In this talk we discuss a new second order parabolic evolution equation

for hypersurfaces in space-time initial data sets, that generalizes mean

curvature flow (MCF). In particular, the 'null mean curvature' - a

space-time extrinsic curvature quantity - replaces the usual mean

curvature in the evolution equation defining MCF.  This flow is motivated

by the study of black holes and mass/energy inequalities in general

relativity. We present a theory of weak solutions using the level-set

method and  outline a natural application of the flow as a parabolic

approach to finding outermost marginally outer trapped surfaces (MOTS),

which play the role of quasi-local black hole boundaries in general

relativity. This is joint work with Kristen Moore.

One of the peculiar features of quantum mechanics is
entanglement. It is known that entanglement is monogamous in the sense
that a quantum system can only be strongly entangled to one other
system. In this talk, I will show how this so-called monogamy of
entanglement can be captured and quantified by a "game". We show that,
in this particular game, the monogamy completely "cancels out" the
advantage of entanglement.
As an application of our analysis, we show that - in theory - the
standard BB84 quantum-key-distribution scheme is one-sided
device-independent, meaning that one of the parties, say Bob, does not
need to trust his quantum measurement device: security is guaranteed
even if his device is completely malicious.
The talk will be fully self-contained; no prior knowledge on quantum
mechanics/cryptography is necessary.

In his talk, Kerry will explore the pressing practical problem of how hurricane activity will respond to global warming, and how hurricanes could in turn be influencing the atmosphere and ocean.

Operators, functions, and functionals are combined in many problems of computational science in a fashion that has the same logical structure as is familiar for block matrices and vectors.  It is proposed that the explicit consideration of such block structures at the continuous as opposed to discrete level can be a useful tool.  In particular, block operator diagrams provide templates for spectral discretization by the rectangular differentiation, integration, and identity matrices introduced by Driscoll and Hale.  The notion of the rectangular shape of a linear operator can be made rigorous by the theory of Fredholm operators and their indices, and the block operator formulations apply to nonlinear problems too, where the convention is proposed of representing nonlinear blocks as shaded.  At each step of a Newton iteration, the structure is linearized and the blocks become unshaded, representing Fréchet derivative operators, square or rectangular.  The use of block operator diagrams makes it possible to precisely specify discretizations of even rather complicated problems with just a few lines of pseudocode.

[Joint work with Nick Trefethen]