Seminar Geometry, Topology, Dynamical Systems (2013-2014)

Sep 17, 24, Oct 1, 8, 14: Changsong Li, Braids and Temperley-Lieb algebra

Oct 22, 29, Nov 12, 19, Dec 3, 10: T. Hagge, An Introduction to the Character Theory of Representations

Oct 26: V. Dragovic, Siebeck-Marden Theorem

Nov 2: M. Dabkowski, Why knot?

Nov 9: M. Dabkowski, Polynomial Knot Invariants

Nov 30: T. Hagge: What is a 3-Manifold?

Dec 7: A. Phung: The number of intersections of plane algebraic curves

Feb 8: I. Zelenko (Texas A&M) : Geometry of nonholonomic distributions with given Jacobi symbol.

Feb 15: M. Dabkowski, Kauffman Bracket Skein Module of a 3-manifold

Feb 18: Derege H.Mussa, Texas A&M University-Commerce, Reconstruction of tetrahedron from Edge length

Feb 25: Gabriele La Nave, Isotropic curvature, macroscopic dimension and fundamental group

Apr 15: O. Makarenkov, A perturbation approach to study the dynamics of nonlinear differential equations

Apr 25

Aykut Satici

Electrical Engineering, University of Texas at Dallas

Swarming with Connectivity via Lagrange-Poincare Equations

One of the important goals of a multi-agent mobile network is coverage or surveillance of a given area. This requires the agents to swarm or move in formation along a desired path/trajectory. In other words, it is desired that the centroid of the formation move along a specified desired trajectory. In addition when avoiding contact with the environment is an issue, we may also want to specify a desired orientation trajectory of the multi-agent system.

While the swarming operation is under way, it is still desired to achieve and maintain a desired connectivity measure whenever information sharing between agents in the network is required. In this work, we propose a framework which nearly decouples the control design for these two potentially conflicting goals by exploiting the inherent symmetries of mechanical systems.

May 2

Oleg Makarenkov

University of Texas at Dallas

A perturbation approach to study the dynamics of nonlinear differential equations, II

Some interesting examples will be presented

May 6, 13

M. Dabkowski, SL(2C) character varieties