SCU Mathematics Colloquium Series Schedule

Winter 2005

**Jan. 11th**Helmer Aslaksen, National University of SingaporeTitle: Heavenly Mathematics

Abstract:At the National University of Singapore I have introduced a General Education Module called "Heavenly Mathematics: Cultural Astronomy". In this talk I will give some samples from the course. Most astronomy books are written from a "high-northern-latitude-centric" point of view. I will start by discussing the motion of the Sun and the Moon from a "hemispherically-correct" point of view, with special emphasis on the needs of "latitudinally-challenged" observers. Some of the questions we will address are: Why do clocks go clockwise? What does the orbit of the Moon around the Sun look like? Which day does the Sun rise earliest in San Francisco, Singapore or Sydney? How do you tell the difference between a waxing crescent Moon and a waning crescent Moon in San Francisco, Singapore or Sydney? I hope that this talk will make you more conscious of the mathematics of the world around you, and give you knowledge that you will enjoy sharing with others for the rest of your life.

**Jan. 25th**Stephen Devlin, USFCATitle: An Introduction to Voting Theory

Abstract:

We give a general overview of the issues involved in the field of voting theory, and look at some of the more famous results from the perspective of linear algebra and representation theory. In particular, the unavoidability of certain "voting paradoxes" can be nicely explained using this framework

**Feb 15th**Ilya Mironov, MicrosoftTitle: One of the central assumptions in cryptography is the hardness of the discrete logarithm problem: given g^{x} find x, where g is a group element of prime order p. In the adversary has only oracle access to the group, the complexity of the problem is about p^{1/2}. Define the complexity of the set $S$ as the number of queries that the adversary has to ask when x is known to belong to S. We show that the adversary can be modeled as a set of lines, such that projections of their intersection points cover S. An open problem is to construct small sets of high complexity. We show several constructions that get us there based on ideas from combinatorial number theory. The tools that we use include Sidon sets and Turan numbers. As a special treat we will prove and use bipartite Menelaus' theorem---an extension of a 2,000+-year old theorem of planar (and projective) geometry. This is joint work Anton Mityagin, UCSD, and Kobbi Nissim, Ben-Gurion University.

**March 1st**Michael B. ScottTitle: An Exact Light like Shock Wave Solution of the Einstein Equations in General Relativity

Abstract: We construct an exact solution of the Einstein equations interpreted as an outgoing spherical shock wave propagating at the speed of light. The solution is constructed by matching a Friedman Robertson Walker (FRW) metric, a geometric model for the universe, to a Tolman Oppenheimer Volkoff (TOV) metric that models a static isothermal spacetime.

Unless noted otherwise, talks will be at 4:00pm Tuesdays. Room O'Connor 206. There will be refreshments before all talks in O'Connor 31 starting around 3:45pm.

If you have a disability and require a reasonable accommodation, please call Aaron Diaz aaron@turing.scu.edu 1-408-554-6811 or 1-800-735-2929 (TTY - California Relay).

*Last Updated: 13 March 2005*