Graduate Algebraic Geometry Seminar Fall 2017: Difference between revisions
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| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement''' | | bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement''' | ||
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| bgcolor="#BCD2EE" align="center" | Title: | | bgcolor="#BCD2EE" align="center" | Title: Spectral Curves and Blowups | ||
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Abstract: | Abstract: | ||
Continuing on from last time, I will now take a closer look at the geometry of the spectral curve. The main construction will be the lifting of a spectral curve to a blow up of the ambient surface, and the main tool for studying the geometry of this new spectral curve will be intersection theory in a surface. | |||
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Revision as of 19:06, 29 September 2016
When: Wednesdays 4:00pm
Where:Van Vleck B321 (Updated Fall 2016)
Who: YOU!!
Why: The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.
How:If you want to get emails regarding time, place, and talk topics (which are often assigned quite last minute) add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is here.
Give a talk!
We need volunteers to give talks this semester. If you're interested contact DJ, or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.
Wish List
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.
- Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)
- A careful explanation of the correspondence between graded modules and sheaves on projective varieties.
- Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things easier)
- Homological projective duality
- The orbit method (for classifying representations of a Lie group)
- Kaledin: geometry and topology of symplectic resolutions
- Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)
- Geometric complexity theory, maybe something like arXiv:1508.05788.
Fall 2016
Date | Speaker | Title (click to see abstract) |
September 14 | DJ Bruce | Vignettes in Algebraic Geometry |
September 21 | Moisés Herradón Cueto | Hilbert's 21 and The Riemann-Hilbert correspondence |
September 28 | Moisés Herradón Cueto | Hilbert's 21 and The Riemann-Hilbert correspondence |
October 5 | n/a | No Seminar Today. |
October 12 | Nathan Clement | Spectral Curves and Higgs Bundles |
October 19 | Nathan Clement | Spectral Curves and Blowups |
October 26 | TBD | TBD |
November 2 | TBD | TBD |
November 9 | TBD | TBD |
November 16 | TBD | TBD |
November 23 | n/a | No Seminar |
November 30 | DJ Bruce | TBD |
December 7 | DJ Bruce | TBD |
December 14 | TBD | TBD |
September 14
DJ Bruce |
Title: Vignettes In Algebraic Geometry |
Abstract: Algebraic geometry is a massive forest, and it is often easy to become lost in the thicket of technical detail and seemingly endless abstraction. The goal of this talk is to take a step back out of these weeds, and return to our roots as algebraic geometers. By looking at three different classical problems we will explore various parts of algebraic geometry, and hopefully motivate the development of some of its larger machinery. Each problem will slowly build with no prerequisite assumed of the listener in the beginning. |
September 21
Moisés Herradón Cueto |
Title: Hilbert's 21 and The Riemann-Hilbert correspondence |
Abstract: Enough with the algebra! Away with the schemes and categories! Consider a differential equation with some singularities, such as y'=1/x. Analysis tells us that its solutions can be extended along paths on the complex plane, but when a path loops around the singular point, 0 in this case, the solution might change. This phenomenon is called monodromy. Hilbert's twenty-first problem asks about the possible inverse of the monodromy construction: if some monodromy is prescribed on the plane with some points removed, is there a nice (Fuchsian), linear differential equation whose solutions have this monodromy? Attempting to solve this problem will quickly take us back to our cozy algebraic geometry world of sheaves and vector bundles. For those of us to whom the word sheaves produces a cold sweat running down our backs, this topic is a great way to motivate and introduce sheaves, and will ultimately give us a reason to care about nontrivial vector bundles. No knowledge (or ignorance) of sheaves is required and the analysis in the talk will be contained in the tiny amount that I myself know. |
September 28
Moisés Herradón Cueto |
Title: Hilbert's 21 and The Riemann-Hilbert correspondence |
Abstract: Enough with the algebra! Away with the schemes and categories! Consider a differential equation with some singularities, such as y'=1/x. Analysis tells us that its solutions can be extended along paths on the complex plane, but when a path loops around the singular point, 0 in this case, the solution might change. This phenomenon is called monodromy. Hilbert's twenty-first problem asks about the possible inverse of the monodromy construction: if some monodromy is prescribed on the plane with some points removed, is there a nice (Fuchsian), linear differential equation whose solutions have this monodromy? Attempting to solve this problem will quickly take us back to our cozy algebraic geometry world of sheaves and vector bundles. For those of us to whom the word sheaves produces a cold sweat running down our backs, this topic is a great way to motivate and introduce sheaves, and will ultimately give us a reason to care about nontrivial vector bundles. No knowledge (or ignorance) of sheaves is required and the analysis in the talk will be contained in the tiny amount that I myself know. |
October 5
No Talk This Week |
Title: n/a |
Abstract: n/a |
October 12
Nathan Clement |
Title: Spectral Curves and Higgs Bundles |
Abstract: I will present some of the backround motivation for the study of Higgs Bundles, mainly pertaining to Nigel Hitchen's 1987 paper. I will then introduce the spectral curve associated to an operator and describe the relevant geometry. |
October 19
Nathan Clement |
Title: Spectral Curves and Blowups |
Abstract: Continuing on from last time, I will now take a closer look at the geometry of the spectral curve. The main construction will be the lifting of a spectral curve to a blow up of the ambient surface, and the main tool for studying the geometry of this new spectral curve will be intersection theory in a surface. |
October 26
TBD |
Title: TBD |
Abstract: TBD |
November 2
TBD |
Title: TBD |
Abstract: TBD |
November 9
TBD |
Title: TBD |
Abstract: TBD |
November 16
TBD |
Title: TBD |
Abstract: TBD |
November 23
No Seminar This Week |
Title: Enjoy Thanksgiving! |
Abstract: n/a |
November 30
TBD |
Title: TBD |
Abstract: TBD |
December 7
TBD |
Title: TBD |
Abstract: TBD |
December 14
TBD |
Title: TBD |
Abstract: TBD |
Organizers' Contact Info