Activities

Background:  This seminar was launched in Spring 2024 with the goal of creating new connections among researchers working  on the circle of ideas related to multigraded syzygies, homological mirror symmetry, derived categories of toric varieties, and more. 

Anyone is welcome to attend this seminar, so please feel free to share this site with anyone you think might be interested.

Logistics: You can sign up for the mailing list here.  The zoom link is here or you can use

Meeting ID: 953 1307 7795 and Passcode: RingsHave1

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 is being planned for the summer of 2027 at the University of Minnesota.  Further details will be made available at a later date.