The Pentagram Map and Ramifications

From October 12 to 15, Richard E. Schwartz (Brown Univ. & Chaire Gretchen and Barry Mazur à l’IHES) and Robert C. Penner (Chaire Schlumberger pour les Sciences mathématiques à l’IHES) will organize a workshop focused on the pentagram map.

With 3 talks per day, spread out over 4 days, leaving time for individualized interactions, it will not be confined to the special topic of the pentagram map, but rather an exploration of the kind of mathematics that it relates to: integrable systems, algebraic dynamics, projective geometry and cluster algebras.

The pentagram map is a geometrically flavored dynamical system defined on polygons by a simple and projectively natural straight-line construction.

Starting with a polygon, one intersects the shortest diagonals in cyclic order to produce a new polygon with the same number of vertices.

Though quite elementary to define, the pentagram map turns out to have a deep structure connected to completely integrable systems, symplectic geometry, cluster algebras, dimers, algebraic dynamics, and moduli spaces.

The same goes for the many generalizations of the pentagram map, some of which are still quite mysterious.

Invited Speakers:

• Vladimir DRAGOVIĆ (UT Dallas)
• Anna FELIKSON (Durham University)
• Misha GEKHTMAN (University of Notre Dame)
• Max GLICK (Google)
• Anton IZOSIMOV (University of Glasgow)
• Rinat KEDEM (University of Illinois Urbana-Champaign)
• Valentin OVSIENKO (CNRS – Université de Reims Champagne-Ardenne)
• Jean-Baptiste STEGLER (Université Paris-Saclay)
• Sergei TABACHNIKOV (Penn State University)
• Béatrice de TILIÈRE (Université Paris Dauphine – PSL)
• Max WEINREICH (CUNY Baruch College)
• Michał ZWIERZYŃSKI (Warsaw University of Technology)

Information and registration on the dedicated webpage