# Erin Pearse

## Associate Professor

**Email:** epearse@calpoly.edu**Office Phone:** 805-756-5558**Office:** 25-341**Office Hours:** MTRF 1:10-3:00pm

## Education

- Postdocs: Cornell University, University of Iowa, University of Oklahoma
- Ph.D., Mathematics, University of California, Riverside, 2006
- B.S., Mathematics, University of California, Riverside, 1999
- B.A., Philosophy, University of California, Riverside, 1998

## About

I am an Associate Professor in the Department of Mathematics at Cal Poly, San Luis Obispo. My dissertation was on connections between fractal geometry and convex geometry (Steiner's formula) and I did postdoctoral work on infinite networks, studied from the point of view of Hilbert spaces. My more recent work pertains to graph-based aspects of data science, including nonlinear dimensionality reduction, optimal transport, and machine learning. I enjoy working on research with undergraduates and have published some papers with undergraduate coauthors.

When I'm not working on mathematics, I work on the climate crisis. I am involved with a number of organizations on and off campus (Institute for Climate Leadership and Regional Resilience, Sunrise Movement, SLO Climate Coalition, Central Coast Climate Coalition, Extinction Rebellion) as an advocate, advisor, activist, and researcher. I encourage any students interested in working to stop the climate catastrophe to reach out to me.

## Research Interests

Fractal geometry and connections to convex geometry and curvature. Fractal analysis, discrete harmonic analysis, energy measures. Resistance forms, infinite networks, and operator-theoretic approaches to their analysis; geometry and curvature of large networks, asymptotic properties of networks. Network-based methods of data analysis, nonlinear dimensionality reduction methods.

## Current and Past Courses Taught

Calculus (142, 143, 241), linear algebra (206, 306, 406), linear analysis (244, 344), methods of proof (248), graph theory (335), LaTeX (351), special problems (400), complex analysis (408, 409), analysis (412, 413, 414), partial differential equations (418), topology (440, 541), numerical optimization (453), real analysis (550).

## Professional Distinctions

Managing Editor of the Journal of Fractal Geometry
(JFG)

External Faculty: Institute for the Applications of Mathematics & Integrated Science (IAMIS).

## Resource Links

http://sunriseslo.com/

https://carbonfreeslo.org/

https://www.ems-ph.org/journals/journal.php?jrn=jfg

## Publications

**Publications**

[24] V. Bonini, C. Carroll, K. Cooper, U. Dinh, S. Dye, J. Frederick, and E. P. J. Pearse. Condensed Ricci Curvature of Complete and Strongly Regular Graphs. Involve, 13(2020), no.4, 559–576.

[23] S. Chen and E. P. J. Pearse. The irrationality measure of π as seen through the eyes of cos(n). Elemente der Mathematik, 75(2020), no.1, 96–105.

[22] Z. Cooperband, E. P. J. Pearse, B. Quackenbush, J. M. Rowley, T. Samuel, M. A. West. On the continuity of entropy of Lorenz maps. Indagationes Mathematicae, 31(2020), 152–165.

[21] P. E. T. Jorgensen and E. P. J. Pearse. Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces. Journal of Mathematical Analysis and Applications, 469(2019), no.2, 765–807.

[20] P. E. T. Jorgensen and E. P. J. Pearse and Feng Tian. Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications. Analysis and Mathematical Physics, 8(2018), no.3, 351–382.

[19] P. E. T. Jorgensen and E. P. J. Pearse. Symmetric pairs of unbounded operators in Hilbert space, and their applications in mathematical physics. Mathematical Physics, Analysis and Geometry, 20(2017), no.2, 14–31.

[18] P. E. T. Jorgensen and E. P. J. Pearse. Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks. Compl. Anal. Oper. Theory, 10(2016), no.7, 1535–1550.

[17] S. Kombrink, E. P. J. Pearse, and S. Winter. Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable. Mathematisches Zeitschrift, 283(2016), no.3–4, 1049–1070.

[16] P. E. T. Jorgensen and E. P. J. Pearse. Spectral comparisons between networks with different conductance functions. Journal of Operator Theory, 72(2014), 71–86.

[15] M. L. Lapidus, E. P. J. Pearse, and S. Winter. Minkowski measurability results for self-similar tilings and fractals with monophase generators. In Fractal geometry and dynamical systems in pure and applied mathematics I: Fractals in pure mathematics, volume 600 of Contemporary Mathematics, p. 185–203. Amer. Math. Soc., Providence, RI, 2013.

[14] P. E. T. Jorgensen and E. P. J. Pearse. Multiplication operators on the energy space. Journal of Operator Theory, 69(2013), 135–159.

[13] P. E. T. Jorgensen and E. P. J. Pearse. A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks. Israel Journal of Mathematics, 196(2013), 113–160.

[12] D. A. Fife, N. Judice-Campbell, E. P. J. Pearse, J. D. Pleitz, and R. Terry. Estimating the effect of academic intervention in a mandatory study skills class. In Proceedings of the 8th National Symposium on Student Retention (ed. S. Whalen), p.164–171, 2012.

[11] E. P. J. Pearse and S. Winter. Geometry of canonical self-similar tilings. Rocky Mountain Journal of Mathematics, 42(2012), no.4, 1327–1357.

[10] P. E. T. Jorgensen and E. P. J. Pearse. Spectral reciprocity and matrix representations of unbounded operators. Journal of Functional Analysis, 261(2011), 749–776.

[9] P. E. T. Jorgensen and E. P. J. Pearse. Gel’fand triples and boundaries of infinite networks. New York Journal of Mathematics, 17(2011), 745–781.

[8] M. L. Lapidus and E. P. J. Pearse. Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators. Advances in Mathematics, 227(2011), no.4, 1349–1398. Equal collaboration.

[7] P. E. T. Jorgensen and E. P. J. Pearse. Resistance boundaries of infinite networks. In Progress in Probability: Boundaries and Spectral Theory, v64, p. 113–143. Birkhauser, 2010.

[6] M. L. Lapidus and E. P. J. Pearse. Tube formulas and complex dimensions of self-similar tilings. Acta Applicandae Mathematica, 112(2010), 91–137.

[5] P. E. T. Jorgensen and E. P. J. Pearse. A Hilbert space approach to effective resistance metrics. Complex Analysis and Operator Theory, 4(2010), 975–1030.

[4] M. Ionescu, E. P. J. Pearse, L. G. Rogers, H.-J. Ruan, and R. S. Strichartz. The resolvent kernel for PCF self-similar fractals. Transactions of the American Mathematical Society 362(2010), no.8, 4451–4479.

[3] M. L. Lapidus and E. P. J. Pearse. Tube formulas for self-similar fractals. In Analysis on Graphs and its Applications, volume 77 of Proceedings of Symposia in Pure Mathematics, p. 211–230. Amer. Math. Soc., Providence, RI, 2008.

[2] E. P. J. Pearse. Canonical self-affine tilings by iterated function systems. Indiana University Mathematics Journal, 56(2007), no.6, 3151–3169.

[1] M. L. Lapidus and E. P. J. Pearse. A tube formula for the Koch snowflake curve, with applications to complex dimensions. Journal of the London Mathematical Society, 74(2006), no.2, 397–414.

**Editorship**

[3] R. G. Niemeyer, E. P. J. Pearse, J. A. Rock, and T. Samuel Horizons of Fractal Geometry and Complex Dimensions., vol 731 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 2019.

[2] D. Carfi, M. L. Lapidus, E. P. J. Pearse, and M. van Frankenhuijsen. Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics, vol 601 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 2013. Equal collaboration.

[1] D. Carfi, M. L. Lapidus, E. P. J. Pearse, and M. van Frankenhuijsen. Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I: Fractals in Pure Mathematics, vol 600 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 2013. Equal collaboration.

**Ph. D. Dissertation**

**Patents**

U.S. Patent App. No.: 14/920,556

Filed: October 22, 2015

Title: Iterated Geometric Harmonics For Data Imputation And Reconstruction Of Missing Data

Inventors: Erin Pearse, Jonathan Lindgren, Chad Eckman, Zachariah Zhang, David Sacco

Applicant: Cal Poly Corporation

Publication No.: US-2016-0117605-A1

Publication Date: April 28, 2016