Graduate Student Seminar 08-09

Abstract: This talk will be an introduction to the theory of orderable groups, with emphasis on examples. The main focus will be "the space of all orderings of a group", a new object of study which has proven very useful in addressing several long-standing open problems. Time permitting, I will also explain those open problems that have been resolved using the space of all orderings of a group, as well as outline directions for future research.

Abstract: By utilizing an appropriate set of projection operators, we discuss when an (arbitrary-dimensional) Lorentzian manifold can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives.

Abstract: The connections between music and mathematics are old and deep. This talk will serve as an introduction to the interplay, with emphasis on using mathematics to uncover musical mysteries in The Beatles "A Hard Day's Night".

Abstract: I will introduce some of the basic concepts of category theory and illustrate with some examples the unifying effect the functorial methodology has on mathematics.

Abstract: In this talk, I will go over the history and basic results in the area. I will start with an introduction to Turing's initial results. I will then discuss the formation of solutions with sharp fronts and sharp spikes.