Superschool on Derived Categories and D-branes

Superschools focus on topics at the interface of Mathematics and Physics. Graduate students and early career researchers, from both Mathematics and Physics, will be guided, in an intense week-long summer school, by the mentors.

String Theory revolutionized not just how we view the physical world but also how we view Mathematics. Conversely, through String Theory, many physicists first became acquainted with beautiful fields of Mathematics, like Algebraic Geometry. The cross pollination of insights and motivations between String Theory and Mathematics led to remarkable insights in both fields. The topic for the Superschool will be Derived Categories in Algebraic Geometry and D-branes in String Theory.

Curriculum: 

The curriculum of the Superschool will consist of approximately 20 hour-long lecture topics developing the foundational ideas for Derived Categories and D-branes and converging to a proof that D-branes in topological type B form a category, which is equivalent to the Derived Category of Coherent Sheaves in the case of a σ-model and equivalent to the Derived Category of Factorizations for a Landau-Ginzburg model. Final lecture topics will explore applications and further directions such as Homological Mirror Symmetry and D-branes in SYZ. All lectures, excluding the introductory and closing lectures, will be prepared and delivered by the participants with guidance from the mentors.

Mentors: 

David Favero, Mathematics, University of Alberta 

Eric Sharpe, Physics, Virginia Polytecnic Institute and State University