Math UConn REU page has moved to

2012 Math UConn REU page was here

2011 Math UConn REU page was here

Probability, Analysis and Mathematical Physics on Fractals

Supervised works by UConn students:

  • Michael J. Ignatowich, Daniel J. Kelleher, Catherine E. Maloney, David J. Miller, Khrystyna Serhiyenko (Nechyporenko), Resistance Scaling of the Pillowcase and Fractalina Fractals, Online Ready, Published: April 14, 2015, Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society, World Scientific doi: 10.1142/S0218348X15500188 arXiv:1204.5815

  • R. Kesler, B. Steinhurst, Casimir Effect on Laakso Spaces, Contemporary Math., Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics, Volume: 601, November 15, 2013 arXiv:1207.2082

  • Daniel J. Kelleher, Tyler M. Reese, Dylan T. Yott, Antoni Brzoska, Analysing properties of the C. Elegans neural network: mathematically modeling a biological system, arXiv:1109.3888 PLoS ONE 7(10): e40483

  • D. Kelleher, B. Steinhurst and C-M.M. Wong, From Self-Similar Structures to Self-Similar Groups, Internat. J. Algebra Comput. (IJAC) 22:7 (2012), 1250056 arXiv:1011.1817

  • Christopher J. Kauffman, Robert M. Kesler, Amanda G. Parshall, Evelyn A. Stamey and Benjamin A. Steinhurst, Quantum mechanics on Laakso spaces, J. Math. Phys. 53, 042102 (2012). arXiv:1011.3567
    see also B. Steinhurst, Dirichlet Forms on Laakso and Barlow-Evans Fractals of Arbitrary Dimension, arXiv:0811.1378 B. Steinhurst Uniqueness of Brownian Motion on Laakso Spaces, Potential Analysis 38 (2013) 281--298 arXiv:1103.0519

  • M. Begue, L. deValve, D. Miller, B. Steinhurst, Spectrum and Heat Kernel Asymptotics on General Laakso Spaces, Fractals 20, (2012), 149--162 DOI: 10.1142/S0218348X12500144 arXiv:0912.2176

  • S. Makisumi, G. Stadnyk, B. Steinhurst, Modified Hanoi Towers Groups and Limit Spaces, International Journal of Algebra and Computation (IJAC) 21:6 (2011) arXiv:0909.3520

  • D. Ford and B. Steinhurst, Vibration Spectra of the m-Tree Fractal, Fractals 18:2 (2010) 157--169. arXiv:0812.2867

  • K. Romeo and B. Steinhurst, Eigenmodes of a Laplacian on Laakso Space, Complex Variables and Elliptic Equations, 54:6, pp. 623-637 (2009). arXiv:0903.4661

    Research supported in part by NSF grant DMS-0505622, and by the University of Connecticut Department of Mathematics


    links to

    Fractals Summer 2012
    departmental page

    Matt Begue at the Frontiers 2011

    Link to Probability, Analysis and Mathematical Physics on Fractals October 2-3, 2010, Syracuse NY

    REU 2010: Daniel Kelleher, Chuen Ming Mike Wong (Princeton University), Christopher Kauffman (University of Rochester), Amanda Parshall (York College of Pennsylvania), Evelyn Stamey (Ithaca College), Robert M Kesler (Princeton University), Ben Steinhurst

    REU 2009: Matthew Begue (UConn), Shotaro Makisumi (Princeton University), Grace Stadnyk (Hamilton College), Levi deValve (UConn), David Miller (Salve Regina University), Ben Steinhurst

    UConn Frontiers 2008: posters of Kevin Romeo, Alon Dagan, Michael Khalil

    Applet that generates random Sierpinski Gaskets

    Applet that computes Green's function of the random Sierpinski Gaskets

    Link to research papers. In particular, other completed works with undegraduate students:

  • M. Begue, D. J. Kelleher, A. Nelson, H. Panzo, R. Pellico and A. Teplyaev, Random walks on barycentric subdivisions and Strichartz hexacarpet, arXiv:1106.5567 Experimental Mathematics, 21(4):402417, 2012

  • Neil Bajorin, Tao Chen, Alon Dagan, Catherine Emmons, Mona Hussein, Michael Khalil, Poorak Mody, Benjamin Steinhurst, Alexander Teplyaev
    Vibration modes of 3n-gaskets and other fractals J. Phys. A: Math. Theor. 41 (2008) 015101 (21pp). pdf file
    Vibration Spectra of Finitely Ramified, Symmetric Fractals Fractals 16 (2008), 243--258. pdf file
    project web page
    older preprint in the Isaac Newton Institute Preprint Series
    Mathematica notebooks for the project

  • B. Boyle, K. Cekala, D. Ferrone, N. Rifkin and A. Teplyaev Electrical Resistance of N-gasket Fractal Networks. Pacific Journal of Mathematics 233 (2007), 15--40.
    pdf file.

  • D. Fontaine, T. Smith and A. Teplyaev Resistance of random Sierpinski gaskets. Quantum Graphs and Their Applications, Contemporary Mathematics 415 (2006), AMS, Providence, RI.
    pdf file The project web page is here.

  • R. Meyers, R. Strichartz and A. Teplyaev Dirichlet forms on the Sierpinski gasket. Pacific Journal of Mathematics 217 (2004), 149-174. pdf file

  • J. Needleman, R. Strichartz, A. Teplyaev and P.-L. Yung Calculus on the Sierpinski gasket: polynomials exponentials and power series. Journal of Functional Analysis 215 (2004), 290--340. pdf files and from

  • E.J. Bird, S.-M. Ngai and A. Teplyaev Fractal Laplacians on the Unit Interval. Ann. Sci. Math. Quebec 27 (2003), 135--168. pdf file

  • B. Adams, S.A. Smith, R. Strichartz and A. Teplyaev The spectrum of the Laplacian on the pentagasket (with), Fractals in Graz 2001 -- Analysis -- Dynamics -- Geometry -- Stochastics, Trends Math., Birkhauser Basel (2003), 1--24. (pdf file)

  • J. Stanley,R. Strichartz and A. Teplyaev Energy partition on fractals. Indiana University Mathematics Journal 52 (2003), 133--156. pdf file

  • O. Ben-Bassat,R. Strichartz and A. Teplyaev What is not in the domain of the Laplacian on a Sierpinski gasket type fractal. Journal of Functional Analysis 166 (1999), 197--217. pdf file

    Some directly or indirectly related pictures: