# 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