Department of Mathematics
3141 Chestnut Street
Philadelphia, PA 19104
phone: (215) 895-6612
fax: (215) 895-1582
Office: Korman 222
Georgi Medvedev received Ph.D. in Mathematics from Boston University in 1999. Before coming to Drexel University in 2002, he was a Veblen Research Instructor at Princeton University and at the Institute for Advanced Study.
Dr. Medvedev teaches courses at all levels. He developed an interdisciplinary graduate course MATH 723 Mathematical Neuroscience.
He serves on the editorial board of Discrete and Continous Dynamical Systems (Series B) .
MATH 291: Vector and Complex Analysis for Engineers
MATH 221: Discrete Mathematics
Dr. Medvedev is interested in dynamics of large (random) networks, continuum and mean limits for network dynamics, combinatorial and stochastic aspects of synchronization and pattern formation in dynamical networks, effects of noise on dynamics of nonlinear systems, and applications to neuroscience.
Dr. Medvedev's research has been supported by National Science Foundation through grants
* H. Chiba and G.S. Medvedev, The mean field analysis for the Kuramoto model on graphs II. Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations, submitted. arxiv
* G.S. Medvedev, The continuum limit of the Kuramoto model on sparse random graphs, Communications in Mathematical Sciences, in press ( arxiv )
* H. Chiba, G.S. Medvedev, and M. Mizuhara, Bifurcations in the Kuramoto model on graphs, Chaos 28, 073109 (2018), abstract, arxiv
* H. Chiba and G.S. Medvedev, The mean field analysis for the Kuramoto model on graphs I. The mean field equation and transition point formulas, Discrete and Continuous Dynamical Systems - A, 39(1), 2019. ( abstract )
* D. Kaliuzhnyi-Verbovetskyi and G.S. Medvedev, The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit, SIAM J. Math. Anal., 50 (2018), no. 3, 2441-2465, abstract pdf
* G.S. Medvedev and X. Tang, The Kuramoto model on power law graphs: Synchronization and Contrast States, Journal of Nonlinear Science, 2018, abstract arxiv
* D. Kaliuzhnyi-Verbovetskyi and G.S. Medvedev, The semilinear heat equation on sparse random graphs, SIAM J. Math. Anal., 49(2), 1333-1355, 2017. abstract pdf
* G.S. Medvedev and J.D. Wright, Stability of twisted states in the continuum Kuramto model, SIAM J. Appl. Dyn. Syst., 16(1), 188-203, 2017. abstract pdf
* P. Hitczenko and G.S. Medvedev, Stability of equilibria of randomly perturbed maps, Discrete and Continuous Dynamical Systems - B, 22(2), 2017. abstract pdf
* G.S. Medvedev and X. Tang, Synchronization of coupled chaotic maps, Physica D304-305, pp. 42-51,2015. abstract
* G.S. Medvedev and X. Tang, Stability of twisted states in the Kuramoto model on Cayley and random graphs, Journal of Nonlinear Science, 2015. abstract arxiv
* G.S. Medvedev, The nonlinear heat equation on dense graphs and graph limits, SIAM J. Math. Analysis, 46(4), 2743-2766, 2014. abstract pdf
* G.S. Medvedev, The nonlinear heat equation on W-random graphs, Archive for Rational Mechanics and Analysis June 2014, Volume 212, Issue 3, pp 781-803, 2014. abstract pdf
* G.S. Medvedev, Small-world networks of Kuramoto oscillators, Physica D 266 (2014), 13-22. abstract arXiv preprint
* P. Hitczenko and G.S. Medvedev, The Poincare map of randomly perturbed periodic motion, J. Nonlin. Sci., Vol. 23(5), pp. 835-861, 2013. (abstract)
Interdisciplinary Workshop on Multiple Scale Systems, Systems with Hysteresis and Trends in Dynamical Systems , Centre de Recerca Matemàtica, Bellaterra May 28th to June 1st, 2018
Stochastic dynamics out of equilibrium, Insttitut Henri Poincare, Paris, France, June 12-16, 2017
Interdisciplinary Workshop on Multiple Scale Systems, Systems with Hysteresis and Trends in Dynamical Systems , Centre de Recerca Matematica, Bellaterra, May 28th to June 1st, 2018
Continuum Limit of the Kuramoto Model on Convergent Graph Sequences, Dynamical Systems Seminar, Kyoto University, July, 2017
Synchronization of coupled systems: Relating network structure to dynamics, Workshop on synchronization and oscillators with generalized coupling, University of Exeter, April 20-22, 2016
The Kuramoto model on Cayley and random graphs, Ohio State University, January 25-29, 2016 (video)
Last modified May 25, 2018.