"The Crazy Thue-Morse Sequence"

The Thue-Morse sequence is a sequence of 0s and 1s beginning

    0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

with highly regular but nonperiodic structure.  It was independently discovered several times between 1850 and 1930 in a variety of contexts -- equal sums of like integer powers, combinatorics on words, differential geometry, and even chess.  I'll talk about several bizarre instances of the Thue-Morse sequence, and I'll describe the modern context of the sequence as the basic example of an "automatic sequence" in theoretical computer science.

"The Tangential Thickness of Spherical Space Forms"

Given two nonhomeomorphic manifolds M and N, it is often important to specify when and if M x R and N x R, or more generally M x R^k and N x R^k for some k>0, are homeomorphic.  In this talk I will introduce a topological k>invariant known as tangential thickness which goes some way to answering this question.  Specifically, I will concentrate on the area of my research in which the manifolds are so called spherical space forms (ie: manifolds of the form S^n/G for G a finite group acting freely on S^n).

Throughout the talk I also hope to introduce some of the tools and techniques used by geometric topologists to tackle classification problems such as this.  The talk should be self-contained and accessible to all with only a basic background of topology and algebra assumed.

Workshop on Informatic Phenomena

"On the Energy Relaxation and Topology of Zeldovich's Neutron Star"

It is often the case that physics leads to interesting and not well understood mathematics. One such case originates from the ideal magneto-hydrodynamics. Physicists suggest that during the evolution of a star, a magnetic field B slowly dissipates its energy until the field reaches its terminal position. The evolution is mathematically very simple and occurs via volume preserving push- forwards of B, but the process is not well understood even in the simplest case of the rotational vector field (y,-x,0). In the talk, I will describe a topological mechanism of energy dissipation for the rotational field proposed by the physicist Yakov Zeldovich and conjecturally described by Michael Freedman. The question remains widely open to this day.

"Long Term Behaviour of a Heat Equation from Eigenestimates"

The first method we learn to solve boundary value problems with is the method of eigenexpansion.  In this talk I will present eigenestimates which, with the method of eigenexpansion, will tell us about the long term behaviour of a heat equation with discontinuous thermal diffusivity

"The Stranger Side of Set Theory"

I will give a short review of axiomatic set theory, bag theory (which is like set theory but without the axiom of extensionality), and graph theory. Then I will show how, using methods from elementary topology, one can construct a universe of non-well-founded sets. I will attempt to describe this universe from two different points of view (one topological and one graph theoretic) and explore a few of its more curious properties. I will also mention how this universe relates to Aczel's non-well-founded sets.

"The Holonomic Systems Approach"

The Holonomic Systems Approach was proposed in the early 1990s by D.  Zeilberger and has turned out to be extremely useful when dealing with special functions in computer algebra. Moreover, his celebrated algorithm for definite hypergeometric summation originates from this approach. We want to give an introduction to the underlying ideas---Ore algebras, Groebner bases, creative telescoping---in an intuitive and therefore non-rigorous way. We also show various examples where these concepts can be successfully applied.

"Determining the biomechanical response of a filiform hair array: A low Reynolds number fluid-structure model"

The cercal  system of the cricket has served as a model sensory system over the last 30 years and has been the subject of many anatomical, developmental, functional, and theoretical studies during that time. This system is composed of two antenna-like appendages covered with hundreds of filiform mechanosensory hairs, and encodes information about the direction and dynamics of low-velocity air currents. Many previous studies have characterized the biomechanics of individual filiform hairs, but only a few have considered the fluid- mediated interaction of closely-packed hairs. These few studies suffer from one of two disadvantages: either the modeled  hair arrangements are limited in extent or configuration, or the computational cost is prohibitive. I present a fast and scalable numerical model of filiform hair motion that can simulate the motion of arbitrary hair arrangements on the cricket cercus. Using this model, I perform numerical simulations that demonstrate the possibility for both damping and synergistic coupling within biologically realistic groupings of filiform hairs.

"TBA"

"TBA"

"RIP: The RNA RNA Interaction Problem"

In this talk we introduce a new algorithm RIP that computes the partition function of RNA-RNA interaction structures. The algorithm is based on a novel grammar and outputs base pairing probability matrix as well as the probabilities of hybrid loops. In addition our algorithm allows to sample the space of interaction structurescan Boltzmann-weighted. We also discuss the RIP-output for several examples that represent challenges for current prediction tools and give a perspective on future work.