Philip L. Bowers: Vita: March 2005 [FSU Math]

Philip L Bowers	March 2005



Education	PhD University of Tennessee, 1983
Email	bowers@math.fsu.edu
Homepage	http://www.math.fsu.edu/~bowers/
Phone	850 644 7405
Academic Positions
Administrative Positions	Associate Chair, Department of Mathematics, Florida State University, 1999-
Regular Positions	Dwight B. Goodner Professor of Mathematics, Florida State University, 2002- Professor, Florida State University, 1996- Associate Professor, Florida State University, 1989-96 Assistant Professor, Florida State University, 1984-89
Visiting Positions	Cambridge University, UK, January-May 1996 University of California, Riverside, April-June 1990 University of Tennessee, May-August 1989 University of Tennessee, May-December 1987
Graduate School	Teaching Assistant, University of Tennessee, 1981-83 Hilton Smith Fellow, University of Tennessee, 1979-81 Dryzer Fellow, University of Tennessee, 1978-79

RESEARCH

Research Interests
I was trained as a topologist, but have moved more and more into geometry and complex analysis and have started dabbling in some applications of mathematics. My continuing interests are

Discrete conformal geometry: conformal tilings; circle packings on riemann surfaces; discrete analytic functions; the type problem for graphs; piecewise flat surfaces and their conformal types; Grothendieck dessins d'enfants;
Geometric group theory: negatively curved, automatic, and CAT(0)-groups; boundaries of groups; metric geometry;
Classical complex analysis: the Koebe uniformization problem;
Applications: discrete conformal flattenings; numerical uniformizations of riemann surfaces and piecewise flat surfaces; flat anatomical mappings;
Quantum: quantum mechanics, quantum field theory, quantum computing.

Presentations

Invited Speaker International Workshop on Visualization and Mathematics 2002, Berlin-Dahlem, Germany, May 2002, Planar conformal mappings of piecewise flat surfaces
Invited Speaker Mini-symposium on Computational Differential Geometry, SIAM Conference GD01: Geometric Design and Computing, Sacramento, California, November 2001, Computing conformal shapes with applications
Invited Speaker Texas Geometry and Topology Conference, Texas Christian University, Fort Worth, Texas, February 2001 (one hour talk), Computing conformal structures of curved surfaces
Invited Seminar Physical Chemistry Seminar, Florida State University, Tallahassee, Florida, February 2001 (one hour talk), Quantum computing, Why? What? When?
Invited Speaker Special Session on Computational Algebraic Geometry for Curves and Surfaces, AMS Annual Meeting, New Orleans, Louisiana, January 2001, Computing conformal structures of curved surfaces
Invited Speaker Special Session on Computational Algebraic Geometry for Curves and Surfaces, AMS Annual Meeting, San Antonio, Texas, January 1999
Invited Speaker Special Session on Conformal Analysis, AMS Regional Meeting, Chattanooga, Tennessee, October 1996
Invited Speaker Special Session on Geometric Topology, AMS Regional Meeting, Chattanooga, Tennessee, October 1996
Invited Seminar Complex Analysis Seminar, Imperial College, University of London, May 1996 (one hour talk)
Invited Seminar Geometric Group Theory and Hyperbolic Geometry Seminar, University of Warwick, UK, March 1996 (one hour talk)
Invited Speaker Florida Topology Conference, University of Florida, October 1994 (forty minute talk)
Invited Speaker Special Session on Geometric Group Theory and Metric Geometry, AMS Regional Meeting, Lexington, Kentucky, March 1994
Invited Speaker 15th Rolf Nevanlina Colloquium, June 1993 (one hour talk)
Invited Seminar University of Tennessee, February 1991 (two one hour talks)
Invited Seminar Area Wide (Southern California) Topology Seminar, California Institute of Technology, June 1990 (one hour talk)
Invited Speaker Fourth Annual Western Workshop in Geometric Topology, Oregon State University, June 1987 (thirty minute talk)
Invited Speaker Special Session on Geometric Topology, AMS Regional Meeting, Logan, Utah, October 1986
Invited Speaker Special Session on Infinite Dimensional Topology, AMS Annual Meeting, Anaheim, California, January 1985
Invited Speaker Special Session on Low Dimensional Topology, AMS Regional Meeting, Richmond, Virginia, April 1984
Invited Speaker Florida Topology Conference, University of Florida, October 1983 (forty minute talk)
Invited Speaker Special Session on Geometric Topology, AMS Regional Meeting, Norman, Oklahoma, March 1983

Refereed Publications

Research Papers: Published

P.L. Bowers, Detecting cohomologically stable mappings, Proc. AMS 86(1982), 679-684.
P.L. Bowers, Embedding Eⁿ/G in euclidean space, Topology Appl. 17(1984), 173-187.
P.L. Bowers, Fake boundary sets in the Hilbert cube, Proc. AMS 93(1985), 121-127.
P.L. Bowers, General position properties satisfied by finite products of dendrites, Trans. AMS 288(1985), 739-753.
P.L. Bowers, Discrete cells properties in the boundary set setting, Proc. AMS 93(1985), 735-740.
P.L. Bowers, Dense embeddings of sigma-compact, nowhere locally compact metric spaces, Proc. AMS 95(1985), 123-130.
P.L. Bowers, An example of a fake s-manifold with a nice locally contractible compactification, Proc. AMS 98(1986), 171-174.
P.L. Bowers, Non-shrinkable ``cell-like'' decompositions of s, Pac. J. Math. 124(1986), 257-273.
M. Bestvina, P.L. Bowers, J. Mogilski, J. Walsh, Characterization of Hilbert space manifolds revisited, Topology Appl. 24(1986), 53-69.
P.L. Bowers, Homological characterization of boundary set complements, Compositio Math. 62(1987), 63-94.
P.L. Bowers, Dense embeddings of nowhere locally compact separable metric spaces, Topology Appl. 26(1987), 1-12.
P.L. Bowers, Limitation topologies on function spaces, Trans. AMS 314(1989), 421-431.
P.L. Bowers, Maximal convex metrics on some classical metric spaces, Geometriae Ded. 291(1989), 125-132.
P.L. Bowers, The Borsuk dimension of a graph and Borsuk's partition conjecture for finite sets, Graphs and Comb. 6(1990), 207-222.
P.L. Bowers, Maximally symmetric homogeneous metrics on manifolds, Math. Proc. Camb. Phil. Soc. 107(1990), 115-126.
P.L. Bowers and K. Stephenson, The set of circle packing points in the Teichmuller space of a surface of finite conformal type is dense, Math. Proc. Camb. Phil. Soc. 111(1992), 487-513.
P.L. Bowers and K. Stephenson, Circle packings in surfaces of finite type: an in situ approach with applications to moduli, Topology 32(1993), 157-183.
P.L. Bowers, The upper Perron method for labeled complexes with applications to circle packings, Math. Proc. Camb. Phil. Soc. 114(1993), 321-345.
P.L. Bowers and K. Stephenson, A branched Andreev-Thurston theorem for circle packings of the sphere, Proc. London Math. Soc. 73(1996), 185-215.
P.L. Bowers and K. Ruane, Fixed points in boundaries of negatively curved groups, Proc. AMS 124(1996), 1311-1313.
P.L. Bowers and K. Ruane, Boundaries of nonpositively curved groups of the form G\times Zⁿ, Glasgow Math. J. 38(1996), 177-189.
P.L. Bowers and K. Stephenson, A ``regular'' pentagonal tiling of the plane, Conformal Geom. Dynam. 1(1997), 58-86. [abs] [ps.gz 868K] [ps 4021K]
P.L. Bowers, Negatively curved graph and planar metrics with applications to type, Michigan Math. J. 45(1998), 31-53. [abs] [ps.gz 78K] [ps 245K] [dvi 103K]
M. Hurdal, P. Bowers, K. Stephenson, D. Sumners, K. Rehm, K. Schaper, D. Rottenberg, Quasi-conformally flat mapping the human cerebellum, in C. Taylor and A. Colchester (eds), Medical Image Computing and Computer-Assisted Intervention - MICCAI'99, Vol. 1679 of Lecture Notes in Computer Science, Springer, Berlin, pp. 279-286, 1999. [abs] [ps.gz 2055K]
P.L. Bowers and M. Hurdal, Planar conformal mappings of piecewise flat surfaces, in Visualization and Mathematics III, Springer-Verlag, 2003, 3-34, 425-26.
P.L. Bowers and K. Stephenson, Uniformizing dessins and Belyi maps via circle packing, Memoirs AMS. 805(2004), Vol. 170, 1-97.

Research Papers: in Progress


: M. Hurdal, K. Stephenson, P. Bowers, D. Sumners, D. Rottenberg, Cortical surface flattening: a quasi-conformal approach using circle packings, 34 pages, submitted for publication.

Research Papers: in Preparation

: P.L. Bowers, Evaluating Feynman path integrals via finite-dimensional path families, in preparation.

Abstracts: Published

Monica K. Hurdal, De Witt L. Sumners, Kelly Rehm, Kirt Schaper, Philip L. Bowers, Ken Stephenson and David A. Rottenberg, A quasi-conformal map of the cerebellar cortex, NeuroImage, vol. 9, no. 6, part 2, pg. S194, 1999.
Monica K. Hurdal, De Witt L. Sumners, Ken Stephenson, Philip L. Bowers and David A. Rottenberg, Generating conformal flat maps of the cortical surface via circle packing, NeuroImage, vol. 9, no. 6, part 2, pg. S195, 1999.
Monica K. Hurdal, De Witt L. Sumners, Ken Stephenson and Philip L. Bowers and David A. Rottenberg, CirclePack: software for creating quasi-conformal flat maps of the brain, NeuroImage, vol. 9, no. 6, part 2, pg. S250, 1999.

Mathematical Reviews of Phil Bowers's papers.

Grant Support

: NSF DMS 0101329, $410,000, Co-PI with DW Sumners, 15 September 2001-31 August 2004.
: Collaborative Research: Computational Conformal Mapping and Scientific Visualization

Doctoral Students
Served as Major Professor in the Department of Mathematics for

Kim Ruane, Boundaries of Groups, PhD Spring 1996. Kim is currently an assistant professor of mathematics at Tufts University in Boston. After graduation from FSU, she spent three years at a postdoctoral position at Vanderbilt University and a year on a postdoctoral fellowship at ETH in Zurich.
Aleksandar Poleksic, Quasiconvex Groups, PhD Summer 1998. Aleksandar is currently a chief scientist at Bionomix, Inc, a biotech firm in Pasadena. Previously, he was a Bioinformatics Programmer at the Cold Spring Harbor Laboratory in New York where he studied protein structure via statistical analysis of protein sequence alignments.
Roger Vogeler, On the Geometry of Hurwitz Surfaces, PhD Summer 2003. Roger holds a post-doctoral position (Ahlfors Fellowship) at the University of Helsinki for the 2003-04 academic year. He has accepted a three year position as an Arnold Ross Assistant Professor at The Ohio State University beginning in Fall 2004.
Bill Wood. Bill has passed the written doctoral qualifiers and I am currently training him in the area of discrete conformal geometry.

Served recently on the Doctoral Committees of

Jeff Denny, Geometry of Proteins with Applications to Solid-State Nuclear Magnetic Resonance, PhD Summer 2000, Department of Mathematics, under the direction of Jack Quine.
Brian Felkel, Decay Estimates on Oscillatory Integrals with Polynomial Phase, PhD Summer 2000, Department of Mathematics, under the direction of Dan Oberlin.
Steve Payne, A Comparison of the Power of an Exact Statistic to that of Wilcoxon's Rank-Sum Statistic and the Student's t-Statistic Under Various Nonnormal Distributions, PhD Summer 2002, Department of Educational Research, under the direction of Ken Brewer.
Justin Barnard, Rationally Justified Belief and Mental Causation: An Epistemic Argument Against Physicalism, PhD Summer 2002, Department of Philosophy, under the direction of Al Mele.
Irma Cruz-White, Topology of Spiral Waves in Excitable Media, PhD Spring 2003, Department of Mathematics, under the direction of De Witt Sumners.
Adam Sipos, Semantic Holism, Instability, and Individualism: Towards a Neo-Fregean Theory of Meaning, PhD Summer 2003, Department of Philosophy.
Chris Jackson. Chris is writing in High Energy Physics under the direction of Laura Riena, Department of Physics.
Partha Srinivasan. Partha is writing in Biomedical Mathematics under the direction of Jack Quine, Department of Mathematics.

TEACHING

Awards

Teaching Incentive Award, FSU, Spring 1999.
Teaching Incentive Award, FSU, Fall 1994.
University Teaching Award, FSU, Spring 1987.

Current Courses

: I am teaching Calculus II and Elementary Topology in the Spring 2005 semester.

Courses Taught at Florida State University 1984-2005

Course Number Course Title Semester Taught^*

MAC 1140 Precalculus Algebra Su 98

MAC 2233 Business Calculus Fa 84, Sp 89

MAC 2311/3311 Calculus I Fa 86, Sp 87 (2), Sp 88 (2), Fa 89 (honors), Fa 92, Sp 94, Sp 97

MAC 2312/3312 Calculus II Su 86 (2), Fa 88, Fa 88 (honors), Fa 90 (2), Fa 91, Sp 93, Fa 93 (2), Fa 94, Su 97 (2), Fa 97, Fa 98 (2), Sp 05

MAD 3104 Discrete Mathematics I Sp 85, Fa 85, Su 94, Su 95, Su 96

MAD 3105 Discrete Mathematics II Sp 86

MAP 3302 ODE's Su 87, Fa 02

MAP 3305 Engineering Math I Su 88

MAS 3301 Modern Algebra Su 92 (2), Su 99

MAA 4402 Complex Variables Sp 99, Sp 02, Sp 03

MAA 4226/5306 Advanced Calculus I Fa 97, Fa 00, Fa 03, Fa 04

MAA 4227/5307 Advanced Calculus II Sp 98, Sp 01, Sp 04

MAT 4906/5932 Qualitative ODE's Fa 86

MTG 4212 College Geometry Sp 94, Sp 95, Fa 95, Sp 97, Sp 98

MTG 4302 Elementary Topology Sp 05

MTG 5316 Elementary Topology I Fa 84, Fa 89, Fa 90, Su 91, Su 93

MTG 5317 Elementary Topology II Sp 85, Sp 89¹

MTG 5326 Topology I Fa 85, Fa 91

MTG 5327 Topology II Sp 86, Sp 92

MTG 5346 Algebraic Topology I Fa 92

MTG 5347 Algebraic Topology II Sp 93

MAS 6939 Advanced Seminar: Cryptography Fa 00, Sp 01

MAT 6939 Advanced Seminar: QUANTUM! Fa 99, Sp 00, Fa 00, Sp 01, Fa 01, Sp02, Fa 02

MAT 6939 Advanced Seminar: Conformal Geometry Fa 02, Sp 03, Fa 03, Sp 04

MTG 6396 Advanced Topics in Topology Su 91, Su 94, Su 98²

MTG 6939 Advanced Seminar: Topology Fa 90, Sp 91, Fa 91, Sp 92, Fa 93, Sp 94, Fa 94, Sp 95

MTG 6939 Advanced Seminar: Geometry Fa 95, Fa 96, Sp 97

REU Research Experience for Undergraduates Su 93 (2 students), Su 94 (2 students)

^* (2) indicates that I taught two sections of the course.
¹ The Spring 89 course was a special topics course entitled ``Matrix Groups''.
² These three courses were entitled ``Hyperbolic Geometry and Fuchsian Groups''.

Courses Developed 1984-2001

MTG 6939 Advanced Seminar: QUANTUM! (Fa 99, Sp 00, Fa 00, Sp 01, Fa 01, Sp 02, Fa 02): I have lectured in every semester beginning Fall 1999 on graduate level quantum mechanics and field theory. A topics list appears on the QUANTUM! Seminar homepage.
MAS 3301 Modern Algebra (Su 99): I did a complete re-evaluation and subsequent redesign of this course in Summer 1999. This course has evolved from an introductory proof-based algebra course for our pure mathematics majors in the seventies to what is now purely a service course to the Mathematics Education Department that attempts to give prospective high school teachers the flavor of modern aspects of algebra. Unfortunately, the course has been taught essentially the same for twenty years, still stressing abstract proofs, and consequently of little use to the present clientele. I believe the redesign succeeds in giving the student valuable experience with abstract concepts by grounding them in concrete models that the student can, and does, understand. The course homepage has a link to pdf files of the homework, which served to direct the course.
MTG 4212 College Geometry (Sp 94, Sp 95, Fa 95, Sp 97, Sp 98): I taught this course during Spring 1994 and began developing a notebook with lectures and exercises suitable for use by others who will teach this course. I continued development when I taught the course again in both Spring and Fall 1995.
MTG 5316-17 Elementary Topology I-II (1984-93): I introduced a set of problems for a Moore method topology course during my first year at FSU. Since then, John Bryant and I have nurtured the development of this course and the problem set has evolved into a list of 149 problems that guide the student through our opinion of what every young graduate student should know about point-set topology.
MTG 5326-27 Topology I-II (1991-92): During the 1991-92 academic year I devised a set of lecture notes for Topology I-II consisting of seven chapters in 192 typewritten pages that develops the material over a somewhat nonstandard topics list.
MTG 6396 Special Topics: Hyperbolic Geometry and Fuchsian Groups (Su 91, Su 94, Su 98): I developed from scratch 28 ``lectures'' in 195 handwritten pages with 43 exercises expounding the basics of this beautiful subject for a summer special topics course. These notes later were used profitably by my two REU students to learn the basics.
MTG 5317 Special Topics: Matrix Groups (Sp 89): I wrote 115 pages of course notes for this special topics course introducing students to Lie groups and Lie algebras via a concrete approach through the topic of matrix groups. I included much material that is not found in the standard texts on this subject.

SERVICE

Administrative Service

: I have served as the Associate Chair of the Mathematics Department since August 1999.

Refereeing and Reviewing

Referee for: Topology and Its Applications, Proceedings of the American Mathematical Society, Transactions of the American Mathematical Society, Glasnik Matematicki, Mathematical Proceedings of the Cambridge Philosophical Society
Reviewer of Calculus Text (Berkey), Saunders College Publishing
Reviewer of Calculus Text (Stewart), Brooks-Cole Publishing
Reviewer for Mathematical Reviews
Reviewer for the National Science Foundation
Reviewer for the National Security Agency

Committee Service

2004-05: Executive Committee, Faculty Evaluation Committee, University COFRS Committee
2003-04: Executive Committee, Faculty Evaluation Committee, Goodner Teaching Awards Committee, Visibility Committee (Chairman, Newsletter), Science Area Promotion and Tenure Committee, AMS Meeting Committee (Chair), AMS-FSU Liaison for March Regional Meeting
2002-03: Executive Committee, Faculty Evaluation Committee, Goodner Teaching Awards Committee, Visibility Committee (Chairman, Newsletter), Science Area Promotion and Tenure Committee (Chairman), Science Area Doctoral Directive Status Subcommittee, College of Arts and Sciences Promotion and Tenure Committee, University Promotion and Tenure Committee, University COFRS Committee
2001-02: Executive Committee, Faculty Evaluation Committee, Goodner Teaching Awards Committee, Visibility Committee (Chairman, Newsletter)
2000-01: Executive Committee, Goodner Teaching Awards Committee, Visibility Committee (Chairman, Newsletter, Web Coordinator)
1999-00: Executive Committee, Faculty Evaluation Committee, University Teaching and Advising Awards Committee (Chairman), Goodner Teaching Awards Committee (Chairman), Visibility Committee (Newsletter), Colloquium Committee (Topology Area Representative), Prelim Policy Committee
1998-99: Faculty Evaluation Committee, Graduate Examination Committee, Graduate Admissions Committee, University Teaching and Advising Awards Committee (Chairman), Promotion and Tenure Committee (Arts and Sciences), Doctoral Directive Status Subcommittee (P&T), Chairman Search Committee (Department of Mathematics), Departmental PEP Committee
1997-98: Faculty Evaluation Committee, Graduate Examination Committee, Graduate Admissions Committee, University Teaching and Advising Awards Committee
1996-97: Departmental PEP Committee, University Teaching and Advising Awards Committee, Colloquium Committee (Chairman and Topology Area Representative)
1995-96: Faculty Evaluation Committee, Colloquium Committee (Chairman), Curriculum Committee, Departmental TIP Committee, Faculty Senate
1994-95: Faculty Evaluation Committee, Colloquium Committee (Chairman and Topology Area Representative), Curriculum Committee (Secretary), Committee to Develop Middle School Probability (Mathematics Education)
1993-94: Faculty Evaluation Committee, Graduate Examination Committee, Colloquium Committee (Chairman and Topology Area Representative), Curriculum Committee, Committee to Develop Middle School Algebra (Mathematics Education)
1992-93: Faculty Evaluation Committee, Graduate Examination Committee, University Curriculum Committee, Colloquium Committee (Chairman), FSU MAA Representative, Calculus Textbook Committee, Departmental Self Study (Committee on Visibility, Departmental Organization, and Welfare)
1991-92: Faculty Evaluation Committee, Graduate Examination Committee, University Curriculum Committee, Colloquium Committee (Topology Area Representative), FSU MAA Representative
1990-91: Library Committee (Chairman), Computer Needs Committee, Colloquium Committee (Topology Area Representative), College Teaching Fellowship Committee, FSU MAA Representative
1989-90: Library Committee, Council for Instruction (University Committee)
1988-89: Library Committee, Council for Instruction (University Committee)
1987-88: Library Committee
1986-87: Library Committee, FSU representative for annual MAA regional meeting (responsibilities include chairing the articulation panel and organizing the banquet)
1985-86: Curriculum Committee (Secretary), FSU representative for annual MAA regional meeting

Invited Service Talks

Florida MAA Meeting, Eckerd College, St. Petersburg, March 1991 (one hour invited address)
Masters Symposium, School of Architecture, Florida A&M University, March 1990 (one and one-half hour talk)
Tenth Annual Tri-State Math and Computer Science Olympiad, Wallace College, Alabama, March 1990 (one hour talk)

Conference Organization

Conference of the Focused Research Group on Computational Conformal Mapping and Scientific Visualization, Wakulla Springs Lodge, Discrete Geometry with Applications to Science and Medicine, Organizing Committee, May 2002
Special Session, 973rd meeting of the AMS, San Diego, CA, Quantum Computing and Information, Organizing Committee, January 2002
Special Session, 962nd meeting of the AMS, New Orleans LA, Geometric Group Theory, Organizing Committee, January 2001
Mobile AL, Geometric Groups at the Gulf, Organizing Committee, May 1999
Special Session, 926th meeting of the AMS, Atlanta GA, Discrete Conformal Geometry, Organizer, October 1997
Special Session, 899th meeting of the AMS, Orlando FL, Discrete Conformal Geometry, Organizer, March 1995
Special Session, 890th meeting of the AMS, Lexington KY, Geometric Group Theory and Metric Geometry, Organizer, March 1994