Tara Taylor's Research

There are many things that interest me, and so my background is quite diverse.  My current research focuses on fractals and topology.  One ongoing project is an investigation of the topological properties of the Sierpinski relatives, a class of fractals that all have the same fractal dimension but different topologies.  Another class of fractals that interests me are fractal trees.  

As an undergraduate student at the University of Winnipeg, I did some work in the area of algebraic graph theory with Dr. William Martin.  For my master's degree at Dalhousie, I worked with Dr. Alan Coley in cosmology.  My master's thesis involved the analysis of cosmological models with dynamical systems.  In May 2005, I successfully defended my PhD thesis "Computational Topology and Fractal Trees" (see below for a link to the thesis), so my current research involves an analysis of fractal trees using methods of computational topology.  My supervisor was Dr. Dorette Pronk of Dalhousie University.

Topology

Topology is a vast, beautiful field in mathematics.  Topology involves a type of geometry that ignores concrete spatial notions such as straightness, convexity and distance, and considers properties such as connectivity, orientability and continuity.  Topology Links

Fractals

Fractals can be used in many areas, such as the study of river drainage systems, the branching of cardiovascular systems, the
distribution of forest growth.  See Fractal Trees.

The Golden Ratio

The golden ratio is a fascinating number that has many interesting properties, including a connection to self-contacting trees that I discovered during my thesis work.  The fractal tree shown at the top of this page scales according to the golden ratio.  Golden Ratio Links

Publications

• '"Excursions through a Forest of Golden Fractal Trees", by T.D. Taylor, in The Beauty of Fractals: 6 Different Views, eds. Denny Gulick and Jon Scott,  entire volume accepted by to the Mathematical Association of America, January 2010.
• "A New Classification of Non-overlapping Symmetric Binary Fractal Trees Using Epsilon Hulls", by T.D. Taylor, Volume 17, Fractals, 365-384, 2009.
• "Topological Bar-codes of Fractals", by Tara D. Taylor, Volume 84 (Convex and Fractal Geometry), Banach
  Center Publications, 181-222, 2009
• "Thin Sets with Fat Shadows: Projections of Cantor Sets" by F. Mendivil and T.D. Taylor, Volume 115, The American Mathematical Monthly, 451-456, 2008.
• "Homeomorphism Classes of Self-contacting Symmetric Binary Fractal Trees'', by Tara D. Taylor, in Fractals, Volume 15, Number 1, pages 9-25, 2007.
• PhD Thesis: "Computational Topology and Fractal Trees"
• "Self-similar Spherically Symmetric Cosmological Models With Two Scalar Fields" ( Classical and Quantum Gravity  (18), 2001, pages 4213-4237)
• "A Grad Student at the Laval Meeting" (Canadian Mathematical Society Notes, Volume 34, number 5, September 2002).  To view this article, click here and turn to page 18

Selected Talks/Posters (needs to be updated)

• "Golden Fractal Trees", talk at the Bridges Conference (Mathematical Connections in Art, Music and Science), San Sebastian/Donostia, Spain, July 2007
• "Topological Barcodes of Fractals", talk at Convex and Fractal Geometry Conference, Bedlewo, Poland, May 2007.
• "Finding Gold in the Forest: Fractal Trees and the Golden Ratio", Joint Meeting of the American Mathematical Society and the Mathematical Association of America, New Orleans, January 2007.
• "New Classifications and Characterizations of Fractal Trees Using Methods of Computational Topology", poster at FRACTAL 2006, Vienna, Austria, February 2006.
• "Finding Gold In The Forest...A Connection Between Fractal Trees, Computational Topology and The Golden Ratio"
• "Butterflies and Mathematics" at the Dalhousie Honours Math Seminar, November 19. 2003.  Click  here to see the slides (but only the text part)
• "Fractals in Nature" at the Dalhousie Honours Math Seminar, February 26, 2003.  Click here to see the slides (only the text part, unfortunately no pictures)
• "An Introduction to the Axiom of Choice" at the Dalhousie Graduate Student Seminar, January 31, 2003.  Click here to see the slides

last updated June 10, 2010