Toric geometry provides a versatile and powerful way of describing large classes of algebraic varieties in terms of simple diagrams (polytopes or fans) in integer lattices. Due to the explicit nature of the data involved, many questions can be addressed with the help of computers. The possibility of describing large numbers of compact and non-compact Calabi-Yau spaces, and a close connection with the gauged linear sigma model, make toric geometry an important tool in the compactification of string theory. 

This programme aims to create a stimulating environment where mathematicians working in string inspired areas of toric geometry meet physicists who use toric geometry as a tool. Recent developments will be discussed over the disciplinary border, thereby facilitating progress on open problems and the formulation of new questions.

Topics

• Toric geometry as an arena for explorations in string theory, where a wide range of questions in physics can be tested with precise mathematical tools.
   
• String theory as an abundant source of intriguing mathematical questions.
   
• Specialist software for research in theoretical physics and mathematics (e.g. Macaulay2 and cytools) and machine learning tools for addressing open questions (e.g. ML libraries for Calabi-Yau metrics).

General structure of the programme

Weeks 1 – 3 (June 15 – July 3): Mainly overview and introductory lectures (roughly two per day).

Week 4 (July 6 – July 10): Workshop week focused on recent results (several 45-minute talks per day).

Weeks 5 (July 13 – July 17): Further lectures (approximately two per day).

For a detailed schedule, see above.