We use persistent homology to analyze predictions of protein
folding by trying to identify global geometric structures that
contribute to the error when the protein is misfolded. The goal is
to find correlations between global geometric structures...
We will showcase persistent homology as a promising new tool for
use in the study of complicated fluid flows. Through a collection
of examples spanning 2D Kolmogorov and Rayleigh-Bénard convection
flows to fully-developed 3D turbulence and...
Extrinsic Flavor: Given a point cloud in R^N sampled from an
unknown probability density, how can we decide whether that
probability density is concentrated near a low-dimensional manifold
M with reasonable...
Using the geometry of sheaves as the common language, this talk
will bridge three separate areas: dynamical systems, signal
processing, and data fusion. Because sheaves model consistency
relationships between local data, they are easily assembled...
Nazarov and Sodin have shown that the zero set of a random real
homogeneous polynomial in n+1 variables and of large degree has
many components and the same is true for the random harmonic such
polynomial ("mono-chromatic waves") .We show that for...
By imposing symmetry on manifolds of exceptional holonomy we get
a variety of differential geometric questions in lower dimensions.
Related to that, one can consider “adiabatic limits”, where the
manifold has a fibration and the fibre size is scaled...
We will discuss the constructions of compact manifolds with
exceptional holonomy (in fact, holonomy $G_{2}$), due to Joyce and
Kovalev. These both use “gluing constructions”. The first involves
de-singularising quotient spaces and the second...
In this lecture we will review the notion of the holonomy group
of a Riemannian manifold and the Berger classification. We will
discuss special algebraic structures in dimensions 6, 7 and 8,
emphasising exterior algebra, and then go on to...
Three fundamental factors determine the quality of a statistical
learning algorithm: expressiveness, optimization and
generalization. The classic strategy for handling these factors is
relatively well understood. In contrast, the radically
different...
