Workgroup on Quantization

The goal of this workgroup is to discuss at a non technical level different examples of uses of the word "quantum" in a large list of mathematical domains.

On one hand we will review different meanings which have been given to the word "quantization" through various techniques of algebraic, geometric, analytic or probabilistic nature. On the other, we will examine some concrete examples, issued from different branches of mathematics, and try at each time to clarify in which of the previously reviewed senses these examples are indeed "quantum".

The spirit of the talks will be to try to convey the main ideas while avoiding as much as possible the technical details in order to allow a large public to have an overall view of this extremely vast domain.

Here is a preliminary list of topics which could be treated (this list will be modulated in the course of the activity of the workgroup according to the participation):

  1. General notions of prequantization and quantization (F. Costantino) (17/2/2017)
  2. Weyl Quantization (J.M. Bouclet) (3/3/2017)
  3. Deformation Quantization (J. Millés) (17/3/2017)
  4. Geometric Quantization (F. Costantino) (7/4/2017)
  5.  Feynmann Integrals and Quantization (T. Benoist) (28/4/2017)

Here is also a list of possible "quantum objects" which could be presented in separated talks :

  1.  Quantum groups (F. Costantino)
  2.  Skein and cluster algebras (T. Le)
  3.  Quantum Graphs (L. Miclo) (7/6/2017)
  4.  Quantum calculus (J. Sauloy)
  5.  q-Special functions and q identities (J. Sauloy)
  6.  Quantum information and quantum computation (see the mini course by Greg Kuperberg)
  7.  Quantum Cohomology (J.F. Barraud)