Events for 02/27/2015 from all calendars

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Title: TGTC, Feb. 27--Mar 1 at University of Houston

Seminar on Banach and Metric Space Geometry

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Galyna Livshyts, Kent State University

Title: On the perimeter of a convex set

Abstract: The perimeter of a convex set in ℝⁿ with respect to a given measure is the measure's density averaged against the surface measure of the set. It was proved by Ball in 1993 that the perimeter of a convex set in ℝⁿ with respect to the standard Gaussian measure is asymptotically bounded from above by n^{1/4}. Nazarov in 2003 showed the sharpness of this bound. We are going to discuss the question of maximizing the perimeter of a convex set in Rⁿ with respect to any log-concave rotation invariant probability measure. The latter asymptotic maximum is expressed in terms of the measure's natural parameters: the expectation and the variance of the absolute value of the random vector distributed with respect to the measure. We are also going to discuss some related questions on the geometry and isoperimetric properties of log-concave measures.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: U Houston

Speaker: TGTC

Title: Texas Geometry and Topology Conference

Abstract: Speakers: Cameron Gordon (UT Austin), Alastair Hamilton (Texas Tech), Laura Matusevich (Texas A&M), Lei Ni (UC San Diego), Colleen Robles (Texas A&M), Mark Stern (Duke), Bernd Sturmfels (UC Berkeley), Steve Zelditch (Northwestern)

URL: Event link

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Ron Douglas, Texas A&M University

Title: Applications of geometrical ideas to operator theory

Abstract: From Beurling's Theorem it follows that a cyclic invariant subspace M of a vector valued Hardy Space, H_ε²(D), is isometrically isomorphic to H²(D). For the Bergman space, L_a²(D), this fails miserably. We show, however, that if M is complimented in L_a,ε²(D) by an invariant subspace, then the result still holds. Along different lines we show that the operator-valued corona theorem for the unit disk fails, reproving a result of Trail which answers in the negative a conjecture of Nikolskii. Again, geometrical ideas are at the heart of the proof which rests on the fact that the Hardy and Bergman shifts are not similar.

Graduate Student Organization Seminar

Time: 5:00PM - 6:30PM

Location: Blocker 220

Speaker: Kaitlyn Phillipson, Texas A&M University

Title: A History of Sylvester's Four Point Problem

Abstract: What is the probability that four points taken at random in the plane will form a convex quadrilateral? Sylvester posed this problem in the Educational Times in 1864. He believed the the correct answer was 3/4; however, he was surprised to find that there were a variety of different answers with equally valid arguments. These disagreements led to a spirited discussion of what ``at random in the plane'' should mean and helped to motivate the development of geometric probability theory. In this talk, I will discuss the history of Sylvester's Four Point Problem, the theorem that arose from it (with some of the pretty mathematical tools used to prove it), and generalizations of Sylvester's Four Point Problem.