Erin P.J. Pearse - Cornell University Mathematics

Erin Pearse — Visiting Assistant Professor

Graduate Student, Mathematics.

Ph.D. June 2006.

Specialization: Fractal Geometry and Analysis

Webpage:	http://www.math.cornell.edu/~erin/
Email:	erin* *@math.cornell.edu
Office:	588 Malott Hall
Phone:	(607) 255-3536
Fax:	(607) 255-7149

	»Curriculum Vita
	»Research Statement
	»Teaching Statement
	»Graduate Transcripts (unofficial)

Ability as Primary Instructor:	»Student's Scores and Comments
	»Sample syllabus and course notes
Ability as Teaching Assistant:	»Student's Scores
	»Student's Comments

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/math-ph/0412029

Canonical self-similar tilings by IFS.
Preprint, Nov. 2005. 17 pages (0.8MB).

Tube formulas and complex dimensions of self-similar 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 self-similar 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.

Self-similar 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 self-similar 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)

Self-similar 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 n-dimensional 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. 51-60, 28 pages)
Math 149A - Probability (Review sheet) (Take-home quiz: Memoryless distributions)
Math 151C - Advanced Calculus / Analysis (Solutions to Rudin - Chap. 10-11, 26 pages)
Math 205D - Topology Summer Preparatory Seminar (document folder) (Worked qualifier problems) (Homework: Munkres 51-60)
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.