Algebra and Algebraic Geometry Seminar Spring 2023: Difference between revisions
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The seminar normally meets 2:30-3:30pm on Fridays, in the room | The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B223. | ||
==Algebra and Algebraic Geometry Mailing List== | ==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). | *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). | ||
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!align="left" | host/link to talk | !align="left" | host/link to talk | ||
|- | |- | ||
| | |February 3 | ||
| | |Dima Arinkin | ||
| | |[[#Dima Arinkin|Intergrating symplectic stacks]] | ||
| | |Local | ||
| | |||
|- | |- | ||
|February 24 | |February 24 | ||
| Line 22: | Line 21: | ||
|TBA | |TBA | ||
|Maxim | |Maxim | ||
|- | |- | ||
|March 10 | |March 10 | ||
| Line 28: | Line 26: | ||
|TBA | |TBA | ||
|Maxim | |Maxim | ||
|- | |- | ||
|March 24 | |March 24 | ||
|[https://www.danieljcorey.com/ Daniel Corey] | |[https://www.danieljcorey.com/ Daniel Corey] | ||
|Degenerations of flag varieties and subdivisions of generalized permutahedra | |[[#Daniel Corey|Degenerations of flag varieties and subdivisions of generalized permutahedra]] | ||
|Rodriguez | |Rodriguez | ||
|} | |} | ||
== Abstracts == | == Abstracts == | ||
=== | === Dima Arinkin === | ||
==== | ==== Integrating symplectic stacks ==== | ||
Shifted symplectic stacks, introduced by Pantev, Toën, Vaquie, and Vezzosi, are a natural generalization of symplectic manifolds in derived algebraic | |||
geometry. The word `shifted' here refers to cohomological shift, which can naturally occur in the derived setting: after all, the tangent space is now not a vector space, but a complex. Several classes of interesting moduli stacks carry shifted simplectic structures. | |||
In my talk (based on a joint project with T.Pantev and B.Toën), I will present a way to generate shifted symplectic stacks. Informally, it involves | |||
integration along a (compact oriented) topological manifold X: starting with a family of shifted symplectic stacks over X, we produce a new stack of | |||
sections of this family, and equip it with a symplectic structure via an appropriate version of the Poincaré duality. | |||
=== Daniel Corey === | |||
==== Degenerations of flag varieties and subdivisions of generalized permutahedra ==== | |||
We study the initial degenerations of the type-A flag varieties, and show how they are related to flag matroid strata and subdivisions of flag matroid polytopes. As applications, we give a complete proof of a conjecture of Keel and Tevelev on log canonical compactifications of moduli spaces of hyperplanes in projective space in general position, and study the Chow quotient of the complete flag variety by the diagonal torus of the projective linear group. This is based on joint work with Olarte and Luber. | We study the initial degenerations of the type-A flag varieties, and show how they are related to flag matroid strata and subdivisions of flag matroid polytopes. As applications, we give a complete proof of a conjecture of Keel and Tevelev on log canonical compactifications of moduli spaces of hyperplanes in projective space in general position, and study the Chow quotient of the complete flag variety by the diagonal torus of the projective linear group. This is based on joint work with Olarte and Luber. | ||
Revision as of 17:45, 20 January 2023
The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B223.
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).
Spring 2023 Schedule
| date | speaker | title | host/link to talk |
|---|---|---|---|
| February 3 | Dima Arinkin | Intergrating symplectic stacks | Local |
| February 24 | Ruijie Yang | TBA | Maxim |
| March 10 | Joerg Schuermann | TBA | Maxim |
| March 24 | Daniel Corey | Degenerations of flag varieties and subdivisions of generalized permutahedra | Rodriguez |
Abstracts
Dima Arinkin
Integrating symplectic stacks
Shifted symplectic stacks, introduced by Pantev, Toën, Vaquie, and Vezzosi, are a natural generalization of symplectic manifolds in derived algebraic geometry. The word `shifted' here refers to cohomological shift, which can naturally occur in the derived setting: after all, the tangent space is now not a vector space, but a complex. Several classes of interesting moduli stacks carry shifted simplectic structures.
In my talk (based on a joint project with T.Pantev and B.Toën), I will present a way to generate shifted symplectic stacks. Informally, it involves integration along a (compact oriented) topological manifold X: starting with a family of shifted symplectic stacks over X, we produce a new stack of sections of this family, and equip it with a symplectic structure via an appropriate version of the Poincaré duality.
Daniel Corey
Degenerations of flag varieties and subdivisions of generalized permutahedra
We study the initial degenerations of the type-A flag varieties, and show how they are related to flag matroid strata and subdivisions of flag matroid polytopes. As applications, we give a complete proof of a conjecture of Keel and Tevelev on log canonical compactifications of moduli spaces of hyperplanes in projective space in general position, and study the Chow quotient of the complete flag variety by the diagonal torus of the projective linear group. This is based on joint work with Olarte and Luber.