Research Activities at the Geometry Center
I am interested on the interaction among Combinatorics,
Real Algebraic Geometry, Optimization, and Symbolic computation.
Recently, I study the topology of smooth real algebraic
hypersurfaces using techniques from combinatorial geometry.
This project is closely related to the understanding of the
space of subdivisions of a convex polytope. I also like to
look at questions about the set of monotone paths on a polytope induced
by a linear functional or about systems of polynomial inequalities.
Jesús holds a joint appointment as a Postdoctoral Research Fellow
at the Geometry Center and as a visiting faculty member
of the School of Mathematics at
the University of Minnesota.
 You can access information on his current
schedule and medium
term plans.
Background
Jesús first studied advanced mathematics at the
School of Sciences of the
National University of México (UNAM), where he obtained a B.S.
in 1989. He was also a research assistant at the
Institute of Mathematics, UNAM.
Jesús received a M.A. from Western Michigan University in 1990,
and later that year transferred to Cornell University.
He received a Ph.D. in applied mathematics from
Cornell in 1995.
Education

Ph.D in applied mathematics, 1995
Cornell University, Ithaca, New York
Dissertation: "Triangulations of Polytopes and Computational Algebra
Dissertation Advisor: Dr. Bernd Sturmfels
M.A in mathematics, 1990
Western Michigan University, Kalamazoo, Michigan
B.S in mathematics, 1989
National University of Mexico
Honors Thesis: On the genus of finite groups
Professional Experience

Employment
 1995  to present: Assistant Professor
School of Mathematics
University of Minnesota, Minneapolis, Minnesota
 1992  1994: Graduate Teaching and Research Assistant
Department of Mathematics
Cornell University, Ithaca, New York
 1988  1989: Free lance technical translator and editor
Mexico City, Mexico
 1987  1988: Research and Teaching Assistant
National University of Mexico
Mexico City, Mexico
Publications
 (with B. Sturmfels, and R. R. Thomas)
Gröbner bases and triangulations of the second hypersimplex,
Combinatorica, vol 15. 1995, pp 409424.
 Gröbner bases and graph colorings,
Beiträge zur Algebra und Geometrie.vol. 36, 1995, pp 8996.
 (with F. Santos)
An effective version of Pólya's theorem on positive definite
forms
Journal of Pure and Applied Algebra, vol 108, 1996, 231240.

A nonregular triangulation of the product of two tetrahedra
Discrete and Computational Geometry, vol 15, 1996, pp 253264.
 (with S. Hosten, F. Santos and B. Sturmfels)
The polytope of all triangulations of a point configuration
Documenta Mathematica J. D.M.V., vol 1, 1996, 103119.
 (with F. Santos and J. Urrutia )
Triangulations with few bistellar neighbors
to appear in Discrete and Computational Geometry.
 (with F. Wicklin)
On the need of convexity in patchworking,
to appear in Advances in Applied Mathematics.
 (with W. Morris)
Qmatrix recognition via secondary and universal polytopes,
submitted to Mathematics of Operations Research.
 (with C. Athanasiadis, V. Reiner and F. Santos)
Projections of cyclic polytopes and their fiber polytopes ,
submitted to European Journal of Combinatorics.
 (with I. Itenberg and E. Shustin)
Flexible combinatorial hypersurfaces ,
in preparation.
Other Works
 PUNTOS, a
MAPLE program for the study of triangulations of convex polytopes
 (with F. Wicklin) Software for the investigation of Viro's Tcurves
and surfaces (topological analysis and graphic display).
This is part of the PISCES project.
 (with F. Wicklin)
Viro's patchworking disproves Ragsdale's conjecture,
Videotape (10 minutes), submitted to MATHVIDEOfest of the
International Congress of Mathematicians, Berlin 1998.
Selected Talks
 Remarks on a combinatorial construction of Viro
(invited speaker) M.I.T. combinatorics seminar, Cambridge MA, December (1997).
 Projections of cyclic polytopes and their fiber polytopes
(invited speaker) E.T.H. Department of Informatics, Zurich Switzerland,
November (1997).
 Hilbert's 16th problem and a combinatorial construction of Viro
(invited speaker) Mathematics Colloquium, University of Illinois, UrbanaChampaign, March (1997).
 Combinatorial models of real algebraic varieties: using computers in their topological classification
(invited speaker) Department of Mathematics and Computer Science, Emory University, March (1997).
 The number of geometric bistellar flips of a triangulation
(invited speaker) Geometric Combinatorics Workshop, MSRI, Berkeley, February (1997).
 Hilbert's 16th problem: a construction of Viro
(invited speaker) Colloquium, Courant Institute of Mathematical Sciences, December (1996).
 Some combinatorial methods in algebraic geometry (invited speaker)
Minicourse presented at the National Politechnic Institute.
Mexico City, Mexico, December 1995.
 A triangulation with few neighbors (invited speaker)
``Algebraic and Geometric Combinatorics'',
Mathematisches Institut Oberwolfach,
OberwolfachWalke Germany, February 1995.
 Classifying triangulations of (0,1)polytopes (invited speaker)
Geometry seminar, School of Computer Sciences,
McGill University, Montreal Canada November 1994.
 Classifying triangulations of (0,1)polytopes (invited speaker)
Geometry seminar, Courant Institute of Mathematical Sciences,
New York University, New York, NY. September 1994.
 Calculo de triangulaciones regulares y aplicaciones (invited
speaker)
Department of Mathematics and Computer Sciences seminar,
University of Cantabria, Santander, Spain July 1994.
 Gröbner bases and triangulations of the second
hypersimplex (invited speaker)
Department of Mathematics seminar,
University of Rochester, Rochester, NY, November 1993.
 Polynomial ideals and enumeration of stable sets and colorings
International Conference on Graph Theory, Combinatorics and
Applications, Kalamazoo, MI (1991)
Jesus Antonio de Loera <deloera@geom.umn.edu>
The Geometry Center
University of Minnesota
400 Lind Hall
207 Church St. S.E.
Minneapolis, MN 55455
(612) 6268308
Jesus can also be reached at
<deloera@math.umn.edu>
School of Mathematics
University of Minnesota
420 Vincent Hall
206 Church St. S.E
Minneapolis MN 55455
(612) 6255099
The Geometry Center Home Page
Comments to:
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Created: Nov 19 1995 
Last modified: September 16 1997