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Math 5010 -- Analysis on Graphs and Networks -- Fall 2018


Description: The course will consist of two parts. The first part will include a selection of basic but important classical topics, with no required prior background besides linear algebra and differential equations. The concrete topics will be borrowed from the classical book "Random walks and electric networks" by Doyle and Snell, and some simpler sections of "Differential Equations on Fractals: A Tutorial" by Strichartz and "Probability on Trees and Networks" by Lyons and Peres. The second part of the course will involve research projects of interest to students and the instructor. The projects can be theoretical, numerical, or both. There will be a variety of topics, and the selection will be made after extensive discussions. In the past similar courses ware taught six times at UConn, resulting in joint publications of students with the instructor in such journals as Pacific J. Math., J. Phys. A: Math. Theor. Experimental Math.

Spectral Graph Theory

A. Brzoska, D.J. Kelleher, H. Panzo, A. Teplyaev, Dual graphs and modified Barlow--Bass resistance estimates for repeated barycentric subdivisions, to appear arXiv:1505.03161

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