Graduate Student - UAB Department of Mathematics

Email: childers@math.uab.edu

Contact Information

Department of Mathematics	Tel. 205-934-2154
University of Alabama at Birmingham
Birmingham AL 35294

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Education

August, 2006            PhD, Applied Mathematics (Minor in Mathematical Applications to Physics and Biology)

2001                           MS, Mathematics

2000                           BS, Mathematics (Minor in French)

Teaching Experience

Spring, 2006	Instructor in Calculus II
2004-05	Mentor in Fast-Track Seminar: Chaos in Ecology
Spring, 2001-04	Teaching assistant in Mathematical Modeling
Fall, 2002	Instructor in Mathematical Modeling
2001-02	Mentor at ASFA High School
2001	Teaching assistant in Intermediate Algebra
Fall, 2000	Instructor in Intermediate Algebra
2000	Teaching assistant in Intermediate Algebra
1998-99	Tutor

Awards

	GAANN Fellowship (Present)
	MCTP Fellowship (2004-05)
	GAANN Fellowship (2003-04)
	GK-12 Fellowship (2001-03)
	Fast-Track Scholarship (1998-2000)

Talks

February 2006:  "Iterations of Critical Points in Complex Dynamics,"  University of Delaware.

June 2005:  "Sequences of Rotation Numbers Imply Degeneracy of a Lamination on the Closed Unit Disk,"  CMS/CSHPM Summer 2005 Meeting, Waterloo, Ontario, Canada.

April 2005:  "Hedgehogs are in the Limit Set of a Recurrent Critical Point,"  AMS Spring Central Sectional Meeting, Lubbock, TX.

March 2005:  "Hedgehogs are in the Limit Set of a Recurrent Critical Point," Spring Topology Conference, Rome, GA.

November 2004:  "Indecomposable Subcontinua of the Plane," Complex Dynamics Graduate Class, Tulane University.

June 2004:  "N-1 Recurrent Critical Leaves are Needed for a Wandering N-sided Polygon,"  Joint Summer Research Conference on Complex Dynamics: Complex Dynamics 25 Years After the Mandelbrot Set, Snowbird, Utah.

May 19th,  2004:  "Wandering Polygons Converge onto Several Recurrent Critical Leaves,"  Nipissing University (North Bay, Ontario) Topology Mini-Conference.

March 25th,  2004:  "Wandering d-polygons in a d-lamination of the Unit Disk Converge to d-1 Recurrent Critical Leaves,"  2004 Spring Topology and Dynamics Conference, Birmingham, AL.

October 7th, 2003:  "The Movement of Prime Ends of Bounded Fatou Domains,"  Complex Dynamics Graduate Seminar, Boston University.

Papers

D. K. Childers, J. C. Mayer, and J. T. Rogers, JR. Indecomposable continua and the Julia sets of polynomials, II, to appear in Topology and Its Applications.

D. K. Childers, J. C. Mayer, H. M. Tuncali, and E. D. Tymchatyn. Indecomposable continua and the Julia sets of rational maps, to appear in Contemporary Mathematics, proceedings of the conference Complex Dynamics: 25 Years After the Mandelbrot Set.

D. K. Childers. Wandering polygons and recurrent critical leaves, to appear in Ergodic Theory and Dynamical Systems.

D. K. Childers. Are there critical points on the boundaries of mother hedgehogs?, submitted 2005.

A. Blokh, D. K. Childers, J. C. Mayer, and L. Oversteegen. Non-degenerate quadratic laminations, in preparation.

Research Plans

    Currently, the main part of my research is in the topology and dynamics of Julia sets of polynomials or, more generally, rational maps. One approach to studying these objects, at least for polynomials, is to study invariant laminations of the unit disk. I am independently working on a project involving renormalizations of a lamination (which is invariant under one of the circle maps f(z) = z^n) . I am also working with my first advisor, Dr. Mayer, on using the properties of rational map’s Fatou set to classify some topological properties of rational Julia sets.

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