Brief Description - Freshman Seminar - Fall 2002
CURTIS T. McMULLEN will offer a seminar on low-dimensional dynamics, geometry and randomness.
Through readings, computer experiments, problems and research, members of the seminar will study simple constructions with rich structure. Fractional dimensional snowflakes, irrational rotations, continued fractions, billiards, tiling patterns and random walks may all be topics for investigation. Examples will make contact with number theory, geometry and analysis.
What would a surface of dimension 2.5 look like? Are some numbers more irrational than others? If you glue a mass of triangles together 7 to a vertex, what do you get? Does a random walker always return home? Can a computer recreate evolution? We will study mathematical models that lend insight into such questions.
The simulation of dynamical systems lends them an empirical reality, complementing what can be deduced by theoretical analysis. Members will be invited to contribute computer programs and graphics to the seminar group, as well as report on their investigations in short presentations, papers and discussions.