Department of Mathematics,
University of California San Diego
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Algebraic Geometry Seminar
Alain H\'enaut
Universit\'e de Bordeaux
On planar web geometry
Abstract:
Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation \textit{F(x,y,y')=0} with y'-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented.
Host: Elham Izadi
October 4, 2019
1:45 PM
AP&M 7321
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