Spring 2010 Seminar Series in Mathematics Apr 26, 2010

This Spring semester we will be having a seminar series funded through the Dean's office. We have 4 or 5 speakers lined up. More information will be posted as it becomes available. For now, we have:

Prof. Kawohl. Wednesday March 10th, 2:30, Room 1S-219

Title: Convex sets of constant width, or why geometry can be of vital importance
Abstract: When is the cross section of a pipe perfectly circular? When its width is independent of the direction in which I measure it, say, with a large caliper? The answer is no, and the fact that this answer was not known to some had tragic consequences, because it contributed to the Challenger desaster. In my talk I present two- and three-dimensional sets of constant width and some of their surprising properties. They can be used to construct drills which drill square holes, for instance, or buttons and balls that cannot roll away. I shall also report on progress in the proof of a mathematical conjecture related to these bodies. There are more pictures than formulas in the lecture. It is suitable for a general (undergraduate and graduate) audience.

Prof. Gabriella Tarantello (University of Rome II) April 7, 2:30pm, 1S-219

Title:On a class of mean field equations and their applications

Abstract: We shall discuss a class of mean field equations on compact surfaces, which arise from the study of gauge field vortices. We present some existence and non-existence results as well as concentration properties of the solution, according to the topological and geometrical properties of the surface. Uniqueness will be also discussed in certain cases.

Professor Lisa B. Warner, Rutgers University. 4/22, 1:30pm

How can mathematics teachers raise the level of mathematical discussion in the classroom?

This presentation will focus on the ways in which several middle school mathematics teachers revised their interactions with their students while participating in a long-term professional development project, based at Rutgers University. Many teachers want their students to go beyond solving mathematical problems on paper to explaining and justifying their solutions to their peers. I will discuss our research on the ways in which teachers can modify their practice to achieve this goal. I will show video excerpts that highlight critical moments in the classroom, to demonstrate the teacher-student dynamic, and also illustrate how an eighth-grade mathematics class evolved as their teacher changed his approach.

Professor Greg Martin, 4/30 11:30AM

Prime numbers: What we know, and what we know we think

Questions about the distribution of prime numbers, and about the existence of prime numbers of special forms, have been stymieing mathematicians for over two thousand years. It's almost necessary to study two different subjects: the theorems about prime numbers that we have been able to prove, and the (vastly more numerous) conjectures about prime numbers that we haven't yet succeeded at proving. In this talk I'll describe many of the open problems (and a few closed ones) concerning the distribution of primes, mentioning when I can some techniques that have been used to attack them.