The Slow Pitch Seminars are arranged by graduate students for graduate students, and provide a forum for professors to present their work, interests and personal sides. Students are encouraged to use these seminars to gain a view of the current work in the department, get a closer look at potential advisors and to glimpse into the person behind the research.
Input from the graduate students of the math department is encouraged. We are constantly looking for suggestions about the format, questions for interviews and the line-up of professors. Please contact Hamid with any comments.
| Time & Date | Location | Speaker | Topic |
|---|---|---|---|
| 1 pm, Thursday, Nov. 17 | Krieger 308 | Chika Mese | The Plateau Problem |
| 1 pm, Thursday, Dec. 8 | Krieger 308 | Bernard Shiffman | Complex Dynamics |
| 1 pm, Thursday, April 6 | Krieger 308 | Florin Spinu | The Selberg Trace Formula |
Suppose that f(z) is a complex polynomial (or more generally a rational or meromorphic function). Start with a point z_0 in C. What is the behavior of the sequence of points z_1=f(z_0), z_2=f(z_1), ... z_{n+1}=f(z_n), ...? Sometimes the sequence will converge, sometimes it will approach a periodic orbit, and sometimes it will exhibit chaotic behavior. You may be familiar with the (usually) fractal "Julia sets" consisting of those points z_0 whose orbits z_1,z_2,z_3,... are chaotic. In fact, Montel's theorem was first discovered when he studied the sequence of iterates f(z), f(f(z)), f(f(f(z))), .... (It converges normally on the complement of the Julia set.)
This subject was first thoroughly investigated in the early 20th century by Fatou, Julia, Montel and others, and has had a recent renaissance. In this talk I will survey some of the classic results in complex dynamics, and indicate how some of these results extend to functions of several complex variables.
Here's a question to think about before the talk: A calculus student asked, "When I entered a number on my calculator and repeatedly hit the 'cosine' key, the result converged to .73908513. But when I entered a number and repeatedly hit the 'sine' key, the result didn't converge to 0. Why did this happen?" Were the student's conclusions correct? Can you answer the student's question?