Up: Geometry Center Alumni
Activities at the Geometry Center
Dr. Burgiel's primary interest is in the study of geometric
realizations of abstract polyhedra. She has made two short videos
about her results in this field, and one longer
video on the polyhedral properties of the uniform
net (10,3)a.
She is working with professor Dennis Stanton to find a
complete classification of realizations of regular maps of types
{3,6}_{b,c} and {6,3}_{b,c}.
Heidi is also collaborating with Jesus De
Loera on a project to use Viro's construction to apply
combinatorial methods to problems in algebraic geometry, and working
with Victor Reiner on
other assorted problems in combinatorial algebraic geometry.
The focus of Dr. Burgiel's educational activities is the use of
computers to teach mathematics. She teaches and helped write the
textbook for the Technology in the Geometry
Classroom course, which teaches the use of high school geometry
software through advanced mathematics projects. She is currently
working on a proposal to offer this course over the internet.
Last year, Heidi was on the instructional team of the University
of Minnesota Calculus Initiative which tested the HTML computer labs developed here at the
Center.
Another internet project that Heidi is very interested in is using the
programming language Java to bring mathematics research to a wider
community. In this project, mathematical problems which can be
approached by checking many simple cases selected according to human
intuition but for which an exhastive search is not feasible are
presented to the Web surfing public. Data generated by visitors to
the Web page is then reported back to the mathematician owner of the
page, who can record and review the results of successful experiments.
(For example, see the Tetris research
page.)
Background
Heidi graduated from the University of Washington in
1995, where she wrote a thesis on the subject of regular polytopes
under Branko Grunbaum. While there, she worked for Jim King
and the IAS/Park
City Program for High School Teachers (formerly the Park City
RGI).
She earned a B.S. in mathematics at MIT with a minor in Writing in 1990.
While there she also took courses in computer science and
astrophysics.
Education
 Ph.D. in Mathematics, August 1995.
University of Washington, Seattle, WA.
Thesis title: Realizations of Regular Maps.
B.S. in Mathematics, June 1990.
Massachusetts Institute of Technology, Cambridge, MA.
Professional Experience

Employment
 PostDoctoral Fellow, The Geometry Center, Minneapolis, MN,
September 1995June 1997.
 Teaching Assistant, IAS/Park City Math Institute (formerly
Park City RGI), Park City, UT, Summer 1993, 1994, 1995.
 Graduate Assistant, University of Washington, Seattle, WA,
September 1993  June 1995.
 Instructor, University of Washington, Seattle, WA, Fall 1994.
``Geometry for Teachers'' computer lab.
 Teaching Assistant, University of Washington, Seattle, WA, 19901994.
 MIT Media Lab, Cambridge, MA, 19891990.
Publications
 H. Burgiel. How to Lose at Tetris. To appear,
Mathematical Gazette, July 1997.
 H. Burgiel and E. Sander. Technology in
the Geometry Classroom. The Geometry Center, August 1996.
 H. Burgiel, D. Franzblau, and K. R. Gutschera. The Mystery
of the Linked Triangles. Mathematics Magazine, April 1996.
 H. Burgiel. Toroidal Skew Polyhedra. Symmetry: Culture and
Science, Volume 6, Number 1, 1995.
Presentations
 SIGGRAPH, Minneapolis/St. Paul chapter, October 1996.
Video: ``The Uniform Net (10,3)a''.
 St. Olaf Mathematics Colloquium, September 1996.
``The mathematics of the game of Tetris''.
 Exploring
Undergraduate Algebra and Geometry with Technology, June
1996, ``Web Publishing for
Teachers''.
 MIT Combinatorics Seminar, December 1995, ``Symmetric
embeddings of regular maps  regular skew polyhedra''.
 University of Minnesota Combinatorics Seminar, October
1995, ``Realizing Regular Maps''.
 Third Interdisciplinary Symmetry Congress, Alexandria, VA,
August 1995. ``Toroidal Skew Polyhedra''.
 Meeting of the Intermountain Section of the MAA,
April 1995. Panel Discussion: ``The IAS/Park City Mathematics
Institute''.
 AMS/MAA Mathfest, MN, August 1994. ``How to Lose at
Tetris''.
 Meeting of the Pacific Northwest section of the MAA,
June 1994. ``How to Lose at Tetris''.
 Five Colleges Regional Geometry Institute, July 1993.
``How to Lose at Tetris''.
Up: Geometry Center Alumni
The Geometry Center Home Page
Comments to:
webmaster@geom.umn.edu
Created: Nov 19 1995 
Last modified: Oct 24 12:15:02 1997