Abstract: In this talk we present a general shadowing result for
normally hyperbolic invariant manifolds. The result does not use
the existence of invariant objects like tori inside the manifold
and works in very general settings. We apply this...
Consider a Calabi-Yau manifold which arises as a member of a
Lefschetz pencil of anticanonical hypersurfaces in a Fano variety.
The Fukaya categories of such manifolds have particularly nice
properties. I will review this (partly still conjectural)...
Abstract: We first examine the existence, uniqueness,
regularity, twist and symplectic properties of compact invariant
cylinders with boundary, located near simple or double resonances
in perturbations of action-angle systems on the annulus
$A^3$...
Abstract: We prove that for any non-trivial perturbation depending
on any two independent harmonics of a pendulum and a rotor there is
global instability. The proof is based on the geometrical method
and relies on the concrete computation of several...
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...
