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
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.
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.
11/28/24. Harmonic exponential terms are polynomial, with T. Borgard.
01/27/21. Corrections to "Expansions of o-minimal structures by
dense independent sets".
12/04/23. ... for "Expansions of the real field by
canonical products".
05/30/23. Corrections to "Expansions of o-minimal
structures by fast sequences".
12/01/18. A correction to "Basics of o-minimality
and Hardy fields".
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''.
These are miscellaneous observations and results that are not necessarily intended for publication, especially in their present form. Please regard them as such.
05/28/23. A tameness condition on definably complete expansions of ordered fields.
02/07/23. Re-examination of an old question.
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).
Please contact me for e- or offprints of papers that have already
been published.