This is from joint works with D. Knopf and I. M. Sigal. In this
talk I will present a new strategy in studying neckpinching of mean
curvature flow. Different from previous results, we do not use
backward heat kernel, entropy estimates or subsequent...
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?"
In the past ten years, the term “heritage” in African art
studies has gone from being a cliché used only by cultural
bureaucrats to a burgeoning academic growth industry, brought into
being by studies of collective memory or national trauma in...
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...
