for this workshop
Homological mirror symmetry and multigraded commutative algebra
at the
American Institute of Mathematics, Pasadena, California
organized by
Christine Berkesch, Michael Brown, David Favero, and Sheel Ganatra
This workshop, sponsored by AIM and the NSF, will be devoted to studying a nascent bridge between commutative algebra and symplectic geometry, with an emphasis on developing Macaulay2 software for homological computations at the interface of these two fields. Recent breakthrough work of Hanlon-Hicks-Lazarev and Favero-Huang employs symplectic techniques to build line bundle resolutions over toric varieties, resolving several conjectures in toric geometry and multigraded commutative algebra. These results have illuminated a striking new connection between commutative algebra and symplectic geometry: this workshop will bring together experts in these fields with the goal of increasing our computational power to study the interplay between them.
The main topics for this workshop are:
- Developing Macaulay2 software to compute the line bundle resolutions over toric varieties constructed by Favero-Huang, Favero-Sapranov, and Hanlon-Hicks-Lazarev.
- Implementing homological constructions arising in symplectic geometry, e.g. Fukaya categories, in Macaulay2.
- Developing Macaulay2 packages for constructing projective resolutions over noncommutative algebras.
- Creating functionality for working with toric stacks in Macaulay2.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than March 18, 2025. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
