I am a Golomb Visiting Assistant Professor at Purdue University in West Lafayette, Indiana. This semester I am teaching 2 sections of MA26600, Ordinary Differential Equations.
In the past I have worked with the REU program at UConn in analysis on fractals. If you are looking for something to do during the summer, you should consider it.
with Fabrice Baudoin. Differential forms on Dirichlet spaces and Bakry-Emery estimates on metric graphs To Appear in Transactions of the AMS. arXiv1604.02520
with Jessica Hyde, Jesse Moeller, Luke Rogers, and Luis Seda. Magnetic Laplacians of locally exact forms on the Sierpinski gasket To appear in Communications on Pure and Applied Analysis (CPAA) arXiv:1604.01340
with Antoni Brzoska, Hugo Panzo, Alexander Teplyaev. Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions, To appear in Discrete and Continuous Dynamical Systems. arXiv:1505.03161
with Patricia Alonso-Ruiz and Alexander Teplyaev. Energy and Laplacian on fractal quantum graphs and Hanoi attractors, J Phys A 49(16) . arXiv 1408.4958
with Nihkaar Gupta, Maxwell Margenot, Jason Marsh, William Oakley, and Alexander 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
with Michael Hinz and Alexander Teplyaev. Metrics and Spectral Triples for Dirichlet and Resistance Spaces. Journal of Noncommutative Geometry 9 (2015), no. 2, 359 – 390. arXiv1309.5937
with Michael J. Ignatowich, Catherine E. Maloney, David J. Miller, Khrystyna Nechyporenko. Computation of Resistance Scaling of the Pillowcase and Fractalina Fractals Fractals Vol No.23, Issue No. 2. arXiv:1204.5815
with Michael Hinz and Alexander Teplyaev. Measures and Dirichlet forms under the Gelfand transform, Journal of Mathematical Science, 2012, Volume 408, Pages 303 – 322. arXiv:1212.1099
with Tyler Reese, Dylan Yott, Toni Brzoska, Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network, PLoS ONE 7(10), (2012). doi:10.1371/journal.pone.0040483
with Matt Begue, Aaron Nelson, Hugo Panzo, Ryan Pellico and Sasha Teplyaev. Random walks on barycentric subdivisions and Strichartz hexacarpet, Experimental Mathematics. 21(4) 2012, pp 402 – 417 arXiv:1106.5567v2
with Ben Steinhurst, Mike Wong. From Self-Similar Structures to Self-Similar Groups, International Journal of Algebra and Computation Vol. 22, No. 07 (2012) arXiv:1011.1817v2
with Sara Chari, Joshua Frisch, Luke Rogers Measurable Riemannian structure on higher dimensional harmonic Sierpinski gaskets Submitted. arXiv1703.03380
Differential forms for fractal subspaces and finite energy coordinates Submitted. arXiv:1701.02684
with Daniel Fontaine and Alexander Teplyaev. Green's function and eigenfunctions on random Sierpinski gaskets.
Frontier Probability Days Salt Lake City, UT, May 2016.
AMS Northeastern Spring Sectional, Stony Brook University, NY. March 2016
Probability/Analysis Seminar University of Cincinnati, October 2015
AMS Western Spring section University of Nevada, Las Vegas, April 2015
Junior Analysis Seminar Purdue University, April 2015
Probability/Analysis seminar University of Cincinnati, April 2015
Probability seminar University of Illinois, Urbana-Champaign, March 2015.
AMS Spring Sectional Michigan State Univ. March 17, 2015.
Purdue Probability Seminar Vector Analysis on Dirichlet forms and Analysis on Fractals. November 13, 2014. Purdue UniversitySlides
Universitat Bielefeld From self-similar groups to intrinsic metrics on fractals. July 2014.
Fractals 5. Short course: Resistance estimates and Harnack inequalities on fractals, part I & II. 2014, Cornell Univ.
Fractals 5. Intrinsic metrics and vectors analysis on fractals. 2014, Cornell Univ.
Fractal Geometry and Stochastics 5. From self-similar groups to intrinsic metrics on fractals. Slides 2014, Jena.
Cornell Analysis Seminar. From self-similar groups to intrinsic metrics on fractals. Slides Fall 2013.