## Erin Pearse Assistant Professor

### Ph.D., University of California, Riverside

**Email:** epearse(∂)calpoly⋅edu « best way to reach me

**Office:** 25-341 **Phone:** 756-5558

**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. Student retention.

Managing Editor of the Journal of Fractal Geometry (JFG)

Member of the Institute for the Applications of Mathematics & Integrated Science (IAMIS).

### Where and when to find me in Fall 2016

COURSE | SECTION | Time | Location |
---|---|---|---|

Introduction to Analysis I | 412-01 | 12:10-1:00pm MTRF | 38-201 |

Introduction to Analysis I | 412-02 | 1:10-2:00pm MTRF | 38-201 |

Office Hours | all | 2:10-3:30pm MR | 25-341 (Faculty East) |

2016 Summer School on Fractal Geometry and Complex Dimensions In celebration of the 60th birthday of Michel Lapidus |

## Publication List — All preprints are available on the __arXiv__

### Fractal geometry and analysis

Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable. (with S. Kombrink and S. Winter) To appear: Mathematisches Zeitschrift arXiv:1501.03764 |

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics. (with co-editors: David Carfí, Machiel van Frankenhuijsen, and Michel L. Lapidus) Contemporary Mathematics vol. 600 and vol. 601. American Mathematical Society Press. |

Minkowski measurability results for self-similar tilings and fractals with monophase generators. (with M. L. Lapidus and S. Winter) 12 pages. Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics, Contemporary Mathematics vol. 600, American Mathematical Society Press, 2013. arXiv:1104.1641 |

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators. (with M. L. Lapidus and S. Winter) Adv. in Math., 227(4):1349–1398, 2011. arXiv:1006.3807 |

Tube formulas and complex dimensions of self-similar tilings . (with M. L. Lapidus) Acta Appl. Math. 112(1):91–136, 2010. arXiv:math/0605527 |

The resolvent kernel for PCF self-similar fractals. (with M. Ionescu, L. Rogers, H. J. Ruan, and R. S. Strichartz) Trans. Amer. Math. Soc. 362(8):4451–4479, 2010. arXiv:0811.4203 |

Geometry of canonical self-similar tilings. (with S. Winter). Rocky Mountain J. Math. 42(4):1–32, 2012. arXiv:0811.2187 |

Tube formulas for self-similar fractals. (with M. L. Lapidus) In "Analysis on graphs and its applications", 211–230. Proc. Sympos. Pure Math., 77, Amer. Math. Soc., Providence, RI, 2008. arXiv:0711.0173 |

Canonical self-affine tilings by iterated function systems.
Indiana Univ. Math. J., 56(6):3151–3169, 2007. arXiv:math/0606111 |

A tube formula for the Koch snowflake curve, with applications to complex dimensions. (with M. L. Lapidus)
J. London Math. Soc. 74(2):397–414, 2006. arXiv:math-ph/0412029 |

### Graphs, networks, and effective resistance

Applications of symmetric pairs to Gaussian fields, Tomita-Takesaki theory, and resistance networks. (with P. E. T. Jorgensen) In review. arXiv:1601.05364 |

Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks. (with P. E. T. Jorgensen) To appear: Compl. Anal. Oper. Theory. arXiv:1512.03463 |

Unbounded containment in the energy space of a network and the Krein extension of the energy Laplacian. (with P. E. T. Jorgensen) In review. arXiv:1504.01332 |

Spectral comparisons between networks with different conductance functions. (with P. E. T. Jorgensen) J. Oper. Theory. arXiv:1107.2786 |

Self-similar fractals as boundaries of networks. 25 pages. In review. arXiv:1104.1650 |

Multiplication operators on the energy space. (with P. E. T. Jorgensen).J. Oper. Theory, 69(1):135–159, 2013 arXiv:1007.3516 |

Spectral reciprocity and matrix representations of unbounded operators. (with P. E. T. Jorgensen) J. Functional Anal., 261(3):749–776, 2011. arXiv:0911.0185 |

Resistance boundaries of infinite networks. (with P. E. T. Jorgensen) In ``Boundaries and Spectral Theory'', volume 64 of Progress in Probability, Birkhauser, 2010. 113–143. arXiv:0909.1518 |

Gel'fand triples and boundaries of infinite networks. (with P. E. T. Jorgensen) New York J. Math., Volume 17:745–781, 2011. arXiv:0906.2745 |

A Hilbert space approach to effective resistance metric. (with P. E. T. Jorgensen) Complex Anal. Oper. Theory, 4(4):975–1013, 2010. arXiv:0906.2535 |

A discrete Gauss-Green identity for unbounded Laplace operators and transience of random walks. (with P. E. T. Jorgensen).
Israel J. Math. 196(1):113–160, 2013. arXiv:0906.1586 |

Operator theory of electrical resistance networks. (with P. E. T. Jorgensen) 380 pages. To appear in Springer's arXiv:0806.3881Universitext series. |

### Machine learning

Iterated geometric harmonics for data imputation and reconstruction of missing data. (with Chad Eckman, Jonathan A. Lindgren, Erin P. J. Pearse, David J. Sacco, Zachariah Zhang) 14 pages. In review. |

### Student Retention

Assessment of remediation in a quasi-experimental setting. (with Jacob D. Pleitz, Dustin A. Fife, Robert Terry, and Nicole Judice-Campbell) 10 pages. In review. |

Estimating the effect of academic intervention in a mandatory study skills class. (with Jacob D. Pleitz, Dustin A. Fife, Robert Terry, and Nicole Judice-Campbell) 10 pages. To appear: Proceedings of Consortium for Student Retention Data Exchange. 2012. |

## Talks and other professional activity

*Linked titles provide access to the most recent talk slides; please email me if you would like a PDF of any of the older talks.*

Co-organizer: Special Session: Fractal Geometry: Mathematics of Fractals and Related Topics. Joint Meetings, Jan. 15-18, 2014. |

Co-organizer: Special Session: Fractal Geometry, Dynamical Systems, and Mathematical Physics AMS Western Sectional meeting, Nov. 2-3, 2013. |

Fractal tube formulas: curvature and measurability. Bremen Winter School on Multifractals and Number Theory, Universität Bremen, Mar. 18, 2013. |

Diffusion Metrics on Networks and Applications in Mathematical Statistics. “Applications of Fractal Geometry & Dynamical Systems Theory to Biology & Physics” IAMIS, Jun. 2012. |

Co-organizer: Special Session "Fractal Geometry in Pure and Applied Mathematics (in memory of Benoit Mandelbrot)". Joint Meetings, Jan. 4-7, 2012. |

Fractal tube formulas: curvature and measurability. PISRS 2011: Analysis, Fractal Geometry, Dynamical Systems and Economics (Permanent International Session of Research Seminars). Messina University, Italy. |

Nongeodesic metrics. AIM Workshop "Geometry of Large Networks", Fall 2011. Palo Alto, CA. |

Self-similar fractals as boundaries of networks. 4th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals / AMS Eastern Sectional Meeting. Fall 2011. Cornell University. |

Self-similar fractals as boundaries of networks. Special session: "Fractals and Tilings" at the AMS Southeastern Sectional Meeting. Mar. 12-13, 2011. Georgia Southern University. |

Co-organizer: Special Session "Fractal Geometry, Dynamical Systems, Number Theory and Analysis on Rough Spaces". AMS Western Sectional Meeting, Nov. 7-8, 2009. |

Tube formulas and self-similar tilings. "Fractals and Tilings", July 6-10, 2009. Strobl, Austria. |

Resistance analysis of infinite networks. "Alp Workshop", July 4-5, 2009. St. Kathrein am Offenegg, Austria. |

Resistance analysis of infinite networks. "Boundaries09", June 29 - July 3, 2009, 2009. Graz, Austria. |

The Prisoner's Dilemma. Invited speaker. April 23, 2009. Grinnell College. |

Resistance analysis of infinite networks. Harmonic Analysis Seminar. April 6, 2009. University of Illinois, Urbana-Champaign. |

Resistance analysis of infinite networks and Boundaries of infinite networks.Operator theory seminar. Mar. 23 and Mar. 31, 2008. University of Iowa. |

Resistance analysis of infinite networks. Interplay of Analysis and Probability in Physics. Dec. 1-6, 2008. Mathematisches Forschungsinstitut Oberwolfach. |

Geometry of self-similar sets I: canonical tilings of the convex hull. "Fractal Geometry and Stochastics 4". Sep. 8, 2008. Greifswald University. |

Co-organizer: "Fractals Connections" miniconference, for the VIGRE summer program at University of Iowa. Jun. 28-29, 2008. |

Operator theory of electrical resistance networks. "Fractal Connections". Jun. 28-29, 2008. University of Iowa. |

Operator theory of electrical resistance networks. "3rd Conference on Analysis and Probability on Fractals". Jun. 11-15, 2008. Cornell University. |

Self-Similar Tilings & Complex Dimensions. "Analysis on Graphs and Fractals", a satellite meeting of the Newton Institute. May 29 - June 2, 2007. Cardiff University, Wales. |

Operator theory of electrical resistance networks. Special session: "Wavelets, Fractals, Tilings and Spectral Measures" at the AMS Western Sectional Meeting. Oct. 4-5, 2006. University of British Columbia. |

Co-organizer: Special Session "Fractal Geometry: Connections to Dynamics, Geometric Measure Theory, Mathematical Physics and Number Theory". AMS Western Sectional Meeting. Apr. 29-30, 2006. San Francisco State University |

Tube formulas and complex dimensions of self-similar tilings. Special session: "Fractal Geometry: Connections to Dynamics, Geometric Measure Theory, Mathematical Physics and Number Theory" at the AMS Western Sectional Meeting. Apr. 29-30, 2006. San Francisco State University. |

Complex dimensions and the Steiner formula. Special session: "Geometry: Convex, Discrete, Differential" at the AMS National Meeting. Jan. 2006. San Antonio, TX. |

Self-similar systems and their complex dimensions. "21st Summer Conference on Topology and its Applications". July 6, 2006. Georgia Southern University. |

I also have slides from expository lectures on fractal strings, dimension theory, convex geometry (curvature and intrinsic volumes), distributions/generalized functions, analysis on fractals, and iteration of rational functions. These are available upon request — just send me an email at epearse(&del;)calpoly.edu. |