# 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

#### 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.

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
don't 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.

#### Preprints (not NSF supported)

01/17/17. *D-minimal expansions of the real field have the C^p zero set property*,
with A. Thamrongthanyalak.

#### Upgrades of some published papers

01/19/17. *...
for ``Tameness in expansions of the
real field''*.

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

11/14/12. *... 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#### Unpublished notes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
04/25/11. *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).