Math 5010  Analysis on Graphs and Networks  Fall 2018

teplyaevmath.uconn.edu
http://www.math.uconn.edu/~teplyaev
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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 BarlowBass 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):402417, 2012
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