Research Interests

Curriculum Vitae

Fixed Point Shifts of Inert Involutions To Appear in DCDS

Mixing Shifts of Finite Type with Non-Elementary Surjective Dimension Representations

Strictly Order n Automorphisms of 1-Sided Shifts of Finite Type

Involutions of Shifts of Finite Type: Fixed Point Shifts, Orbit Quotients, and the Dimension Representation (PhD Thesis)

Dynamical Systems Inset in SciDac Review Spring 2007 Issue 3 p. 48

Embedding finite order automorphisms

2006 Spotlight Paper: Polynomial Matrices in Symbolic Dynamics

2006 Spotlight Talk: Embedding finite order automorphisms

Preliminary Oral Exam: Counterexamples to the Shift Equivalence Conjecture

 

 

Preprints, Papers, and CV

My current research interests are in dynamical systems, specifically symbolic dynamics and automorphism groups of shifts of finite type. I am also interested in the application of symbolic dynamics to hyperbolic dynamics.

Current Problems:

¨ I am currently writing up an example of a symbolic extension of the dynamical system (S¹, id). This example involves constructing a certain zero entropy substitution shift space. This problem was originally asked by D. Burget based on the work of J. Buzzi and Boyle and Tomasz Downarowicz .

¨ I am also trying to generalize several classes of examples of mixing shifts of finite type with surjective dimension representations. These examples are the only known examples of MSFTs with surjective dimension representations that come necessarily from non-elementary strong shift equivalences. The first class is presented in my thesis (Chapter 5) linked below.

¨ I am also looking at examining invariants of hyperbolic sets of continuous dynamical maps.

I am also preparing papers addressing:

¨ Mixing shifts of finite type with Non-elementary surjective dimension representations.

¨ Fixed point shifts of inert automorphisms. To Appear in Discrete and Continuous Dynamical Systems.

¨ The quotient spaces of 1-sided SFT by strictly order n automorphisms.

I have an interest into several other problems dealing with various aspects of matrix theory and the classification problem of mixing SFTs.

High school at North Carolina School of Science and Mathematics .
             High school research:

             Duke University in statistics

             North Carolina State University in math, statistics, and physics.

Undergrad at North Carolina State University:
             BS in Mathematics and BS in Physics

             Research in algebra, mathematical physics, optics, and solid state              physics.

Graduate School at University of Maryland College Park

             PhD in Mathematics in May 2008: Involutions of Shifts of Finite              Type: Fixed Point Shifts, Orbit Quotients, and the Dimension              Representation

Written Qualifiers in Algebra, Geometry/Topology, and Ordinary              Differential Equations.

             Research in symbolic dynamics with interest in automorphism g             roups of shifts of finite type, fixed point sets of involutions,              algebraic dynamics, and K-Theory