Events for 11/20/2009 from all calendars

Working Seminar in Geometry

Location: Milner 317

Speaker: Jeanne Clelland, U. Colorado

Title: Introduction to the Backlund transformation.

Abstract: An introductory talk for graduate students. All are welcome. To be followed by a talk in the Geometry Seminar (M 216) at 4 o'clock.

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:40PM

Location: BLOC 627

Speaker: Gregory Berkolaiko, Texas A&M

Title: Counting nodal domains on graphs

URL: Link

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: MILN 317

Speaker: Simon Guest, Baylor

Title: A Solvable Version of the Baer–Suzuki Theorem

Abstract: Let G be a finite group, and take an element x in G. The Baer–Suzuki states that if every pair of conjugates of x generates a nilpotent group then the group generated by all of the conjugates of x is nilpotent. It is natural to ask if an analogous theorem is true for solvable groups. Namely, if every pair of conjugates of x generates a solvable group then is the group generate by all of the conjugates of x solvable? In fact, this is not true. For example, if x has order 2 in a (nonabelian) simple group G then every pair of conjugates of x generates a dihedral group (which is solvable), but the normal subgroup generated by all of the conjugates of x must be the whole of the nonabelian simple group G, which of course is not solvable. There are also counterexamples when x has order 3. However, the following is true:
1. Let x ∈ G have prime order p ≥ 5. If every pair of conjugates of x generates a solvable group then the group generated by all of the conjugates of x is solvable.
2. Let x ∈ G be an element of any order. If every 4-tuple of conjugates x, x^g₁, x^g₂, x^g₃ generates a solvable group then the group generated by all of the conjugates of x is solvable.
We will discuss these results, some generalizations, and some of the methods used in their proof.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: MILN 216

Speaker: J. Clelland, U. Colorado

Title: Backlund transformations and Darboux integrability for nonlinear wave equations

Abstract: We prove that a second-order Monge-Ampere equation for one function of two variables is connected to the flat wave equation by a Backlund transformation if and only if it is integrable by the method of Darboux at second order. The proof relies on a geometric formulation of a Backlund transformation as a certain type of exterior differential system and its associated differential invariants. This is joint work with Thomas Ivey of The College of Charleston.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: MILN 317

Speaker: Alex Poltoratski, Texas A&M University

Title: Entire functions and gap theorems

Abstract: In my talk I will discuss solutions to two problems of classical analysis obtained using an approach recently developed in our joint papers with Nikolai Makarov. A sequence of real numbers is called a Polya sequence if any entire function of exponential type zero that is bounded on that sequence is a constant. The first problem that I will discuss is an old problem by Polya and Levinson that asks for a description of such sequences. This part is based on joint work with my student Mishko Mitkovski. The second problem is the Beurling's gap problem. If X is a closed set on the real line, denote by G_X the supremum of the size of the gap in the support of the Fourier transform of μ, taken over all non-trivial complex measures μ supported on X. I will present a formula for G_X in terms of metric characteristics of X.