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). For a detailed (partially still tentative) schedule, see above.
Week 1 will feature introductions to the software tools CYtools, Macaulay2 and PALP. For maximum benefit, you can try to install the corresponding packages before the respective talks, following the instructions given at the following pages.
cy.tools/docs/getting-started/
github.com/Macaulay2/M2/wiki, and github.com/mikestillman/stringtorics
hep.itp.tuwien.ac.at/~kreuzer/CY/CYpalp.html
If you need help, that can be provided during the "Informal meetings" on Tuesday (after the morning coffee break).
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 specialized talks and discussion sessions (one or two per day).