# Programme

### Organisers : Benoît Bertrand, Erwan Brugallé, Ilia Itenberg, Grigory Mikhalkin

## Paris, May 9^{th} 2012

#### Institut de mathématiques de Jussieu, Jussieu

** 10:30 Coffee**

**11:15 Alexander Varchenko** (University of North Carolina at Chapel Hill)

Critical points of master functions and integrable hierarchies

I will review the properties of master functions, which initially appeared in hypergeometric solutions of KZ equations, and explain how critical points of master functions are related to integrable hierarchies.

**14:30 Johan Bjorklund** (Université de Genève)

Flexible isotopy classification of flexible knots

In this talk we will define flexible knots, objects meant to capture the topological properties of real algebraic knots, and then use them to introduce flexible isotopy, that is, an isotopy which is at all times a flexible knot. We will also briefly present Viro's encomplexed writhe using Ekholms interpretation in terms of the shade number. It will be shown that two genus 0 flexible knots of degree d are flexibly isotopic, if and only if, their real parts are smoothly isotopic and their encomplexed writhes coincide. If time allows we will also see that there are comparatively "many" flexible knots compared to real algebraic knots of a given degree (considered up to flexible and rigid isotopy respectively).

** 15:30 Coffee**

** 16:00 Stepan Orevkov ** (Université Paul Sabatier, Toulouse)

Planar real algebraic curves and transversal links

We generalize the method of braids to the case of several pencils of lines.