KB application/pdf