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Schedule - February 11, 2006

List of Faculty Speakers

• Keith Conrad, Mathematics, University of Connecticut
  Heuristics for Prime Statistics (Abstract)

  It's been known since Euclid that there are infinitely many prime numbers. But more refined questions about primes quickly lead into unsolved problems.

  For instance, how often should we run into primes of the form n² + 1? Or how often should we expect to find twin primes (primes differing by 2, such as 3 and 5 or 101 and 103)? Questions like these are still open, but probabilistic heuristics suggest what the answers should be. We will discuss these heuristics, how they stand up to the numerical evidence, and why anyone would care about these questions in the first place.

• Maria Zuber, Geophysics, MIT
  Measuring Seasonal Changes on Mars
• Wendy Hagen-Bauer, Astronomy, Wellesley
  Probing the Atmosphere of a Red Supergiant Star with the Hubble Space Telescope (Abstract)

  I'll spend about half the talk on the background material of stellar evolution (especially that they lose mass in the red giant phase), and then talk about my research program which uses ultraviolet spectra obtained by Hubble. A hot companion goes into eclipse behind the supergiant, and as it emerges from eclipse, its orbital motion provides a probe of the structure of the supergiant's atmosphere as we observe the effect of the atmosphere on the light passing through it.

• Peter Schultz, Geology, Brown University
  Deep Impact (Abstract)

  The Deep Impact mission collided with a comet on July 4 (2005). This was a unique NASA mission that positioned a probe so that it could collide. The results of this large cratering experiment are providing the first data for interpreting the inside of a medium-age comet. Recently the team reported the first discovery of icy dirt in a few large areas. The presentation will briefly describe some of the first results.

• Jeffrey Brock, Mathematics, Brown University
  Angle defects, total curvature, and the polyhedral Gauss-Bonnet theorem (Abstract)

  The celebrated Gauss-Bonnet theorem relating the curvature of a surface to its topology represents a fundamental tool in differential geometry. In this talk I will discuss a more first-principles "polyhedral" version of this theorem using simple notions from high school geometry, and some basic elements of combinatorial topology (no integration required). I'll then show why most good things in math, as in life, are hyperbolic.

• Ian Dell'Antonio, Astronomy, Brown University
  Using Gravitational Lensing to Measure Dark Matter and Dark Energy (Abstract)

  In the last decade, we have come to realize that the primary components of the Universe are very different from the matter we are familiar with. The dominant components today are dark matter (an unknown substance that behaves gravitationally like ordinary matter) and dark energy (an even stranger substance with a repulsive gravitational effect), in a roughly 1:3 ratio.

  Measuring the distribution in space and the time evolution of the energy densities of dark matter and dark energy will be key to understanding what they are, and one of the most promising ways to address this issue is gravitational lensing.

  I'll review the technique of weak gravitational lensing and show how it can be used to measure dark matter and dark energy. I will also present the state of current experiments in this field, and discuss the prospects for advances in the next decade.

• Richard Schwartz, Mathematics, Brown University
  Triangular Billiards (Abstract)

  I plan to talk about what happens when you play billiards on a triangular pool table with a frictionless infinitesimally small ball. Amazingly, it has been unknown for 200 years if one can find, for any shaped triangular table, a way to hit the ball so that it endlessly traces out the same path. This has seemed to be a completely intractible problem in dynamics but I will talk about some progress that I have made on it in the past year using computer-aided methods. For a lot of my talk I will demonstrate McBilliards, a videogame-like computer program made by myself and Pat Hooper to investigate this problem.

List of Student Speakers

• David Anton Karpuk, Mathematics, Boston College
  The Complex Structure of Elliptic Curves (Abstract)

  

• Inna Zakharevich, Mathematics, Harvard University
  Hilbert's Third Problem (Abstract)

  In 1900 Hilbert presented a list of twenty-three unsolved problems in a presentation of his personal view of the direction of mathematics. I will discuss the third of these problems: the question of whether given any two polyhedra of equal volume it is possible to dissect one into several polyhedra and rearrange it into the other.