Non-Commutative Algebraic Geometry

About

Inspired by physics and sheer mathematical curiosity, we take you on a ride exploring the ideas pushing the boundaries of the notion of Space! You get a taste and overview of the cutting-edge mathematical concepts employed in non-commutative algebraic geometry and its application in the physical theory of homological mirror symmetry.

The subject of Non-Commutative Algebraic Geometry (NCAG) pushes the boundaries of the concept of space by using algebraic and categorical models in contexts where classical point-set based representations fail.

This summer school is aimed at gaining understanding of key concepts and examples that motivate NCAG and which see their application in Homological Mirror Symmetry (HMS), which has its origins in mathematical physics

The programme provides two parallel courses, one on Algebraic Models for Spaces (AMS) and one on HMS, which consist each of lectures by experts in the field and highly interactive problem sessions in groups tailored to a shared background knowledge. In the AMS course, we furnish the background to model non-commutative spaces, working towards A-infinity algebras and quasi-categories as models for infinity-categories.
In the HMS course, we illustrate the idea of NCAG by Mirror Symmetry (MS) by starting from Classical Mirror Symmetry as an exchange of numerical data between “mirror” complex and symplectic space. From there, we build towards Kontsevich’ HMS conjecture.
The programme also includes one or two afternoons of research talks by experts in the field.

Target group

The summer school is designed for both recent Master students and beginning PhD students with a background in Mathematics or Mathematical physics who have an active interest in algebra and geometry

Fee info

The tuition fee includes breakfast and lodging in a single room at the A-stay hotel for the entire duration from Sunday June 29th until Friday July 11th (except for UA students); lunch, coffee, tea and refreshments on weekdays; and a social activity with all participants. The tuition fee does not include travel