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...
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...