Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Strong Minimality And Algebraic Relations Between Solutions For Poizat's Family Of Equations
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.
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Strong Minimality and Algebraic Relations between Solutions for Poizat's Family of Equations
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