Georgia Institute of Technology College of Sciences

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.

We will state Serre's fundamental finiteness and vanishing results for the cohomology of coherent sheaves on a projective algebraic variety. As an application, we'll prove that the constant term of the Hilbert Polynomial does not depend on the projective embedding, a fact which is hard to understand using classical (non-cohomological) methods.

In 1979 Valiant gave algebraic analogs to algorithmic complexity problem such as $P \not = NP$. His central conjecture concerns the determinantal complexity of the permanents. In my lecture I shall propose geometric and algebraic methods to attack this problem and other lower bound problems based on the elusive functions approach by Raz. In particular I shall give new algorithms to get lower bounds for determinantal complexity of polynomials over $Q$, $R$ and $C$.