(Inspiration for our excellent seminar name comes from the Many Cheerful Facts seminar, the Rest of Algebraic Geometry seminar, and the Homological Reading and Discussion seminar ;)
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This is a seminar for those looking to learn and review the basics of algebraic geometry (Hartshorne-level material) from varying perspectives.
It is jointly organized with Adam Boocher, Mike Daub, George Melvin, Damien Mondragon, Pablo Solis, Harold Williams, and Paul Ziegler. Thanks guys!
(Inspiration for our excellent seminar name comes from the Many Cheerful Facts seminar, the Rest of Algebraic Geometry seminar, and the Homological Reading and Discussion seminar ;) |
Schedule of talks (YYYY.MM.DD):
| Date | Speaker | Title | "Postract" |
| 2009.02.12 | Andrew Critch | Cartier and Weil divisors and invertible sheaves | A diagram summary |
| 2009.02.19 | Pablos Solis | Maps to projective space and curves of low genus | Curves and stuff |
| 2009.02.26 | Paul Ziegler | Relating cohomology theories | |
| 2009.03.05 | Damien Mondragon | Etale cohomology | |
| 2009.03.12 | Adam Boocher | What good is Riemann-Roch anyway? (Part I) | |
| 2009.03.19 | Adam Boocher | What good is Riemann-Roch anyway? (Part II) | |
| 2009.04.02 | Pablos Solis | More on curves of low genus | |
| 2009.04.08 | Andrew Critch | The cannonical embedding | |
| 2009.04.15 | Harold Williams | Hopf algebras |
Abstracts:
Thursday, Feb. 12
Speaker: Andrew Critch
Title: Cartier and Weil divisors and invertible sheaves
Abstract: I'll start by giving some motivation for the study of invertible sheaves
and divisors, and summarize precisely the various correspondences
between them.
"Postract": A diagram summary incorporating material from R. Hartshorne's text and R. Vakil's notes.
Thursday, Feb. 19
Speaker: Pablos Solis
Title: Maps to projective space and curves of low genus
Abstract: The talk will mostly focus on smooth curves X over \mathbb{C} and the
relation between maps to projective space and invertible sheaves on X.
I'll introduce the language of linear systems and discuss some subset
of the Riemann-Roch theorem, the canonical embedding, and curves of
genus < 5.
"Postract": Curves and stuff.
Thursday, Feb. 26
Speaker: Paul Ziegler
Title: Relating cohomology theories
Abstract: This talk will give an overview of the relationship between singular cohomology and sheaf cohomology.
If time permits, their relationship to other theories such as De Rham cohomology will be discussed.
Thursday, Mar. 5
Speaker: Damien Mondgragon
Title: Etale cohomology
Abstract: In this talk, I will motivate and introduce Etale Cohomology. I will also
touch on descent theory and compute an example.
Thursday, Mar. 12 and 19
Speaker: Adam Boocher
Title: What good is Riemann-Roch anyway? (How to actually compute cohomology)
Abstract: I'll talk a bit about why cohomology is interesting geometrically and
how it gives many invariants which can be used to help classify
projective varieties. After the initial flourish, we'll only talk
about smooth projective curves, and (by solving exercises in
Hartshorne) will see some examples.