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University of North Texas at Dallas

Title: Invariants in Low Dimansional Topology and Topological Dynamics

DirectorsNoureen Khan, Byungik Kahng

Dates of Program: May 12 - August 8, 2014


The project is a continuation of the investigators’ NREUP 2012 and 2013 projects. This year’s NREUP project aims to improve those of the previous years’ still further, by expanding its scope on the targeted students.

Problem 1. Invariants of Virtual Knots. There are infinitely many flat virtual diagrams that appear to be irreducible, but so far there is no known technique to prove this conjecture. More specifically, how can one tell whether a virtual knot is classical? Or, are there non-trivial virtual knots whose connected sum is trivial? The latter question cannot be resolved by classical techniques, but it can be analyzed by using the surface interpretation for virtuals.

Problem 2. Controllability and approximate control of the maximal/minimal invariant sets of a class of non-linear control dynamical systems with singular disturbance.  Invariant set theory is one of very few reliable tool, under the singular disturbance that prohibits the use of traditional calculus-based tools. The controllability is often the first problem that must be resolved. Here, we focus upon the controllability of the optimal cases, the maximal and/or the minimal invariant sets.

Student Researchers Supported by MAA:

Mathew Gomez 
Mark Lugo 
Javier Mondragon 
Delia Rojas 

Program Contacts:

Lloyd Douglas

Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences.