# Jeffrey A. Diller

### Professor

Department Chair

B.A., University of Dayton, 1988

Ph. D., University of Michigan, 1993

Email: Diller.1@nd.edu

Office: 255B Hurley Hall

Phone: (574) 631-7083

Fax: (574) 631-6579

For additional information see Jeffrey Dillerâ€™s Personal Page.

**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, and to this end I have done enough computer experimentation that I now find fascinating even the programming aspects of understanding dynamical systems.

**Selected Publications**

- 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
- Jeffrey Diller, Romain Dujardin, and Vincent Guedj, Dynamics of meromorphic map-pings with small topological degree II: Energy and invariant measure, Comment. Math. Helv. 86 (2011), no. 2, 277-316, DOI 10.4171/CMH/224. MR2775130
- 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
- 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
- J. Diller and C. Favre, Dynamics of bimeromorphic maps of surfaces, Amer. J. Math. 123 (2001), no. 6, 1135-1169. MR1867314

Please direct questions and comments to: Diller.1@nd.edu