Chris Miller's Home Page

Generic departmental webpage

The Formalities
Christopher L. Miller
Associate Professor

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

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

Education

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.

"The virtue of model theory is its ability to organize succinctly the sort of tiresome algebraic details associated with elimination theory.'' (G. Sacks, 1972)

Publications

A must-read: J.S. Milne's Tips for Authors; click here and then look for the link near the bottom of the left panel.

Preprints

(Please contact me for e- or offprints of papers that have already been published.)

07/02/09. Expansions of o-minimal structures on the real field by trajectories of linear vector fields.

07/01/09. Generic expansions of ordered structures, with A. Dolich and C. Steinhorn.

11/29/08. Expansions of the real field by open sets: definability versus interpretability, with H. Friedman, K. Kurdyka, and P. Speissegger.

Revised 03/18/08 (some minor typos fixed). Structures having o-minimal open core, with A. Dolich and C. Steinhorn, to appear in Trans. Amer. Math. Soc.

Upgrades

2/19/06. ... for ``Avoiding the projective hierarchy in expansions of the real field by sequences''.

2/5/05. ... for ``Geometric categories and o-minimal structures''.

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Unpublished notes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.

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

Revised 12/15/06. A trichotomy for expansions of R_{an} by trajectories of analytic planar vector fields (with Patrick Speissegger).

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

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

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

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

Some Links

LAOS (Logicians at Ohio State)

MAMLS (Mid-Atlantic Mathematical Logic Seminar)

ASL (Association for Symbolic Logic)

Deconstructing Evaluations , by Paul Trout