Chris Miller

Department of Mathematics
The Ohio State University
231 W. 18th Avenue
Columbus, OH 43210

e-mail: (my last name) at math dot osu dot edu
office: Math Tower 758
office phone: (614) 292-9363
FAX: (614) 292-1479


B.A.  Mathematics, University of California, Santa Barbara, 1988.
Ph.D. Mathematics, University of Illinois at Urbana-Champaign, 1994. Thesis Advisor: L. van den Dries.

Research Interests

I am interested primarily in applications of logic---specifically, model theory---to real analytic geometry, geometric measure theory, asymptotic analysis, and questions of differentiability and analyticity of real functions, via studying sets and functions that are definable in "well-behaved'' (e.g., o-minimal) first-order structures on the field of real numbers. Determining which structures should be regarded as well behaved is part of the job.

NOTE:  As of May 13,  2011, I will no longer be posting any new NSF-supported (as opposed to older or updated) research material here, because I do not want to deal with the current NSF requirements for posting on personal web pages.Rather, I will post new NSF-supported material on preprint servers such as arXiv and MODNET.  Please contact me for e- or offprints of papers that have already been published.

Upgrades of some published papers

dvi pdfps 9/7/12. ... for ``Avoiding the projective hierarchy in expansions of the real field by sequences''.

dvipdfps 11/14/12. ... for ``Geometric categories and o-minimal structures''.

dvipdfps 9/2/03. ... for ``Expansions of the real field with power functions''.

Unpublished notes

These are miscellaneous observations and results that are not necessarily intended for publication, especially in their present form. Please regard them as such.

dvipdfps 03/25/09. AP-sets of rationals define the natural numbers, with A. Dolich.

dvipdfps Revised 04/25/11. A trichotomy for expansions of R_{an} by trajectories of analytic planar vector fields (with Patrick Speissegger).

dvipdfps Revised 12/15/06. A weak growth dichotomy for d-minimal expansions of the real field.

dvipdfps Revised 12/15/06. Definable choice in d-minimal expansions of ordered groups.

dvipdfps Revised 12/15/06. D-minimal expansions of the real field have the exchange property.

dvipdfps 8/7/03. Status of the o-minimal two-group question (with Sergei Starchenko).