Ken Golden : Mathematics of Sea Ice
- Applied Math and Analysis ( 15 Views )Sea ice undergoes a marked transition in its transport properties at a critical temperature of around -5 C. Above this temperature, the sea ice is porous, allowing percolation of brine, sea water, nutrients, biomass, and heat through the ice. In the Antarctic, this critical behavior plays a particularly important role in air-sea-ice interactions, mixing in the upper ocean, in the life cycles of algae living in the sea ice, and in the interpretation of remote sensing data on the sea ice pack. Recently we have applied percolation theory to model the transition in the transport properties of sea ice. We give an overview of these results, and how they explain data we have taken in the Antarctic. We will also describe recent work in developing inverse algorithms for recovering the physical properties of sea ice remotely through electromagnetic means, and how percolation processes come into play. At the conclusion of the talk, we will show a short video on a recent winter expedition into the Antarctic sea ice pack.
Roger Temam : Mathematical Problems in Meteorology and Oceanography
- Applied Math and Analysis ( 32 Views )We will review the primitive equations of the atmoshere and the ocean and their coupling. We will descibe some mathematical poblems that they raise, some recent results and some less recent ones.
Cole Graham : Fisher–KPP traveling waves in the half-space
- Applied Math and Analysis ( 74 Views )Reaction-diffusion equations are widely used to model spatial propagation, and constant-speed "traveling waves" play a central role in their dynamics. These waves are well understood in "essentially 1D" domains like cylinders, but much less is known about waves with noncompact transverse structure. In this direction, we will consider traveling waves of the Fisher–KPP reaction-diffusion equation in the Dirichlet half-space. We will see that minimal-speed waves are unique (unlike faster waves) and exhibit curious asymptotics. The arguments rest on the theory of conformal maps and a powerful connection with the probabilistic system known as branching Brownian motion.
This is joint work with Julien Berestycki, Yujin H. Kim, and Bastien Mallein.
Zane Li : Interpreting a classical argument for Vinogradovs Mean Value Theorem into decoupling language
- Applied Math and Analysis ( 122 Views )There are two proofs of Vinogradov's Mean Value Theorem (VMVT), the harmonic analysis decoupling proof by Bourgain, Demeter, and Guth from 2015 and the number theoretic efficient congruencing proof by Wooley from 2017. While there has been some work illustrating the relation between these two methods, VMVT has been around since 1935. It is then natural to ask: What does previous partial progress on VMVT look like in harmonic analysis language? How similar or different does it look from current decoupling proofs? We talk about a classical argument due to Karatsuba that shows VMVT "asymptotically" and interpret this in decoupling language. This is joint work with Brian Cook, Kevin Hughes, Olivier Robert, Akshat Mudgal, and Po-Lam Yung.