The 2013 Indiana Undergraduate Research Conference
Monday, July 22, 2013
How to get here and there:
- Google maps to Rawles Hall, the home of the Mathematics Department.
- An interactive campus map and a pdf campus map.
- 8:30-9:30 - Registration and reception, Rawles Hall Lounge
- 9:30-10:00 - Opening remarks, Woodburn Hall (WH) 003
- Welcome by David Clemmer, Associate Dean for Natural and Mathematical Sciences and Research, and Robert and Marjorie Mann Chair of Chemistry
- Kevin M. Pilgrim, Director of Undergraduate Studies, Department of Mathematics, Indiana University
- 10:00-12:10 - Parallel sessions
- 12:10-1:45 - Lunch, with some IU graduate students, at the Tudor Room, Indiana Memorial Union
- 1:45-3:20 - Parallel sessions
- 3:30-4:00 - Tea, Rawles Hall Lounge
- 4:00-5:00 - Plenary lecture, Woodburn Hall (WH) 004
Rodrigo Perez, Department of Mathematics, IUPUI,
Title: Siegel disks
When a complex analytic map $f$ takes a topological disk $D$ to itself so that $f:D \longrightarrow D$ is conjugate to an irrational rotation, we say that $D$ is a Siegel disk of $f$.
Problems about Siegel disks are among the most subtle in complex dynamics. Broadly speaking, existence questions marry dynamical systems and number theory (realizable rotation numbers must satisfy some kind of Diophantine condition), while questions about the structure of $D$ tend to involve topological arguments (the boundary $B = \partial D$ can be an indecomposable continuum).
Apparently then, Siegel disks have something to offer to people in many areas of Mathematics. In this talk I will give basic definitions and examples. Then I will describe the state of the art in the field, and conclude with a number of open problems.
Note to speakers:
All rooms have the following: blackboard, overhead projector, Mac and PC with USB drives, built-in computer projector, ``vga'' cables for laptop hookup, screen, and internet access. Speakers bringing Mac laptops and laptops with only ``dvi'' output need to bring their own ``vga'' adapter.
Kevin M. Pilgrim