Algebra and Algebraic Geometry Seminar Fall 2022: Difference between revisions
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==== Computing Galois groups of finite Fano problems ==== | ==== Computing Galois groups of finite Fano problems ==== | ||
A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of the 27 lines on a smooth cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group that acts on these linear spaces and controls the complexity of computing them in coordinates via radicals. Galois groups of Fano problems have been studied both classically and modernly and have been determined in some special cases. We use computational tools to prove that several Fano problems of moderate size have Galois group equal to the full symmetric group, each of which were previously unknown. | |||
Revision as of 19:24, 1 September 2022
The Seminar takes place on Fridays at 2:30 pm, either virtually (via Zoom) or in person in room B235 Van Vleck.
Algebra and Algebraic Geometry Mailing List
- Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).
Fall 2022 Schedule
| date | speaker | title | host/link to talk | |
|---|---|---|---|---|
| October 7th | TBA | TBA | Reserved for the arithmetic geometry workshop | |
| October 14th | Thomas Yahl | Computing Galois groups of finite Fano problems | Rodriguez | |
| November 4th | Chris Eur | TBD | Wang |
Abstracts
Thomas Yahl (TAMU)
Computing Galois groups of finite Fano problems
A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of the 27 lines on a smooth cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group that acts on these linear spaces and controls the complexity of computing them in coordinates via radicals. Galois groups of Fano problems have been studied both classically and modernly and have been determined in some special cases. We use computational tools to prove that several Fano problems of moderate size have Galois group equal to the full symmetric group, each of which were previously unknown.