Jeffrey A. Diller

Associate Professor

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

Research Interests

My current work is in multivariable complex dynamics. Generally speaking, I use tools from pluripotential theory and smooth ergodic theory to obtain a probabilistic picture of the dynamics of a rational map of complex projective space. Tackling all rational maps at once in any dimension would seem at present to be a bit ambitious, so I pay particular attention to birational and to holomorphic maps in dimension two. Birational maps have the advantage of being invertible, but they also present the challenge of being indeterminate at certain points. This situation is exactly reversed for holomorphic maps, so in a sense I am pursuing the two extremes of dynamical behavior in complex dimension two. New suggestions for interesting maps to consider are always welcome!

Selected Publications

• J. Diller and C. Favre. Dynamics of Bimeromorphic Maps of Kahler surfaces. To appear in the American Journal of Mathematics.
• J. Diller and M. Jonsson. Topological entropy of saddle sets in P². Duke Math Journal, 103:261-278, 2000
• J. Diller. Lyapunov exponents for birational maps of P². To appear in Commentarii Mathematici Helvetici.
• J. Diller and D. Barrett. A new example of Riemann surfaces with Corona. To appear in Journal of Geometric Analysis.
• J. Diller and D. Barrett. Contraction properties of the Poincare series operator. Michigan Math Journal, 43:519-538, 1996.

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