PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov.

Title:Behind the Hofstadter's butterfly: the competition between order and chaos
Seminar:MASS Colloquium
Speaker:Svetllana Jitomirskaya, University of California Irvine
Abstract:
Hofstadter's butterfly was maybe the first beautiful fractal produced in a numerical experiment (in 1976, before the word fractal came into existence). We will discuss some interesting features of the models behind it, called quasiperiodic operators, an area of strong interplay of ergodic theory, dynamical systems, probability, functional and harmonic analysis. Quasiperiodic operators feature a fascinating competition between randomness (ergodicity) and order (periodicity), that is often resolved on a deep arithmetic level. The interest in those models was enhanced by strong connections with some major discoveries in physics, such as integer quantum Hall effect, experimental quasicrystals, quantum chaos theory, as well as graphene. Quasiperiodic operators provide central or important models for all four. We will not talk much about physics but will touch upon a related question of how the difference between rationals and irrationals can play a role in nature.

Room Reservation Information

Room Number:MB113
Date:10 / 21 / 2010
Time:11:15am - 12:05pm