Homological mirror symmetry and multigraded commutative algebra
August 18 to August 22, 2025
at the
American Institute of Mathematics,
Pasadena, California
organized by
Christine Berkesch,
Michael Brown,
David Favero,
and Sheel Ganatra
Original Announcement
This workshop 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:
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Developing Macaulay2 software to compute the line bundle resolutions over toric varieties constructed by Favero-Huang, Favero-Sapranov, and Hanlon-Hicks-Lazarev.
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Implementing homological constructions arising in symplectic geometry, e.g. Fukaya categories, in Macaulay2.
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Developing Macaulay2 packages for constructing projective resolutions over noncommutative algebras.
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Creating functionality for working with toric stacks in Macaulay2.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Workshop videos
