Difference between revisions of "Graduate Algebraic Geometry Seminar Fall 2017"

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Abstract: I will present the basic ideas neccesary to understand (1) the original statement of Hodge decomposition and the idea of the proof and (2) the proof given by Pierre Deligne and Luc Illusie of the analagous statement on schemes of characteristic p>0 given some special lifting condition. A brief argument extends the result to schemes of characteristic 0. If time permits, I will give an idea of what Professor Caldararu's more geometric take on the situation might be in his seminar talk this Friday.
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Abstract: I will present the basic ideas neccesary to understand (1) the original statement of Hodge decomposition and the idea of the proof and (2) the proof given by Pierre Deligne and Luc Illusie of the analagous statement on schemes of characteristic p>0 given some special lifting condition. A brief argument extends the result to schemes of characteristic 0. If time permits, I will give an idea of what Professor Caldararu's more geometric take on the situation might be.
 
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Revision as of 09:58, 28 September 2011

Wednesdays 4:30pm-5:30pm, B309 Van Vleck

The purpose of this seminar is to have a talk on each Wednesday by a graduate student to help orient ourselves for the Algebraic Geometry Seminar talk on the following Friday. These talks should be aimed at beginning graduate students, and should try to explain some of the background, terminology, and ideas for the Friday talk.

Give a talk!

We need volunteers to give talks this semester. If you're interested contact David. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.

Fall 2011 Semester

Date Speaker Title (click to see abstract)
September 14 (Wed.) Lalit Jain Introduction
September 21 (Wed.) David Dynerman Artin Stacks
September 28 (Wed.) Nathan Clement Hodge Theory and the Frobenius Endomorphism

September 14

Lalit Jain
Title: Introduction

Abstract: In this talk I'll present a few of the basic concepts of scheme theory and provide several motivating examples.Schemes are a fundamental object in modern algebraic geometry that greatly generalize varieties. The target audience is new graduate students who have had no (or perhaps only a classical) introduction to algebraic geometry.

September 21

David Dynerman
Title: Artin Stacks

Abstract: This is a preparatory talk for Yifeng Lui's seminar talk. Yifeng will be talking about recent developments in defining sheaves on Artin stacks, so I will attempt to define an Artin stack and hopefully work out an example or two.

September 28

Nathan Clement
Hodge Theory and the Frobenius Endomorphism: The curious tale of calculus in characteristic p>0.

Abstract: I will present the basic ideas neccesary to understand (1) the original statement of Hodge decomposition and the idea of the proof and (2) the proof given by Pierre Deligne and Luc Illusie of the analagous statement on schemes of characteristic p>0 given some special lifting condition. A brief argument extends the result to schemes of characteristic 0. If time permits, I will give an idea of what Professor Caldararu's more geometric take on the situation might be.