Student Geometry/Topology SeminarFall 2011
3-4 pm Tuesday Afternoons 3866 East Hall
Schedule of Talks
|September 13th||Organizational Meeting||Come with ideas of topics you might want to hear about or talk about.|
|September 20th||Geoffrey Scott||Morse Theory and Morse Homology|
|September 27th||Emily Clader||An Introduction to Gromov-Witten Theory|
|October 4th||Jeff Meyer||Lie Groups|
|October 11th||Andy Zimmer||Dynamics on Lie Groups|
|October 18th||No meeting||Fall break|
|October 25th||Will Abram||K Theory|
|November 1st||Robin Lassonde||Artin Groups|
|November 8th||KK Leung||Emily Dickinson: poet or Zoll manifold?|
|November 15th||Tengren Zhang||Teichmuller Theory|
|November 22nd||Will Abram||Cobordisms|
|November 29th||Mark S. or Jordan W.|
|December 6th||Mark S. or Jordan W.|
Nothing here yet!
Come to the organizational meeting on the 13th to plan future talks.
Morse Theory and Morse Homology
Geoffrey Scott - September 20, 2011
Morse theory is a collection of techniques to understand the topology of a manifold by studying the critical points of a real-valued function on that manifold. In the first half of my talk, I will summarize the results of classical Morse theory and explain how a Morse function yields a cell decomposition of the manifold. In the second half, I will present a modern approach to Morse theory called Morse Homology. As well as being an easy-to-understand way to think about the homology of a manifold, the ideas of Morse Homology can be applied to infinite-dimensional manifolds, such as certain loop spaces and path spaces of a manifold. These infinite-dimensional applications lie at the core of a fast-growing field of mathematics called Floer theory.
An Introduction to Gromov-Witten Theory
Emily Clader - September 27, 2011
Gromov-Witten invariants lie at the heart of a recent surge of development in the intersection between mathematics and physics. While these invariants have deep and often mysterious connections to other geometric data, Gromov-Witten theory is, at least under some simplifying assumptions, simply a piece of enumerative geometry. For example, one can use Gromov-Witten invariants to encode and to answer such classical questions as the number of conics through five points in the projective plane. In this talk, I will present the basic definitions of Gromov-Witten theory and explain its enumerative interpretation.
Lie Groups: A Survey
Jeff Meyer - October 4, 2011
What is a Lie group? When and for what purpose were they created? What are they used for now, and why would geometers care about them? In this survey talk, I will attempt to answer these questions. First imagined by Sophus Lie for a single purpose, Lie groups now touch every branch of mathematics. With a simple blend of algebra and geometry we can prove astounding results. With this talk I hope to give a sense of where Lie groups have been and where they are headed.
About The Seminar
This seminar is organized by and run by University of Michigan graduate students. Past topics have come from many different areas of geometry and topology, such as:
- Twisted K-theory (algebraic topology)
- Morse theory (differential topology)
- Quasi-isometries of symmetric spaces (differential geometry)
- Growth of groups (geometric group theory)
- Fundamental group of a compact semisimple Lie group (Lie group theory)
- Mathematical physics (differential topology)
For more past topics, see the "past seminar" links on the sidebar. Talks can be a broad survey of a theory or a focused discussion of a single result (or anywhere in between... the space of possibilities is path connected).
For information, or to volunteer to speak on any topic you wish, contact: