Chris Miller's Home Page


Math 949, Sp08

Generic departmental webpage

Fields program on o-minimality and real-analytic geometry

The Formalities

Christopher L. Miller
Associate Professor 

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

e-mail:miller@math.ohio-state.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

dvipdfps 

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.)

dvi pdfps 1/3/08. Structures having o-minimal open core (with A. Dolich and C. Steinhorn).

Upgrades

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

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

dvipdfps 9/23/03. ... for ``Expansions of the real line by open sets: o-minimality and open cores''.

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Unpublished notes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 Revised 12/15/06. 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).

Some Links

LAOS (Logicians at Ohio State)

MAMLS (Mid-Atlantic Mathematical Logic Seminar)

ASL (Association for Symbolic Logic)

Deconstructing Evaluations , by Paul Trout
 

Diversity

 
The young fellow who proposed this title was perhaps a fair sample of the kind of stuff we were made of. He was young, ignorant, good-natured, well-meaning, trivial, full of romance, and given to reading chivalric novels and singing forlorn love-ditties. He had some pathetic little nickel-plate aristocratic instincts, and detested his name, which was Dunlap; detested it, partly because it was nearly as common in that region as Smith, but mainly because it had a plebian sound to his ear. So he tried to enoble it by writing it in this way: d'Unlap. That contented his eye, but left his ear unsatisfied, for people gave the new name the same old pronunciation---, emphasis on the front end of it. He then did the bravest thing that can be imagined,--- a thing to make one shiver when one remembers how the world is given to resenting shams and affectations; he began to write his name so: d'Un Lap.
            --- From The Private History of a Campaign that Failed,  by Mark Twain (1892)
A great column by  Michelle Malkin

Ohio Association of Scholars on OSU's Diversity Action Plan

 Roger Clegg on diversity on National Review Online

 CENTER FOR EQUAL OPPORTUNITY