Office: Room 716, Mathematics building; tel: 6212742
I grew up and went to school in Moscow, Russia. Graduated from the Moscow Institute of Electronics and Mathematics (MIEM) in 1976 with the diploma in Applied Mathematics (a rough equivalent of the MS degree.) I started my research with Mikhail Agranovich who was (and still is) a professor in MIEM. After couple of years, I decided that I would like to move to the US. That move took time, but, finally, in 1987 I found myself in Boston, MA. I went to Graduate School, and in 1989 I got my PhD in Mathematics from MIT. Victor Guillemin was my dissertation advisor. For two years, I was an Adjunct Assistant Professor in UCLA, and, from 1991, I am on the faculty in the University of Arizona.
My field of research is spectral geometry. The motion of an object, say, of a membrane, is usually modeled by a differential equation. A membrane has natural frequencies that a person with a perfect ear is able to distinguish (my ear is far from being perfect.) To compute these frequencies, one has to find the spectrum of the corresponding differential operator. The spectrum depends on the shape (the geometry) of the membrane. Most people know that a bigger drum has lower tones, and usually it is not difficult to distinguish a violin from a bass. Spectral geometry studies all kind of relationships between the spectrum and the geometry. Some research in spectral geometry is motivated by theoretical physics. Here is the list of my publications.
I have taught Precalculus, Calculus I,II,III; upper division
undergraduate courses in ODE and PDE; graduate courses in Complex Analysis,
Principles of Analysis, PDE, Hilbert and Banach spaces, Geometry/Topology,
Global Differential Geometry, and Spectral Geometry (a special topics course.)
In the Spring of 2004, I taught a special topics course "Introduction to micro-local analysis." Here you can find links to some notes that I wrote while teaching the course.
In the Spring of 2013, I teach Math. 559B (Lie Groups and Lie Algebras).
If you wish, you can take a look at a rather disorganized picture gallery.