Professional materials

Profile Image

Erin Pearse Assistant Professor

Ph.D., University of California, Riverside

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

Office: 25-0341 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.

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

Managing Editor of the Journal of Fractal Geometry (JFG)

Where and when to find me in Fall 2014

COURSE SECTION Time Location
Calculus IV 241-13 1:10-2:00pm MTRF 10-225
Linear Analysis II 143-12 3:10-4:00pm MTRF 38-219
Calculus IV 241-13 4:10-5:00pm MTRF 38-220
Office Hours all 10:10am-12:00pm MR 25-0341 (Faculty East)

Publication List — All preprints are available on the arXiv

Fractal geometry and analysis

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

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. Operator 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 Universitext series. arXiv:0806.3881

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.