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.
Member of the Institute for the Applications of Mathematics & Integrated Science (IAMIS).
Where and when to find me in Winter 2013
Intro to Analysis I
|412-01||9:10-10:00 a.m. MTRF||38-0135 (Math &: Science)|
|Office Hours||all||10:10-12:00 p.m. Tue and Fri||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) To appear: Contemporary Mathematics American Mathematical Society Press.
|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) 20 pages.
Rocky Mountain J. Math. 42(4):1327–1357, 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-adjoint extensions of network Laplacians and applications to resistance metrics. (with P. E. T. Jorgensen) 30 pages. In review. arXiv:1103.5792|
|Multiplication operators on the energy space. (with P. E. T. Jorgensen)
28 pages. In review. 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) 31 pages. To appear: Israel J. Math. 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
|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 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(∂)calpoly⋅edu.