# Lennie Friedlander

### Professor of Mathematics

Office: Room 716, Mathematics building; tel: 6212742

E-mail: friedlan@math.arizona.edu

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,
Real 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 2016, I teach
Math. 528B (Banach and Hilbert Spaces)