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SUMMARY:Joel Nagloo (City University of New York)
DTSTART:20201110T170000Z
DTEND:20201110T175000Z
DTSTAMP:20260422T220758Z
UID:20w5206/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/20w5206/4/">
 Schwarzian equation\, automorphic functions and functional transcendence</
 a>\nby Joel Nagloo (City University of New York) as part of BIRS workshop:
  Algebraic Dynamics and its Connections to Difference and Differential Equ
 ations\n\n\nAbstract\nBy a Schwarzian differential equation\, we mean an e
 quation of the form $S_{\\frac{d}{dt}}(y) +(y')^2 R(y) =0\,$ where $S_{\\f
 rac{d}{dt}}(y)$ denotes the Schwarzian derivative and $R$ is a rational fu
 nction with complex coefficients. The equation naturally appears in the st
 udy of automorphic functions (such as the modular $j$-function): if $j_{\\
 Gamma}$ is the uniformizing function of a genus zero Fuchsian group of the
  first kind\, then $j_{\\Gamma}$ is a solution of some Schwarzian equation
 .\n\nIn this talk\, we discuss recent work towards the proof of a conjectu
 re/claim of P. Painlev\\’e (1895) about the irreducibility of the Schwar
 zian equations. We also explain how\, using the model theory of differenti
 ally closed fields\, this work on irreducibility can be used to tackle que
 stions related to the study of algebraic relations between the solutions o
 f a Schwarzian equation. This includes\, for example\, obtaining the Ax-Li
 ndemann-Weierstrass Theorem with derivatives for all Fuchsian automorphic 
 functions.\n
LOCATION:https://researchseminars.org/talk/20w5206/4/
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