
Erin Pearse — Visiting Assistant Professor 
Graduate Student, Mathematics.
Ph.D. June 2006.
Specialization: Fractal Geometry and Analysis
Papers
A tube formula for the Koch snowflake curve, with applications to complex dimensions
(with M. L. Lapidus), J. London Math. Soc., accepted Sept. 2005. 18 pages.
arXiv link: http://arxiv.org/abs/mathph/0412029
Canonical selfsimilar tilings by IFS.
Preprint, Nov. 2005. 17 pages (0.8MB).
Tube formulas and complex dimensions of selfsimilar tilings.
(with M. L. Lapidus
Preprint, May 2006. 61 pages (0.8MB).
arXiv link: http://arxiv.org/abs/math.DS/0605527
Note: arXiv version lacks symbol glossary and subject index, due to arXiv automation script bug.
Complex dimensions of selfsimilar systems.
Ph. D. Dissertation (draught), Feb. 2006. 135 pages (1.7MB).
Advisor: Michel L. Lapidus
(Abstract and introduction)
(Slides from the defense)
Talks
Here are notes & slides from some of the talks that I've given.
Selfsimilar tilings and their complex dimensions.
(Talk Slides)
Presented: 21st Summer Conference on Topology and its Applications, July 6 (Statesboro, GA)
Tube formulas and complex dimensions of selfsimilar tilings
(Talk Slides)
Presented: AMS Western Sectional, April 2006 (San Francisco, CA)
Curvature and convexity
(Week 1: Curvature Talk Slides)
(Week 2: Convexity Talk Slides)
Presented: UC Riverside Mathematical Physics Seminar (Jan. 2006)
Complex dimensions and the Steiner formula
(Talk Slides)
Presented: AMS National 2006 (San Antonio, TX)
Selfsimilar tilings and complex dimensions
(Talk Slides)
Presented: 2nd Annual Conference on Analysis and Probability on Fractals (Cornell University)
A tube formula for the Koch snowflake curve, with applications to complex dimensions
(Talk Slides)
Presented: AMS Western Sectional 2004 (UNM, Albuquerque, NM), and also at
AMS Central Sectional 2004 (Northwestern, Evanston, Il)
Distributions and the Descent Method
(Talk Notes)
(Talk Slides)
Presented: UC Riverside Mathematical Physics Seminar (Jan. 2005)
An introduction to fractal geometry, dimension, and nonsmooth analysis
(Talk Notes)
Presented: UC Riverside Graduate Student Seminar (Jan. 2005)
Introduction to LaTeX
(Talk Slides)
(Talk Notes)
(Examples)
Presented: UC Riverside Graduate Student Seminar (Oct. 2004)
Iteration of rational functions
(Talk Notes)
(Talk Slides)
Presented: UC Riverside Mathematical Physics Seminar (Nov. 2003)
The ndimensional Laplacian
(Talk Notes)
Presented: UC Riverside Mathematical Physics Seminar (June 2003)
Characterizing the measurability of fractal strings (A primer for FGNT)
(Talk Notes)
Presented: Oral Examination (May 2003)
A primer on dimension theory
(Talk Notes)
Presented: UC Riverside Mathematical Physics Seminar (Jan. 2003)
Material from courses I've taught
Math 023  Linear Algebra for Business
(Lecture Notes  87 pages)
(Syllabus)
(Homework 01)
(Homework 02)
(Homework 03)
(Homework Guide)
Math 046  Differential Equations
(Lecture Notes  150 pages)
(Syllabus)
Math 121  Game Theory
(Review sheet)
Math 145B  Algebraic Topology
(Solutions to Munkres  Chap. 5160, 28 pages)
Math 149A  Probability
(Review sheet)
(Takehome quiz: Memoryless distributions)
Math 151C  Advanced Calculus / Analysis
(Solutions to Rudin  Chap. 1011, 26 pages)
Math 205D  Topology Summer Preparatory Seminar
(document folder)
(Worked qualifier problems)
(Homework: Munkres 5160)
Math 209D  Real Analysis Summer Preparatory Seminar
(document folder)
(Homework list)
(Worked qualifier problems)
(Lecture Notes  62 pages!)
Basic Survival Tools  a very brief student's guide to some basic principles of functions & sets, for any math course with proofs.
The Fundamental Mantras of Compactness  a very brief student's guide to the key properties of compactness.
Note: Most material beyond this point is kept here for easy access by myself and a few friends,
and is probably of limited interest to anyone else.
Graphics, Plots, Diagrams
Britta's square snowflake
Mesh approximation of the Devil's Staircase
The Cantor String
Miscellaneous
Translation (by me) of G. Matheron's paper, "The Steiner formula for erosions."
Translations (by me) of some sections of Laurent Schwartz's "Theory of Distributions"
Galois correspondence and relations between the subfields of the 20th cyclotomic field (from a sketch by James Dolan)
Constructing the subfields of the 20th cyclotomic
Coursework
Algebra (from Hungerford)
Exercises v5.1
Exercises v5.2
Exercises v5.3
Exercises v5.4
Exercises v5.5
Exercises v5.8
Algebraic Topology
Munkres, Chapter 9
Differential Topology
Homework 2
Homework 3
Midterm
Differential Equations
ODEs  211A Homework
ODEs  211A Final
ODEs  211B Homework
PDEs  212 Midterm
PDEs  212 Final
Probability & Stochastics
Probability  217A Final
Stochastics Homework
