Nick Addington - Infinite-Dimensional Manifolds: What's the Deal?
The deal is, Banach spaces.
Garrett Alston - Teichmüller Spaces
No abstract.
Links
- Schedule
- Current Abstracts
- Abstracts, Fall 2008
- Abstracts, Spring 2008
- Abstracts, Fall 2007
- Abstracts, Spring 2007
Jo Nelson - Orbifolds, or the Aspiration to be a Manifold that Falls Short
I will talk about the basics of orbifolds including what makes an orbifold good or bad. Then I'll talk about some nice theorems involving coverings of good orbifolds and geometric structures that they admit. This is from Peter Scott's extensive paper on the geometries of 3-manifolds, titled "The Geometries of Three Manifolds."
Noah Kieserman - Liouville Numbers through the Eyes of Obstruction Theory
I will explain some of the algebraic structure that governs the deformation theory of a particular object. Everything will be illustrated in an example where the obstruction theory detects the Liouville phenomenon, a la KAM theory.
Antonio Ache - Gauge Transformations: An Example
We will show an example in PDE that motivates the idea of finding "good gauges". We will then briefly explain the general setting in Gauge theory and finally we will comment on the main result in Uhlenbeck's 1982 paper, where the existence of these gauges is guaranteed under suitable hypotheses that we will later mention.
Stefan Müller - Applications of Moser's Argument to the Study of Geometric Structures
We consider a smooth manifold with an additional geometric structure, for example a Riemannian metric, a volume form, or a symplectic form. If the previous sentence makes sense to you, this talk should be fairly easy to follow. We are interested in studying this additional structure rather than the underlying topological or smooth structure of the manifold. We examine some basic questions in the case of a volume or symplectic form using Moser's argument. After outlining the general argument, we apply it to prove Darboux's theorem, obtain the classification of (closed connected) symplectic surfaces, derive a result for volume-preserving diffeomorphisms, which we in turn apply to the study of the homotopy type of the group of volume-preserving diffeomorphisms, and prove Moser's stability theorem for symplectic structures.
Jason Murcko - CR Manifolds and the Extension Problem
No abstract.
Nick Addington - Sean Paul's Talk from September, at 1/2-Speed (Part I)
In Part I, our goal is to answer two questions:
- What is the Chow form?
- What did Cayley do in 1848?
We will cover enough classical algebraic geometry to answer the first question (lots of Grassmannians), and, time permitting, say a word about the global sections O(d) and state Sean's answer to the second.
Part II will be an introduction to Geometric Invariant Theory, in the spirit of EGA V.
Michael Childers - The Hopf Invariant
Following Bott and Tu, and Hatcher.
Junwu Tu - Some Algebras in Physics
No abstract.
Sarah Matz - The Fundamental Groupoid and Van Kampen's Theorem
Lino Amorim - On manifolds homeomorphic to the 7-sphere
I am very happy to give a talk since I realize this will make the world a better place. Another possible title for this talk would be: "How to win a Fields Medal with a 6 pages paper". So I think this will be of interest to everybody.