##### 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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