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Dynamical systems, especially symbolic dynamics, topological dynamics, and combinatorial dynamics. Game theory, including connections with dynamics. Geometric group theory, and more broadly, asymptotic geometry and topology, including connections with dynamics.

Prof. Geller's research primarily relates to low dimensional, topological, and symbolic dynamics, with increasing connections to asymptotic geometry/topology and geometric group theory. Some current projects include: an investigation into the effect of the asymptotic geometry of large random and nonrandom finite graphs on the existence of critical behavior for threshold dynamics on the graphs (with computational assistance by B. Ramsey); an attempt to extend work of Ceccherini-Silberstein, Machi, Scarabotti, and of Gromov on cellular automata on the Cayley graph of an amenable group to address a conjecture of Furstenberg on the nonamenable case (with T. Sinclair); and a program to complete the classification of the lamplighter groups up to quasi-isometry, with possible broader dynamical implications

Publications & Professional Activities

Microdynamics for Nash Maps (with B. Kitchens and M. Misiurewicz), Discrete and Continuous Dynamical Systems 27 (2010), 1007-1024.

Dynamics of the Nash Map in the Game of Matching Pennies (with R. Becker, S. Chakrabarti, B. Kitchens and M. Misiurewicz), Journal of Difference Equations and Applications 13 (2007), 223-235.

Irrational Life (with M. Misiurewicz), Experimental Mathematics 14 (2005), 271-275.

Minimal Combinatorial Models for Maps of an Interval with a Given Set of Periods (with L. Block, E. Coven and K. Hubner), Ergodic Theory and Dynamical Systems 23 (2003), 707-728.

The Symbolic Dynamics of Tiling the Integers (with E. Coven, S. Sylberger and W. Thurston), Israel Journal of Mathematics 130 (2002), 21-27.

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