Abstract 1: In recent years, weak lensing of the cosmic
microwave background (CMB) has emerged as a powerful tool to probe
fundamental physics. The prime target of CMB lensing surveys is the
lensing potential, which is reconstructed from observed...
We describe two extensions, called the virtual Morse-Bott index
and circle-equivariant virtual Morse-Bott index, of the classical
Morse-Bott index of a Morse-Bott function on a smooth manifold to
the setting of (a) suitably defined analytic...
The regularity theory for the Navier-Stokes equation will be
reviewed. Motivations from Kolmogorov’s phenomenological theory of
turbulence will be discussed. Rigorous mathematical results are
obtained to confirm some of the phenomenologies.
I will discuss joint work with McLean and Smith, lifting the
results of Seidel, Lalonde, McDuff, and Polterovich concerning the
topology of Hamiltonian fibrations over the 2-sphere from rational
cohomology to complex cobordism. In addition to the...
We consider variational principles related to V. I. Arnold's
stability criteria for steady-state solutions of the
two-dimensional incompressible Euler equation. Our goal is to
investigate under which conditions the quadratic forms defined by
the...
I will present the cosmological weak lensing results from the
Dark Energy Survey (DES) using its first three years of data, taken
on the 4m Blanco telescope at CTIO. This analysis spans the full
DES footprint, more than 4000 sq. deg. of sky, with...
As solutions can be efficiently verified, any NP-complete
problem can be solved by exhaustive search. Unfortunately, even for
small instances the running time for exhaustive search becomes very
high.
Abstract 1: The time delay measured between the images of
gravitationally lensed quasars probes a combination of angular
diameter distances and the mass profile of the lens. Observational
campaigns to measure such systems have reported a...
Legendrian torus knots were classified by Etnyre and Honda. I
will explain the classification of Legendrian torus links. In
particular, I will describe restrictions on the Legendrian torus
knots that can be realized as the components of a Legendrian...
