IMSE lunchtime seminar: December 4, at noon

We meet in Grainger Libraryroom 335. The last IMSE seminar of the year will have

Naira Hovakimyan, MechSE, talking on Planning with monsieur Bezier

 We will introduce a heuristic planar trajectory-generation framework for multiple vehicles. Desired feasible trajectories are generated using Pythagorean Hodograph Bezier curves that satisfy the dynamic constraints of the vehicles, and guarantee spatial separation between the paths for safe operation. It is shown that the trajectory generation framework can be cast into a constrained optimization problem where a set of (sub)optimal desired trajectories are obtained by minimizing a cost function. To show the efficiency of the algorithm, a simulation example is given, where three fixed-wing Unmanned Aerial Vehicles are following and coordinating along feasible trajectories that are generated by the algorithm.
followed by

Richard Laugesen, Math, who, sticking with the French, speaks about
The Laplacian: conjectured spectral bounds

Eigenvalues of the Laplacian have intrigued physicists and mathematicians for hundreds of years. They represent physical quantities such as frequencies of drums and energy levels of quantum particles, while encoding geometric information such as area and perimeter.

I will discuss recent numerical work (not by me) that hints at a possible isoperimetric type inequality for high energies.

(This talk is accessible to anyone who has heard of the trigonometric eigenfunctions of the rectangle or the Bessel eigenfunctions of the disk.)

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