"Complex Lagrangians, Integrable Systems, and Quantization"

Symplectic geometry is the natural framework for describing classical mechanics, with the position and momentum coordinates lying in a symplectic phase space. Mirror symmetry was discovered over three decades ago in theoretical physics. Since then, it has been a deep mystery appearing in many frontiers of mathematics. In general, it appears to be a hidden relation between symplectic geometry and complex algebraic geometry. More recent discoveries link it with several other areas of mathematics and physics. Still, as of today, there is no systematic understanding of mirror symmetry.

The main goal of this focused research group is to establish a universal tool to study geometric problems and quantization arising in modern frontiers of geometry and topology. In particular, the project aims at constructing a large class of concrete models that would demonstrate all aspects of mirror symmetry. We will bring expertise from different areas of mathematics and will use a variety of techniques. They will also organize workshops, summer schools, and conferences, aimed at training early researchers in this area, disseminating recent results and facilitating further advances and breakthroughs.

Image credit: by E. Kienzle, from S. Rayan and E. Kienzle's paper "Hyperbolic band theory through Higgs bundles"

For more Math art by Elliot Kienzle check his website