Seminars and Colloquia by Series

Color-Critical Graphs on Surfaces

Series
Graph Theory Seminar
Time
Thursday, December 3, 2009 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Carl Yerger – Math, GT
A fundamental question in topological graph theory is as follows: Given a surface S and an integer t > 0, which graphs drawn in S are t-colorable? We say that a graph is (t+1)-critical if it is not t-colorable, but every proper subgraph is. In 1993, Carsten Thomassen showed that there are only finitely many six-critical graphs on a fixed surface with Euler genus g. In this talk, I will describe a new short proof of this fact. In addition, I will describe some structural lemmas that were useful to the proof and describe a list-coloring extension that is helpful to ongoing work that there are finitely many six-list-critical graphs on a fixed surface. This is a joint project with Ken-ichi Kawarabayashi of the National Institute of Informatics, Tokyo.

An Extension of the Cordoba-Fefferman Theorem on the Equivalence Between the Boundedness Maximal and Multiplier Operators

Series
Analysis Seminar
Time
Wednesday, December 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alexander Stokolos – Georgia Southern University
I will speak about an extension of Cordoba-Fefferman Theorem on the equivalence between boundedness properties of certain classes of maximal and multiplier operators. This extension utilizes the recent work of Mike Bateman on directional maximal operators as well as my work with Paul Hagelstein on geometric maximal operators associated to homothecy invariant bases of convex sets satisfying Tauberian conditions.

Cohomology and the Riemann-Roch theorem

Series
Other Talks
Time
Wednesday, December 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Kangkang Wang – School of Mathematics, Georgia Tech
We will present a sheaf-theoretic proof of the Riemann-Roch theorem for projective nonsingular curves.

Variational problems involving area.

Series
Research Horizons Seminar
Time
Wednesday, December 2, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
John McCuan – School of Mathematics, Georgia Tech –
I will describe several geometrical problems that arise from the minimization of some sort of integral functional and the basic relation between such minimization and partial differential equations. Then I will make some further comments on my favorite kind of such problems, namely those that have something to do with minimizing area of surfaces under various side conditions.

The fluid dynamics of feeding and swimming in the upside down jellyfish, Cassiopea xamachana

Series
Mathematical Biology Seminar
Time
Wednesday, December 2, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Laura Miller – University of North Carolina at Chapel Hill
The Reynolds number (Re) is often used to describe scaling effects in fluid dynamics and may be thought of as roughly describing the ratio of inertial to viscous forces in the fluid. It can be shown that ’reciprocal’ methods of macroscopic propulsion (e.g. flapping, undulating, and jetting) do not work in the limit as Re approaches zero. However, such macroscopic forms of locomotion do not appear in nature below Re on the order of 1 − 10. Similarly, macroscopic forms of feeding do not occur below a similar range of Reynolds numbers. The focus of this presentation is to describe the scaling effects in feeding and swimming of the upside down jellyfish (Cassiopeia sp.) using computational fluid dynamics and experiments with live animals. The immersed boundary method is used to solve the Navier-Stokes equations with an immersed, flexible boundary. Particle image velocimetry is used to quantify the flow field around the live jellyfish and compare it to the simulations.

Thin domains with a highly oscillating boundary

Series
PDE Seminar
Time
Tuesday, December 1, 2009 - 15:01 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jose Arrieta – Universidad Complutense de Madrid; visiting faculty at GT
In this talk we will present several results concerning the behavior of the Laplace operator with Neumann boundary conditions in a thin domain where its boundary presents a highly oscillatory behavior. Using homogenization and domain perturbation techniques, we obtain the asymptotic limit as the thickness of the domain goes to zero even for the case where the oscillations are not necessarily periodic. We will also indicate how this result can be applied to analyze the asymptotic dynamics of reaction diffusion equations in these domains.

The Jones slopes of a knot

Series
Geometry Topology Seminar
Time
Monday, November 30, 2009 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Stavros Garoufalidis – Georgia Tech –
I will discuss a conjecture that relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. I will present examples, as well as computational challenges.

Limbless locomotion: how snakes use friction to move

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 30, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
David Hu – Georgia Tech ME
How do animals move without legs? In this experimental and theoretical study, we investigate the slithering of snakes on flat surfaces. Previous studies of slithering have rested on the assumption that snakes slither by pushing laterally against rocks and branches. In this combined experimental and theoretical study, we develop a model for slithering locomotion by observing snake motion kinematics and experimentally measuring the friction coefficients of snake skin. Our predictions of body speed show good agreement with observations, demonstrating that snake propulsion on flat ground, and possibly in general, relies critically on the frictional anisotropy of their scales. We also highlight the importance of the snake's dynamically redistributing its weight during locomotion in order to improve speed and efficiency. We conclude with an overview of our experimental observations of other methods of propulsion by snakes, including sidewinding and a unidirectional accordion-like mode.

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