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May 2012
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Events for May 2012:

4 (Friday) Analysis Seminar
Uniqueness for a hyperbolic inverse problem with angular control of the coefficients
Prof. Rakesh (University of Delaware)
2:00 pm, Hylan 1106A
Let $u=u(x,t)$ be the solution of the initial value problem $u_{tt} - \Delta_x u + q(x) u = \delta(x,t)$ in $\mathbb{R}^3 \times [0,T]$ with zero initial data. Let $S$ be the unit sphere in $\mathbb{R}^3$ and $C= S \times [0,T]$ the space time cylinder with axis along the $t$ axis. We show that the map $F : q \mapsto (u, u_r)|_C$ is injective if $T$ is large enough and $q$ is restricted to a class of potentials whose angular derivatives are dominated by their radial derivatives. This is based on work done with Paul Sacks.
9 (Wednesday) Analysis Seminar
"Rearrangement properties of the Hilbert transform".
Enrico Laeng, Milano Politecnico
1:00 pm, Hylan 1106A

14 (Monday) NumberTheory Seminar
On the joint problem in Euclidean space
Xiaoqing Tang (University of Rochester)
2:00 pm, Hylan 1106A
A celebrated result due to Guth and Katz, previously explored by Bourgain and others, says that the number of joints determined by $N$ lines in ${\Bbb R}^3$ is $O(N^{\frac{3}{2}})$. We shall give a simple proof of this fact and discuss some interested related probabilistic issues.
16 (Wednesday) Honors BA Presentation
Rank numbers for bent ladders
Peter Richter
2:00 pm, Hylan 1106A
A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph P2 Pn . We investigate the impact of "bending" the ladder on the rank number. It turns out that in many cases the rank number does not change, and in others the rank number di§ers by only 1. We consider the two extremes of bent ladders, the Örst where there is a single bend, and in the others the number of bends is maximized.