1. useful lecture notes about analysis on weighted graphs 
2. pure point spectrum on some infinite weakly selfsimilar graphs 
3. resistance estimates on some selfsimilar graphs, such as the octacarpet 
4. spectral decimation and HKE on selfsimilar weighted graphs (such as pqmodel) 
5. AC currents on graphs 
6. hypergraphs and elements of differential geometry 
7. approximations of nonsmooth structures by graphs 
plan for Friday September 7, 2018
plan for Wednesday September 12, 2018
With some links:
1. useful lecture notes about analysis on weighted graphs

2. pure point spectrum on some infinite weakly selfsimilar graphs, based on
L. Malozemov and A. Teplyaev, Pure point spectrum of the Laplacians on fractal graphs. Journal of Functional Analysis 129 (1995), 390–405. pdf file + long list of other works 
3. resistance estimates on some selfsimilar graphs, such as the octacarpet, based on
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 arXiv:1505.03161 B. Boyle, K. Cekala, D. Ferrone, N. Rifkin and A. Teplyaev, Electrical Resistance of Ngasket Fractal Networks. Pacific Journal of Mathematics 233 (2007), 15–40. pdf file + long list of other works 
4. spectral decimation and HKE on selfsimilar weighted graphs (such as pqmodel)
U.Andrews, J.P.Chen, G.Bonik, R.W.Martin, A.Teplyaev, Wave equation on onedimensional fractals with spectral decimation. J. Fourier Anal. Appl. 23 (2017) 994–1027. doi:10.1007/s0004101694946 arXiv:1505.05855 wave equations animation J.P.Chen, A.Teplyaev, Singularly continuous spectrum of a selfsimilar Laplacian on the halfline, Journal of Mathematical Physics, 26 May 2016 Vol.57, Issue 5 DOI: 10.1063/1.4949471 arXiv:1509.08875 Neil Bajorin, Tao Chen, Alon Dagan, Catherine Emmons, Mona Hussein, Michael Khalil, Poorak Mody, Benjamin Steinhurst, A. Teplyaev Vibration modes of 3ngaskets and other fractals J. Phys. A: Math. Theor. 41 (2008) 015101 (21pp). pdf file.pdf 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.pdf L. Malozemov and A. Teplyaev, Selfsimilarity, operators and dynamics. Mathematical Physics, Analysis and Geometry 6 (2003), 201–218. pdf file + long list of other works 
5. AC currents on graphs
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/10.1088/17518121/aa7a66 arXiv:1605.03890 Power dissipation in fractal FeynmanSierpinski AC circuits, Journal of Mathematical

6. hypergraphs and elements of differential geometry

7. approximations of nonsmooth structures by graphs (see arXiv:1511.08499 for an introduction)
A graph discretization of the Laplace–Beltrami operatorDmitri Burago;Sergei Ivanov;Yaroslav Kurylev
ISSN: 1664039X , 16640403; DOI: 10.4171/JST/83
Journal of spectral theory. 2014, Vol.4(4), p.675714
