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CIRM – Centre International de Rencontres Mathématiques

The idea of making space noncommutative is probably as old as quantum mechanics, but it has developed considerably since the mid 80’s in various directions, from pure mathematics to theoretical physics, yielding some phenomenological predictions in high energy physics. The aim of this conference is the interplay between noncommutative geometry and physics.

CIRM – Centre International de Rencontres Mathématiques

Friezes, introduced 50 years ago by Coxeter, are patterns of integers defined by a simple, local condition. They consist of a finite (or infinite) number of rows written in a lattice, starting with a row of 0s and a row of 1s and satisfying a local SL2-rule: for any four neighbours a, b, c, d forming a diamond we require ad − bc = 1. Since the discovery of links to cluster algebras of type A, a plethora of generalisations have been studied in the last decades. With this workshop, we will provide a platform to establish new links between friezes and research areas in geometry, algebra and combinatorics.

Algebra,    Graph Theory and Combinatorics

CIRM – Centre International de Rencontres Mathématiques

This big event will be the concluding conference of the semester. As is, presentations will cover a wide variety of topics from Real Algebraic Geometry and Birational Geometry. Most of the targeted speaker will be experts of the three subdomains we discuss in the project and some people are already involved in the other events but we want also to bring these subjects to a larger audience and some speakers will discuss of hot subjects from other parts of Real Algebraic Geometry and Birational Geometry.

CIRM – Centre International de Rencontres Mathématiques

The interactions between dynamics and geometry in dimensions up to three are fertile, they have been at the origin of many recent discoveries. A particularly nice example is the genericity of the set of three-dimensional Reeb flows admitting infinitely many periodic orbits. These interactions are also at the heart of a number of current research programs around the world in various directions. Transverse geometric structures (possibly singular), for example, represent a promising line of work for the study of Anosov flows in dimension three. Methods and concepts from one-dimensional dynamical systems, singular geometric structures on surfaces (of which translation surfaces are the paradigmatic example) and three-dimensional flows are fundamental. These ideas permeate a large part of mathematics, inspiring many higherdimensional notions, but are not as well-known as they should be by a wider public of young researchers in geometry and dynamics. The aim of this summer school is to help filling this gap, through three in-depth mini-courses on circle diffeomorphisms, translation surfaces and the dynamics of three-dimensional Reeb flows.