Title: Geometry, Meet Origami
Abstract: In this talk, we will go back in time to the ancient Greeks (or at least your high school geometry class) and take a good look at what we can draw with a compass and straight-edge. The answer is “Not Much!,” at least when compared to what a little paper folding will get us. Come prepared to trisect some angles, double some cubes, and scoff at the circle squarers.
Title: So You Think Your Errors Are Random…
Abstract:
In the development of radio frequency systems for digital communications, great attention is given to achieving low error rate performance.
Oversimplification of assumptions, however, such as treating bit errors as independent, identically distributed (iid) events may lead to seriously flawed
projections of performance. An examination of the statistical behavior of error sequence correlation shows how reasonable observation schemes supported by
computer-based models can yield useful insight into likely system performance.
Title: Perspectives on Rank 1 Perturbations
Abstract:
The central question in perturbation theory is as follows. Let A and B be linear transformations; think of (NxN)-matrices or differential operators.
we know the eigenvalues of A and have partial information about B. What can we say about the eigenvalues of A+B?
The perturbation is said to be of rank 1, if we assume that B is a vector projection. This seemingly simple example (a) exhibits a surprisingly rich theory with connections
to harmonic analysis and operator theory; and (b) arises naturally in mathematical physics via a change of boundary conditions of a second order differential operator.
Title: Finding Cyclic Vectors
Abstract: In perturbation theory, the cyclicity (i.e. completeness of the forward orbit for some vector) of an operator is often a natural assumption
in the hypothesis of many results. We discuss two sets of results. (a) We consider rank one perturbations and some applications concerning the
locations where functions of the Payley-Wiener class are allowed to have zeros. (b) We study so-called Anderson-type Hamiltonians (a
generalization of random Schroedinger operators) and state that under mild conditions, every non-zero vector is cyclic almost surely. This result is
related to the long-standing problem of Anderson localization.
Title: GRAM-SCHMIDT TYPE ALGORITHMS
Advisor: Pete Brooksbank
Title: An Empirical Study of the Zeros of L-Functions.
Advisor: Nathan Ryan
Title: Analysis of Five Diagonal Reproducing Kernels
Advisor: Paul McGuire and Greg Adams
Title: How a Mathematician Defeated the Enigma (and a pitch for doing math at NSA).
Abstract:
Have you ever wondered how the German Enigma cryptographic device was defeated in World War II? Come see how a mathematician helped shorten the war by two years, and learn some math and history along the way. You will also have the opportunity to learn about mathematical summer internships and careers at NSA.
College-level mathematics is exciting and empowering, and the Mathematics Department wants your experience to begin in the best way possible! We are providing and requiring a 6-week online preparation course—the ALEKS Prep. for Calculus—for all students who will take MATH 201. Results from previous years show that working through this online course will get you started on the path to success in college calculus.
The Prep. for Calculus course will be available starting July 19. The deadline for completion for Fall Calculus enrollment is Aug. 29; we recommend you start by Aug 1. Students with a Spring Calculus enrollment may choose to complete this requirement over the summer or over winter break.
To get started, read the Prep. for Calculus Information sheet then visit the Bucknell ALEKS Prep. for Calculus Moodle page.
Title: Sticks and Stones
Abstract: In addition to their value as pure entertainment, games provide a rich environment in which to prototype ideas meant for application in a variety of fields: mathematics, computer science, and biology to name a few. In this talk I will introduce two games, one involving sticks and one involving stones, both of which are easy to play. Despite their simplicity, the games are remarkably useful: I will use them as an introduction to some important ideas involving the theory of algorithms. In particular, I will introduce the notion of dynamic programming, a general purpose tool commonly used to solve problems involving (biological) sequence alignment. The talk requires no background and is meant for a general student audience.