Erin Pearse   —   Visiting Assistant Professor
           

 Graduate Student, Mathematics.

  Ph.D. June 2006.

 

Specialization:  Fractal Geometry and Analysis

 

Webpage: http://pi.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.

 


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