Deformation Theory, Homological Mirror Symmetry
and Noncommutative Geometry
The University of Copenhagen
May 18 - 22, 2015
Homological mirror symmetry (HMS), upon its conception in Kontsevich's 1994 ICM address has enjoyed a great deal of attention. This is currently a battleground of many advance and active areas of research in mathematics and in theoretical physics, requiring a vast collection of machineries and techniques that are accessible only to a few specialists. In this masterclass, we will explore the links between HMS and another equally interesting and revolutionary area of research called noncommutative geometry (NCG). As it is understood today, NCG enjoys two almost non-communicating schools of thought, one popularized by Alain Connes and the one that has known to be noncommutative algebraic geometry. HMS is closer to the latter but hopefully, connections to the first will be explored. Deformation theory, which lies at the heart of HMS and NCG will play a crucial role.
There will be 4 minicourses, covering different connections between HMS, NCG and deformation theory. In addition, there will be problem solving and discussion sessions accompanied by preliminary lectures to topics that are necessary but less accessible. The goal of the masterclass is to bring together experts working actively in the said research areas and graduate students working in closely related fields.
- Lars Halvard Halle (University of Copenhagen)
- Ludmil Katzarkov (University of Vienna)
- Ryszard Nest (University of Copenhagen)
- Yan Soibelman (Kansas State University)
- The Nakano vanishing theorem for equivariant noncommutative Kähler structures. Réamonn Ó Buachalla
- Infinitessimal deformations of quasicoherent sheaves. Francesco Meazzini
- Mirror symmetry and cluster algebras. Man Wai Cheung