Jeffrey Diller

Professor

Education

B.A., University of Dayton, 1988
Ph. D., University of Michigan, 1993

Research Groups

Algebra and Algebraic Geometry, Analysis and Partial Differential Equations

Research Area

Complex Analysis and Geometry, Dynamical Systems

Bio

Research Interests

I study multi-variable complex dynamics. Using tools from pluripotential theory, complex algebraic geometry and dynamical systems, my goal is to understand the behavior of rational maps of two or more variables under iteration. So far, I have mostly concentrated on the case of plane birational maps, and this work has led to a general probabilistic picture for the dynamics of such maps. I am currently interested in extending this picture to higher dimensions and non-invertible rational maps. I am also interested in understanding the dynamics of particular examples in much greater detail. For this last purpose, computer experimentation often plays a crucial role in building the understanding and intuition needed to make mathematical progress.

Selected Publications

• (3) Jeffrey Diller and Jan-Li Lin, Rational surface maps with invariant meromorphic two-forms, Math. Ann. 364 (2016), no. 1-2, 313-352, DOI 10.1007/s00208-015-1211-2. MR3451389
• (8) Jeffrey Diller, Romain Dujardin, and Vincent Guedj, Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure, Comment. Math. Helv. 86 (2011), no. 2, 277-316, DOI 10.4171/CMH/224. MR2775130
• (16) Jeffrey Diller, Daniel Jackson, and Andrew Sommese, Invariant curves for birational surface maps, Trans. Amer. Math. Soc. 359 (2007), no. 6, 2793-2991, DOI 10.1090/S0002-9947-07-04162-1. MR2286065
• (18) Eric Bedford and Jeffrey Diller, Real and complex dynamics of a family of birational maps of the plane: the golden mean subshift, Amer. J. Math. 127 (2005), no. 3, 595-646. MR2141646
• (26) J. Diller and C. Favre, Dynamics of bimeromorphic maps of surfaces, Amer. J. Math. 123 (2001), no. 6, 1135-1169. MR1867314
• With Kyounghee Kim. \Real and complex dynamics of rational surface automorphisms". Experimental Math, vol 30, pp 172-190 (2021).
• With Jason Bell and Mattias Jonsson. \A Transcendental Dynamical Degree". Acta Mathematica, vol 125, pp 193-225 (2020).