# Help yourself

In 1966 Kac asked the question "Can one hear the shape of a drum?",
i.e. do the frequencies of a drum's vibration fully determine its
shape? For plane domains with fixed boundary (which are the closest
to the physical drums), this question was answered in the negative by
Gordon, Webb and Wolpert (GWW) in 1992. Their construction based on
the so-called Sunada method (1984) that uses representation theory.
Various proofs, generalizations and applications of this construction
exist; in particular one recent application is in the study of Dirac
points in the spectrum of graphene, by A.Comech and myself. The above
link illustrates a proof (due to Chapman) of the GWW example using
foldable paper models.

### CRM school "Geometric and Computational Spectral Theory"

lec1.m, lec2.m.

### Quantum Graph package for Matlab
(and examples of its use)

This is a class file containing routines for setting up a quantum
graph, computing its eigenvalue and computing and plotting its
eigenfunctions. It was developed basing on the code by Phuongmai Truong
and Ram Band with the primary aim of aiding in understanding the
behavior of the zeros of the eigenfunctions.

It is part I of a 2-lecture attempt of explaining how
Goedel's Incompleteness Theorem is proved. In these lecture notes a
criterion of incompleteness is given and a non-enumerable set is
constructed.

A short lecture prepared for 2007 Mini Math Fair at Texas A&M
University (part of 2007 Math Awareness Month activities). It is aimed at
school children and their parents.

A presentation on Buffon's needle problem for Aggieland Saturday 2012.

A talk on agreement between semiclassical expansions in chaotic
transport and RMT predicitions.

This file was last modified on Tuesday, 15-Sep-2015 15:24:11 CDT.