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.

This event is hosted by the Centre for Symmetry and Deformation and the Department of Mathematical Sciences at the University of Copenhagen.


Contributed talks:

  • 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

Lecture Notes:

Organised by Lars Halvard Halle and Clarisson Rizzie Canlubo.