The Department of Mathematics welcomes Shiwen Zhang, visiting assistant professor of mathematics, Michigan State University.
His topic: "From Eigenvalues to Fractals"
The eigenvalue problem for a finite-dimensional matrix can be easily understood. A natural question is how about an infinite-dimensional matrix? In this talk, we will give a brief introduction on eigenvalue problems of infinite-dimensional matrices. A simple but important example of an infinite-dimensional matrix is the almost Mathieu operator which arises naturally from quantum mechanics. One interesting and surprising fractal phenomenon of this operator is the so-called Cantor Spectrum.
We will discuss Hofstadter's butterfly and Ten Martini Problem about the Cantor Spectrum of the almost Mathieu operator. In the end, we will see some other planar fractal problems in geometric measure theory and probability theory.
- Join us for a reception at 4 p.m., in King Building, 203
- Lecture will follow at 4:30 p.m., in King Building, 239