Holomorphic Dynamics and Geometry of Surfaces (02/25 --> 06/25)

The objective of the semester is to impulse new interactions between holomorphic dynamics, geometric structures on surfaces and the interaction between these two topics.

Over the past 10 years, much progress has been made in describing fine aspects of the geometry of translation/dilation/affine surfaces along with dynamical systems naturally attached to them. Similarly, holomorphic dynamics and, in particular, dynamical systems of parabolic nature, have been the object of a number of impressive works. Of particular importance for us are the connections between translation/affine structures on surfaces and local/global dynamics of parabolic maps. Whereas these connections have been known for a while, recent progress independently made in each area suggests that time is ripe to push them to a whole new level. In many respects, the activities of this special semester will revolve around these interactions. More precisely, this semester has a twofold aim, namely:

• bring together experts in holomorphic dynamics and on geometry/dynamics of the above mentioned structures on surfaces to develop fruitful collaboration fostering new advances in both topics;

• train a number of PhD students in the methods of both areas with an eye out for the convergence points between them.

There will be three workshops:
- February 10 to 14. Tangent to the Identity Germs and Affine Surfaces
- April 7 to 11. Translation, Dilation, Affine and other Structures on Surfaces
- une 9 to 13. JHH80 Dynamical Developments: Degenerations of Flat Surfaces and Rational Maps

During the semester, several activities (from informal meetings to series of lectures) will take place around the following experts:

• Marco Abate (Pisa)

• Matthieu Astorg (Orléans)

• Fabrizio Bianchi (Pïsa)

• Filippo Bracci (Roma)

• Selim Ghazouani (London)

• Elise Goujard (Bordeaux)

• Lorena Lopez-Hernanz (Madrid)

• Jasmin Raissy (Bordeaux)

• Helena Reis (Porto)

• Matteo Ruggiero (Paris)

• Ferran Valdez (Mexico)

• Gabriela Weitze-Schmithuesen (Saarbrücken)

• Anja Randecker (Heidelberg)

• Guillaume Tahar (Beijing)

Organizing committee:
- Fabrizio Bianchi, fabrizio.bianchi@unipi.it, Università di Pisa (Italy)
- Xavier Buff, xavier.buff@math.univ-toulouse.fr, Université Toulouse 3
- Slavyana Geninska, slavyana.geninska@math.univ-toulouse.fr, Université Toulouse 3
- Julio Rebelo, rebelo@math.univ-toulouse.fr, Université Toulouse 3