Often mathematicians refer to a "beautiful" result or a
"beautiful" proof. In this special lecture, Enrico Bombieri,
Professor Emeritus in the School of Mathematics, addresses the
question, "What is beauty in mathematics?"
For all practical purposes, the Micali-Vazirani algorithm,
discovered in 1980, is still the most efficient known maximum
matching algorithm (for very dense graphs, slight asymptotic
improvement can be obtained using fast matrix
multiplication)...
A `toy model' for studying the probabilistic distribution of
nodal curves of eigenfunctions of linear operators arises from the
Laplacian on the standard real 2-torus. Here the eigenvalues are
associate to integers m that are sum of two squares...
We study open-closed orbifold Gromov-Witten invariants of toric
Calabi-Yau 3-orbifolds with respect to Lagrangian branes of
Aganagic-Vafa type. We prove an open mirror theorem which expresses
generating functions of orbifold disk invariants in terms...
We study the nonlinear Klein-Gordon equation, in one dimension,
with a qudratic term and variable coefficient qubic term. This
equation arises from the asymptotic stability theory of the kink
solution.Our main result is the global existence and...
A general algebraic formalism for the mathematical modeling of
physical systems is sketched. This formalism is sufficiently
general to encompass classical and quantum-mechanical models. It is
then explained in which way quantum theory differs in an...