Date | Speaker | Title: |
---|---|---|
27/2 | Amites Sarkar (Western Washington) | Partitioning Random Geometric Covers |
6/3 |   | No seminar |
13/3 | Chris Bose | Strange Eigenmodes for Invertible, Measure Preserving Systems |
17/3 | Ethan Coven (Wesleyan) | Every odometer is a cellular automaton |
20/3 | Vipul Periwal (NIH) | A model of liver regeneration  |
27/3 | Mike Hochman (Princeton) | Local entropy and projections of dynamically defined fractals |
3/4 | Bob Burton (Oregon State) | A Brief Illustrated Story About Square Ice in The Random Snow |
Date: 13th Match
Speaker: Chris Bose (UVic)
Title: Strange Eigenmodes for Invertible, Measure Preserving Systems
Abstract:
The term strange eigenmode in dynamical systems refers to a
situation where some large-scale structure persists for
an uncharacteristically long time under action by an otherwise
mixing flow. This curious and not-very-well-defined concept has been
observed in nature (ocean flows, for example) and in some mathematical
models.
For one-dimensional uniformly expanding dynamics a reasonable explanation for the phenomenon can be given through the presence of large, non-peripheral eigenvalues for the associated transfer operator (acting on a suitable space of regular functions)
For mulidimensional uniformly hyperbolic systems, this theory breaks
down and one must instead look at an expanded space of 'functions' to
serve as the eigenmode. We present a preliminary report.
This is joint work with Gary Froyland, School of Mathematics and Statistics, University of New South Wales, AUSTRALIA
Date: 17th March
Speaker: Ethan Coven (Wesleyan)
Title: Every odometer is a cellular automaton
Abstract:
An odometer is the +1 map on a countable product of finite cyclic
groups, addition with "carrying." Think of an old-fashioned car odometer
with spinning wheels. A one-dimensional cellular automaton is a map given
by a local rule on a space of sequences with entries from a finite alphabet.
In two dimensions, think of the Game of Life.
I will show that every odometer is topologically conjugate to a "gliders
with reflecting walls" cellular automaton, and I will characterize those
odometers that are topologically conjugate to cellular automata with the
simplest, non-trivial, algebraic local rules: $x_i \mapsto x_i + x_{i+1}
\mod n$.
Date: 20th March
Speaker: Vipul Periwal (NIH)
Title: A model of liver regeneration
Abstract:
The network of interactions underlying liver regeneration is robust
and precise with liver resections resulting in controlled hyperplasia
(cell proliferation) that terminates when the liver regains its lost
mass. The interplay of cytokines and growth factors responsible for
the inception and termination of this hyperplasia is not well
understood. A model is developed for this network of interactions
based on the known data of liver resections. This model reproduces
the relevant published data on liver regeneration and provides
geometric insights into the experimental observations. The
predictions of this model are used to suggest two novel strategies for
speeding up liver mass recovery and a strategy for enabling liver mass
recovery in cases where a resection leaves less than 20$\%$ of the
liver that would otherwise result in complete loss of liver mass.
Spring 2006 |
Fall 2006 |
Spring 2007 |
Spring 2008 |