Math Department Colloquia and Video Series

The Math Department Colloquia are a series of talks intended for a general audience. Everyone is encouraged to attend and the talks are directed at people who have a reasonable comprehension of the topics in undergraduate mathematics. Come meet our undergraduates, graduate students and faculty as well as our distinguished guest speakers.

For fall 98, our colloquia are generally going to be Thursdays at 1pm. There will be a refreshements beforehand.

Hyperbolic Tessellations and Escher's Art

Friday, Nov 13, 3:10pm in MCL 162

Dr. Jennifer Taback, from the UC Berkeley Mathematics Department

Everyone is familiar with the regular Euclidean tessellations of the plane by equilateral triangles, squares and hexagons. What kind of geometry would we have to impose on the plane to make regular octagons tessellate, say 8 to a vertex? I will talk (interactively) about this type of geometry, called hyperbolic geometry, and contrast some basic properties of hyperbolic geometry with those of Euclidean geometry. We have all seen examples of hyperbolic geometry in some of Escher's tessellations. Together we will examine these drawings, and look for their hyperbolic symmetries.

Brownian motion and the shape of a region's boundary.

Thursday, Nov 19, 1:10pm in S139

Dr. Lesley Ward, from the Harvey Mudd College Mathematics Department

A random walker starts walking from a point P inside a region S. Let h(r) be the probability that the first place the walker hits the boundary is within distance r of P. If we know h(r) for every r, can we determine the shape of the boundary of S? In this talk, we'll see that the answer is no.

If we know the boundary, what can we say about h(r)? We'll give some conditions h(r) must satisfy, and look at examples where we can compute h(r) exactly. Our main technique uses conformal mappings and harmonic measure; neither of these is a prerequisite for the talk. This is joint work with Byron Walden.

Not Knot

The 20 minute video Not Knot , produced by the Geometry Center at the University of Minnesota. "Not Knot" is a computer-generated video which illustrates some important ideas from knot theory and hyperbolic geometry.

Above images on this page are copyrighted by The Geometry Center, University of Minnesota and are from the video "Not Knot", distributed by A.K. Peters, Wellesley, MA. Used with permission.

Iterative Algebra and Dynamic Modeling

Thursday, Oct 29, 1:10pm in S139

Dr. Kurt Kreith, from the UC Davis Department of Mathematics
Abstract: What if computers had been invented 500 years earlier? How might the study of mathematics have been affected by such an event? And now that computer technology has become so commonplace, what are its implications for the study and application of mathematics? These questions underlie a book project and a course I am offering at Davis High School on "Iterative Algebra and Dynamic Modeling." Starting with two familiar problems

• solving quadratic equations, and
• solving a system of 2 linear equations in 2 unknowns

Thurs, Oct 15, 1pm in Peters 390
Crystals and Shortest Networks

Dr. Frank Morgan, a well-known lecturer and researcher in the field of minimal structures, discusses the notion of shortest networks of paths between a collection of points. He also discusses connections between the notions of minimal size structures and crystals.

Thurs, Oct 8, 1pm in Peters 390
Fractals, the Colors of Infinity

The Mandelbrot set is a beautiful and remarkable discovery. This video, narrated by Arthur C. Clark, illustrates how simple formulae can lead to complicated results. The video explains the Mandelbrot set, what it means, and some of the mathematical revolutions inspired by its discovery.

This video is an introduction to the mathematics of cryptography, data compression and electronic information transmission. Encryption and ciphers are introduced as tools for communication in a wide variety of settings including postal codes, Universal Product Codes, as well as public-key cryptography, a widely- used data-security tool. Come join math majors and faculty for an interesting video- free popcorn provided!

Thurs, Sept 24: 12:30pm in Peters 390
N is a Number

This documentary covers the life of Paul Erdos, a remarkable and unusual mathematician. Erdos was a prolific contributor (over 1500 papers, well over 100 coauthors) to many fields of mathematics, including analysis, probability, number theory, geometry, and combinatorics. He and Selberg discovered an elementary proof of the prime number theorem, and Erdos was among the founders of the fields of random graphs and extremal set theory. He encouraged and has influenced countless young people.

Thurs, Sept 17: 12:30pm in Peters 390
Outside In

The award-winning computer animation Outside In explains the amazing discovery, made by Steve Smale in 1957, that a sphere can be turned inside out by means of smooth motions and self intersections, without cutting or tearing. It convincingly demonstrates how valuable visualization can be in the communication of mathematics. This 20-minute video is nicely done and will be accompanied by popcorn!

Previous colloquia
• S98 colloquia, schedule here.
• F97 colloquia, schedule here.
• 96-97 colloquia, schedule here.