Quantization is the mathematical tool to understand the transition between classical and quantum mechanics. Intuitively, classical mechanics is the limit of quantum mechanics as the quantum parameter tends to zero and, conversely, quantization is “an algorithm by which a quantum system corresponds to a classical dynamical one” (F.A. Berezin).
The ultimate goal of this workshop is to provide a survey of the most recent trends in mathematics and physics revolving around this idea. We will focus in particular on novel research directions in representation theory and moduli spaces aiming at a unified view built on new inputs from derived algebraic geometry. The workshop will pivot on the following main topics.
- Quantum Groups, in particular Yangians and quantum loop algebras, and their role in mathematical physics and in algebraic geometry as highlighted in the recent work following Costello-Yamazaki-Witten, Maulik-Okounkov, and Schiffmann-Vasserot.
- Coulomb and Higgs Branches, in the approach developed by Braverman-Finkelberg-Nakajima, and their various applications ranging from affine Grassmannians and cluster theory to symplectic duality and shifted Yangians.
- Deformation Quantization, studied through the lenses of Derived Algebraic Geometry, as in the recent work by Calaque, Safronov, et al.
The above influential research directions are currently having a strong broad impact in geometry, algebra, and mathematical physics. Their originality crucially resides in the use of new methods originally developed in derived algebraic geometry. The latter can eventually be regarded as the right framework for the solution of many problems arising in quantization theory.
The workshop is by invitation only.
Speakers.
Léa Bittmann (Université de Strasbourg)
Bozec Tristan (Université Angers)
Li Wei (Institute of Theoretical Physics, Chinese Academy of Sciences)
Tudor Dimofte (University of Edinburgh)
Sachin Gautam (The Ohio State University)
Iva Halacheva (Northeastern University)
Benjamin Hennion (Université de Paris-Saclay)
David Hernandez (Université Paris Cité)
Hiraku Nakajima (Kavli IPMU, the University of Tokyo)
Gabriele Rembado (Université de Montpellier)
Sarah Scherotzke (University of Luxembourg)
Claudia Scheimbauer (TU Munchen)
Valerio Toledano Laredo (Northeastern University)
Ben Webster (University of Waterloo)
Masahito Yamazaki (Kavli IPMU, the University of Tokyo)
Yaping Yang (University of Melbourne)
Organizers.
Andrea Appel (Università di Parma)
Lara Bossinger (Universidad Nacional Autónoma de México)
Giovanni Felder (ETH)
Mauro Porta (Université de Strasbourg)
Francesco Sala (Università di Pisa)
Olivier Schiffmann (Université de Paris Saclay)
