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SCU Mathematics Colloquium Series Schedule
Spring 1998
SCU Mathematics Colloquium Series Schedule
Spring 1998
Talks will be at 4:00 Tuesdays in O'Connor 206. There will be refreshments before all talks in O'Connor 31 starting around 3:40pm.
Title: Can we compress a secret?
It's generally accepted that people will not carry around a car key as heavy as their car, even if it provided absolute protection against car thieves. Along the same lines, it would be very desirable to compress a secret cryptographic key to a small amount of information that we could carry around with us. Around fifty years ago, Claude Shannon proved that under at least one model of security, it is impossible to compress a secret. In spite of this, we routinely use ad hoc encryption methods that use short keys to encrypt long messages. In this lecture I'll describe the evolution of encryption design principles from Shannon to today, the engineering requirements that have appeared since the time of Shannon, and some of the mathematical research questions that arise from them.
Title: Lattice geometry and pythagorean triangles
By reflecting a quadratic or regular triangular lattice about an appropriate line, there will occur in the superposition a Moire' effect with a new quadratic or regular triangular lattice of enlarged scale. These lattices are related to Phythagorean triangles or corresponding "Pythagorean 120o triangles", i.e. triangles with integer side lengths and an angle of 120o. These lattices also yield a geometric visualization of the usual parametrization of primitive Pythagorean triangles and Pythagorean 120o triangles.
Title: The cake-cutting problem, the ham sandwich theorem and other topics in culinary mathematics
The Intermediate Value Theorem of freshman calculus has many interesting corollaries and we explore some of them in this talk. In particular we show that it is always possible to divide a cake fairly and that, if different people value different parts differently, everyone can get more than their fair share.
A graph-theoretic approach to problems in elementary and combinatorial geometry
Using topological graph theory, planar and spherical graph models we solve some conjectures and problems of Grunbaum on Venn diagrams. In this talk I will focus on those results that are related to convex and strongly convex Venn diagrams. I will talk about the possibilities of drawing these diagrams with convex figures (k-polygons, circles, ellipses, triangles, ...). One of our results corrects some erroneous statements that started with John Venn more than a century ago in 1880 and have been repeated frequently by others since then. Some of the results are joint results with R. E. Pippert.
Computing with harmonic functions
This expository talk describes the mathematics behind algorithms for computing solutions to many problems involving harmonic functions. One such problem is the Dirichlet problem: given a polynomial in n variables, find the harmonic function on Euclidean n-space that agrees with the given polynomial on the unit sphere.
Title: The fundamental group: What a beautiful idea
The lists of talks from previous quarters are available via this archive link.
Last Updated: 3 April 1998
Maintainer: dsmolarski@scu.edu