research

office: MONT 429
office hours:   contact info
phone: (860)486-3206

email:  teplyaevatuconn.edu
http://www.math.uconn.edu/~teplyaev


Reviews of my published papers are available at MathSciNet and Zentralblatt MATH. These cites often provide links to the published articles. Preprints are in arXiv. Link to research with undergraduate students and google scholar profile.

 


preprints:

  1. Gamal Mograby, Maxim Derevyagin, Gerald V. Dunne, Alexander Teplyaev Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs arXiv:2003.11190
  2. Adrien Dekkers Anna Rozanova-Pierrat Alexander Teplyaev Mixed boundary valued problem for linear and nonlinear wave equations in domains with fractal boundaries hal-02514311
  3. Malcolm Gabbard, Carlos Lima, Gamal Mograby, Luke G. Rogers, Alexander Teplyaev Discretization of the Koch Snowflake Domain with Boundary and Interior Energies arXiv:2002.04680
  4. Maxim Derevyagin, Gerald V. Dunne, Gamal Mograby, Alexander Teplyaev Perfect quantum state transfer on diamond fractal graphs arXiv:1909.08668
  5. Antoni BrzoskaCourtney GeorgeSamantha JarvisLuke G. RogersAlexander Teplyaev
    Spectral properties of graphs associated to the Basilica group (2019) arXiv:1908.10505
  6. Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev BV functions and fractional Laplacians on Dirichlet spaces, (2019) arXiv:1910.13330
  7. Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates, (2019) arXiv:1903.10078
  8. Patricia Alonso-Ruiz, Michael Hinz, Alexander Teplyaev, Rodrigo Treviño, Canonical diffusions on the pattern spaces of aperiodic Delone sets, (2018) arXiv:1801.08956
  9. M. Gordina, M. Röckner, A. Teplyaev, Singular perturbations of Ornstein-Uhlenbeck processes: integral estimates and Girsanov densities, (2018) arXiv:1801.00761
  10. B. Steinhurst and A. Teplyaev, Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals, arXiv:1204.5207

publications:

  1. Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates, to appear in Calculus of Variations and PDE (2020) arXiv:1811.11010
  2. Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev  Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities Journal of Functional Analysis, Volume 278, Issue 11, 15 June 2020 doi.org/10.1016/j.jfa.2020.108459 arXiv:1811.04267
  3. Analysis, Probability and Mathematical Physics on Fractals Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications: Volume 5 doi.org/10.1142/11696 | March 2020 Pages: 596
    Edited By: Patricia Alonso Ruiz (Texas A&M University, USA), Joe P Chen (Colgate University, USA), Luke G Rogers (University of Connecticut, USA), Robert S Strichartz (Cornell University, USA) and Alexander Teplyaev (University of Connecticut, USA)
  4. Eric Akkermans, Joe P. Chen, Gerald Dunne, Luke G. Rogers, Alexander Teplyaev, Fractal AC circuits and propagating waves on fractals, arXiv:1507.05682 Cornell Fractals 6 proceedings, 2020. doi.org/10.1142/11696
  5. Simone Creo, Maria Rosaria Lancia, Paola Vernole, Michael Hinz, Alexander Teplyaev, Magnetostatic problems in fractal domains, arXiv:1805.08262 Cornell Fractals 6 proceedings, 2020. doi.org/10.1142/11696
  6. Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss, Alexander Teplyaev, Internal DLA on Sierpinski gasket graphs, arXiv:1702.04017 to appear in the proceedings of Analysis and Geometry on Graphs and Manifolds (International Conference at the University of Potsdam, Germany), London Mathematical Society Lecture Note Series: 461, Cambridge University Press, pp 126–155, 2020.
  7. A. Brzoska, D.J. Kelleher, H. Panzo, A. Teplyaev, Dual graphs and modified Barlow–Bass resistance estimates for repeated barycentric subdivisions, Discrete & Continuous Dynamical Systems – S February 2019, Volume 12, Issue 1, pages 27-42 doi: 10.3934/dcdss.2019002 arXiv:1505.03161
  8. M. Hinz, A. Teplyaev, Densely defined non-closable curl on topologically one-dimensional Dirichlet metric measure spaces, Mathematische Nachrichten Volume 291, August 2018, Issue 11-12, pages 1743–1756 DOI: 10.1002/mana.201600467  arXiv:1505.02819
  9. Joe P. Chen, Michael Hinz, Alexander Teplyaev, From non-symmetric particle systems to non-linear PDEs on fractals, Stochastic partial differential equations and related fields, 503–513, Springer Proc. Math. Stat., 229, 2018. doi.org/10.1007/978-3-319-74929-7 arXiv:1702.03376
  10. Joe P. Chen, Alexander Teplyaev, Konstantinos Tsougkas, Regularized Laplacian determinants of self-similar fractals. Letters in Mathematical Physics (2017) Open Access https://doi.org/10.1007/s11005-017-1027-y arXiv:1610.10062
  11. Michael Hinz, Maria Rosaria Lancia, Alexander Teplyaev, Paola Vernole, Fractal snowflake domain diffusion with boundary and interior drifts, J. Math. Anal. Appl. 457 (2018), no. 1, 672–693. https://doi.org/10.1016/j.jmaa.2017.07.065 arXiv:1605.06785
  12. Joe P. Chen, Luke G. Rogers, Loren Anderson, Ulysses Andrews, Antoni Brzoska, Aubrey Coffey, Hannah Davis, Lee Fisher, Madeline Hansalik, Stephew Loew, Alexander Teplyaev, Power dissipation in fractal AC circuits. J. Phys. A: Math. Theor. 50 (2017) 325205 (20pp) doi.org/10.1088/1751-8121/aa7a66 arXiv:1605.03890
  13. U.Andrews, J.P.Chen, G.Bonik, R.W.Martin, A.Teplyaev, Wave equation on one-dimensional fractals with spectral decimation. J. Fourier Anal. Appl. 23 (2017) 994–1027. doi:10.1007/s00041-016-9494-6 arXiv:1505.05855 wave equations animation
  14. J.P.Chen, A.Teplyaev, Singularly continuous spectrum of a self-similar Laplacian on the half-line, Journal of Mathematical Physics, 26 May 2016 Vol.57, Issue 5 DOI: 10.1063/1.4949471 arXiv:1509.08875
  15. P. Alonso-Ruiz, D. Kelleher, A. Teplyaev, Energy and Laplacian on Hanoi-type fractal quantum graphs. J. Phys. A: Math. Theor. 49 (2016) 165206 doi:10.1088/1751-8113/49/16/165206 arXiv:1408.4658
  16. D. Lenz, A. Teplyaev, Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces. Trans. Amer. Math. Soc., 368 (2016) 4933-4956. arXiv:1310.5650
  17. D. Kelleher, M. Hinz, A. Teplyaev, Metrics and spectral triples for Dirichlet and resistance forms. J. Noncommut. Geom., vol. 9, no. 2 (2015) arXiv:1309.5937
  18. M. Hinz, A. Teplyaev, Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals. Trans. Amer. Math. Soc. 367 (2015), 1347–1380. Corrigendum Trans. Amer. Math. Soc. 369 (2017), 6777–6778. arXiv:1206.6644
  19. J.P.Chen, S. Molchanov, A.Teplyaev, Spectral dimension and Bohr’s formula for Schrodinger operators on unbounded fractal spaces. J. Phys. A: Math. Theor. 48 (2015) 395203 arXiv:1505.03923
  20. J. F.-C. Chan, S.-M. Ngai, A. Teplyaev, One-dimensional wave equations defined by fractal Laplacians. Journal d’Analyse Mathematique, vol. 127 (2015) 219-246. pdf file wave equations video
  21. D. Kelleher, N. Gupta, M. Margenot, J. Marsh, W. Oakley, A. Teplyaev, Gaps in the spectrum of the Laplacian on 3N-Gaskets. Communications on Pure and Applied Analysis (CPAA) Pages: 2509 – 2533, Volume 14, Issue 6, November 2015 arXiv:1408.4294
  22. M. Hinz, A. Teplyaev, Closability, regularity, and approximation by graphs for separable bilinear forms. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 441 (Veroyatnost i Statistika. 22):299-317, 2015. Springer: J. Math. Sci. (2016) 219 807–820 doi:10.1007/s10958-016-3149-7 arXiv:1511.08499
  23. M. Hinz, A. Teplyaev, Finite energy coordinates and vector analysis on fractals, Progress in Probab. 70, Fractal Geometry and Stochastics V, Birkhauser, 2015, pp. 209-227. arXiv:1501.04541
  24. M. Hinz, A. Teplyaev, Dirac and magnetic Schrodinger operators on fractals. J. Funct. Anal. 265 (2013), 2830–2854. arXiv:1207.3077
  25. M. Hinz, M. Rockner, A. Teplyaev, Vector analysis for local Dirichlet forms and quasilinear PDE and SPDE on fractals, Stochastic Process. Appl. 123 (2013), 4373–4406. arXiv:1202.0743
  26. B. Steinhurst and A. Teplyaev, Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals, Lett. Math. Phys. 103 (2013) 1377–1388. arXiv:1011.5485
  27. M. Hinz, D. Kelleher, A. Teplyaev, Measures and Dirichlet forms under the Gelfand transform. Probability and statistics 18, Zapiski Nauchnyh Seminarov POMI 408, (2012), 303–322; reprinted in Journal of Mathematical Sciences (Springer, 2013) arXiv:1212.1099
  28. M. Hinz, A. Teplyaev, Vector analysis on fractals and applications. Contemporary Mathematics Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics 601 (2013) 147– 164. arXiv:1207.6375
  29. E. Akkermans, G. Dunne, A. Teplyaev and R. Voituriez, Spatial Log periodic oscillations of First-Passage observables in fractals. arXiv:1207.3298 Phys. Rev. E 86, 061125 (2012)
  30. 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):402-417, 2012
  31. M. Ionescu, L. G. Rogers, A. Teplyaev, Derivations and Dirichlet forms on fractals, arXiv:1106.1450, Journal of Functional Analysis, 263 (8), p.2141-2169, Oct 2012
  32. K.Hare, B. Steinhurst, A. Teplyaev and D. Zhou, Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals, arXiv:1105.1747, Math. Res. Lett. 19 (2012), 1–17.
  33. R.S. Strichartz and A. Teplyaev, Spectral analysis on infinite Sierpinski fractafolds, arXiv:1011.1049 Journal d’Analyse Mathematique, 112 (2012) 255–297.
  34. E. Akkermans, G. Dunne, and A. Teplyaev, Thermodynamics of photons on fractals. Phys. Rev. Lett. 105 230407 (2010) arXiv:1010.1148
  35. M.T. Barlow, R.F. Bass, T. Kumagai, and A. Teplyaev, Uniqueness of Brownian motion on Sierpinski carpets. J. Eur. Math. Soc. (JEMS) 12 (2010), 655-701.
    updated preprint pdf file or arXiv:0812.1802
    see also Supplementary notes for “Uniqueness of Brownian motion on Sierpinski carpets”
  36. L. Rogers and A. Teplyaev, Laplacians on the basilica Julia set. Commun. Pure Appl. Anal. 9 (2010), no. 1, 211–231.
    pdf file or arXiv:0802.3248
  37. E. Akkermans, G. Dunne, and A. Teplyaev, Physical Consequences of Complex Dimensions of Fractals, 2009 EPL 88 (Europhysics Letters) https://doi.org/10.1209/0295-5075/88/40007
    preprint pdf file, arXiv:0903.3681
  38. L. Rogers, R. Strichartz and A. Teplyaev, Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals. Trans. Amer. Math. Soc. 361 (2009) 1765-1790.
    pdf file.
  39. V. Nekrashevych and A. Teplyaev, Groups and analysis on fractals, Analysis on Graphs and its Applications, Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc., 77 (2008), 143–180.
    pdf file.
  40. P. Exner, J.P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev, Editors. Analysis on Graphs and Its Applications, Proceedings of Symposia in Pure Mathematics, AMS, 77 (2008).
  41. Neil Bajorin, Tao Chen, Alon Dagan, Catherine Emmons, Mona Hussein, Michael Khalil, Poorak Mody, Benjamin Steinhurst, A. Teplyaev
    Vibration modes of 3n-gaskets and other fractals J. Phys. A: Math. Theor. 41 (2008) 015101 (21pp). pdf file
  42. Neil Bajorin, Tao Chen, Alon Dagan, Catherine Emmons, Mona Hussein, Michael Khalil, Poorak Mody, Benjamin Steinhurst, A. Teplyaev 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
  43. A. Teplyaev, Harmonic coordinates on fractals with finitely ramified cell structure Canadian Journal of Mathematics, 60 (2008), 457-480.
    pdf file
  44. K. Okoudjou, L. Saloff-Coste and A. Teplyaev, Weak uncertainty principle for fractals, graphs and metric measure spaces. Trans. Amer. Math. Soc. 360 (2008), 3857-3873
    pdf file from arXiv.org
  45. A. Pelander and A. Teplyaev, Products of random matrices and derivatives on p.c.f. fractals. Journal of Functional Analysis, Volume 254, Issue 5, 1 March 2008, Pages 1188-1216
    pdf file.
  46. 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.
  47. A. Pelander and A. Teplyaev, Infinite dimensional i.f.s. and smooth functions on the Sierpinski gasket. Indiana Univ. Math. J. 56 (2007), 1377–1404
    pdf file.
  48. A. Teplyaev, Spectral zeta functions of fractals and the complex dynamics of polynomials, Trans. Amer. Math. Soc. 359 (2007), 4339-4358.
    pdf file from arXiv.org
  49. B.M. Hambly, V. Metz and A. Teplyaev, Self-similar energies on post-critically finite self-similar fractals, (with), J. London Math. Soc. 74 (2006), 93–112.
    pdf file from http://www.mathematik.uni-bielefeld.de/fgweb/
  50. 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.
  51. A. Teplyaev, A note on the theorems of M. G. Krein and L. A. Sakhnovich on continuous analogs of orthogonal polynomials on the circle, Journal of Functional Analysis 226 (2005), 257-280.
    pdf file from arXiv.org
  52. R. Meyers, R. Strichartz and A. Teplyaev, Dirichlet forms on the Sierpinski gasket. Pacific Journal of Mathematics 217 (2004), 149-174. pdf file
  53. A. Teplyaev, Energy and Laplacian on the Sierpinski gasket. Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot, Part 1. Proceedings of Symposia in Pure Mathematics 72, Amer. Math. Soc., (2004), 131–154. pdf file
  54. A. Teplyaev, Spectral zeta function of symmetric Sierpinski gasket type fractals. Fractal Geometry and Stochastics III, Progress in Probability 57, Birkhauser (2004), 245–262.
  55. 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 arXiv.org
  56. 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
  57. L. Malozemov and A. Teplyaev, Self-similarity, operators and dynamics. Mathematical Physics, Analysis and Geometry 6 (2003), 201–218. pdf file
  58. 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)
  59. J. Stanley,R. Strichartz and A. Teplyaev, Energy partition on fractals. Indiana University Mathematics Journal 52 (2003), 133–156. pdf file
  60. A. Teplyaev, Gradients on fractals. Journal of Functional Analysis 174 (2000), 128–154. pdf file
  61. 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
  62. A. Teplyaev, Spectral analysis on infinite Sierpinski gaskets. Journal of Functional Analysis 159 (1998), 537–567. pdf file
  63. L. Malozemov and A. Teplyaev, Pure point spectrum of the Laplacians on fractal graphs. Journal of Functional Analysis 129 (1995), 390–405. pdf file
  64. J.S. Geronimo and A. Teplyaev, A difference equation arising from the trigonometric moment problem having random reflection coefficients — an operator-theoretic approach. Journal of Functional Analysis 123 (1994), 12–45. pdf file
  65. A. Teplyaev, Continuous analogues of random polynomials that are orthogonal on the circle. Teoria Veroyatnostey i Primeneniya 39 (1994), 588–604; English translation in Theory Probab. Appl. 39 (1995), 476–489. pdf file
  66. A. Teplyaev, Absolute continuity of the spectrum of random polynomials that are orthogonal on the circle and their continual analogues. Zapiski Nauchnyh Seminarov LOMI, 194 (1991), 170–173; English translation in Journal of Math. Sciences 75 (1995), 1982–1985. pdf file
  67. A. Teplyaev, The pure point spectrum of random orthogonal polynomials on the circle. Doklady Akad. Nauk SSSR 320 (1991), 49–53; English translation in Soviet Math. Dokl. 44 (1992), 407–411. pdf file (E) and pdf file (R)
  68. A. Teplyaev, Properties of polynomials that are orthogonal on the circle with random parameters. Zapiski Nauchnyh Seminarov LOMI 177 (1989), 157–162; English translation in Journal of Soviet Mathematics 61 (1992), 1931–1934. pdf file

 


unpublished:

  1. G.Bonik, J.P.Chen, A.Teplyaev, Heat kernels on 2d Liouville quantum gravity: a numerical study. arXiv:1411.1738
  2. M. Hinz, A. Teplyaev, Energy measure closability for Dirichlet forms. arXiv:1211.2135
  3. Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev, BV functions and Besov spaces associated with Dirichlet spaces, (2018) arXiv:1806.03428