Does the world embody beautiful ideas? This is a question that
people have thought about for a long time. Pythagoras and Plato
intuited that the world should embody beautiful ideas; Newton and
Maxwell demonstrated how the world could embody...
The PCP theorem (Arora et. al., J. ACM 45(1,3)) asserts the
existence of proofs that can be verified by reading a very small
part of the proof. Since the discovery of the theorem, there has
been a considerable work on improving the theorem in terms...
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...
