RESEARCH

Research Interests

• 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.

Invited Research Talks

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

Refereed Publications

Research Papers: Published

1. P.L. Bowers, Detecting cohomologically stable mappings, Proc. AMS 86(1982), 679-684.
2. P.L. Bowers, Embedding Eⁿ/G in euclidean space, Topology Appl. 17(1984), 173-187.
3. P.L. Bowers, Fake boundary sets in the Hilbert cube, Proc. AMS 93(1985), 121-127.
4. P.L. Bowers, General position properties satisfied by finite products of dendrites, Trans. AMS 288(1985), 739-753.
5. P.L. Bowers, Discrete cells properties in the boundary set setting, Proc. AMS 93(1985), 735-740.
6. P.L. Bowers, Dense embeddings of sigma-compact, nowhere locally compact metric spaces, Proc. AMS 95(1985), 123-130.
7. P.L. Bowers, An example of a fake s-manifold with a nice locally contractible compactification, Proc. AMS 98(1986), 171-174.
8. P.L. Bowers, Non-shrinkable ``cell-like'' decompositions of s, Pac. J. Math. 124(1986), 257-273.
9. M. Bestvina, P.L. Bowers, J. Mogilski, J. Walsh, Characterization of Hilbert space manifolds revisited, Topology Appl. 24(1986), 53-69.
10. P.L. Bowers, Homological characterization of boundary set complements, Compositio Math. 62(1987), 63-94.
11. P.L. Bowers, Dense embeddings of nowhere locally compact separable metric spaces, Topology Appl. 26(1987), 1-12.
12. P.L. Bowers, Limitation topologies on function spaces, Trans. AMS 314(1989), 421-431.
13. P.L. Bowers, Maximal convex metrics on some classical metric spaces, Geometriae Ded. 291(1989), 125-132.
14. P.L. Bowers, The Borsuk dimension of a graph and Borsuk's partition conjecture for finite sets, Graphs and Comb. 6(1990), 207-222.
15. P.L. Bowers, Maximally symmetric homogeneous metrics on manifolds, Math. Proc. Camb. Phil. Soc. 107(1990), 115-126.
16. 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.
17. 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.
18. P.L. Bowers, The upper Perron method for labeled complexes with applications to circle packings, Math. Proc. Camb. Phil. Soc. 114(1993), 321-345.
19. 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.
20. P.L. Bowers and K. Ruane, Fixed points in boundaries of negatively curved groups, Proc. AMS 124(1996), 1311-1313.
21. P.L. Bowers and K. Ruane, Boundaries of nonpositively curved groups of the form G\times Zⁿ, Glasgow Math. J. 38(1996), 177-189.
22. 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]
23. 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]
24. 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]

Research Papers: in Progress

P.L. Bowers and K. Stephenson, Uniformizing dessins and Belyi maps via circle packing, accepted for publication, Memoirs AMS. [abs] [ps.gz 2002K]

M. Hurdal, K. Stephenson, P. Bowers, D. Sumners, D. Rottenberg, Cortical surface flattening: a quasi-conformal approach using circle packings, 25 pages, preprint (to be submitted to NeuroImage).

Abstracts: Published

1. 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.
2. 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.
3. 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.

Doctoral Students

• 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 Bioinformatics Programmer at the Cold Spring Harbor Laboratory in New York where he studies protein structure via statistical analysis of protein sequence alignments.
• Roger Vogeler is my current student. He has passed the written qualifiers and has been working with me in geometric group theory and low dimensional topology since September 2000. He is preparing for his ATE, which is scheduled for April 2001.

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 Advanced Calculus II in Spring 2001 as well as running QUANTUM! Seminar, in which I speak each week on topics in quantum mechanics and quantum field theory.

Courses Taught at Florida State University 1984-2001

Courses Developed 1984-2001

MTG 6939 Advanced Seminar: QUANTUM! (Fa 99, Sp 00, Fa 00, Sp 01)

I lectured in academic year 1999-2000 on graduate level quantum mechanics. The idea was to give a series of lectures that develop quantum mechanics in a mathematically honest and rigorous way. Though the general theory was developed, after the first semester the lectures concentrated on finite-dimensional, or at worst, discrete spectrum, quantum systems. This frees one from the difficulties that arise from continuous spectra and gets one quickly into the heart of the quantum paradoxes and the main goal of the study, quantum computing. The seminar continued in academic year 2000-01 and has evolved into a seminar on quantum field theories. The quantum computing component has broken off as a separate seminar, which Washington Mio is running. 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 Texts for Saunders College Publishing
• Reviewer for Mathematical Reviews
• Reviewer for the National Science Foundation
• Reviewer for the National Security Agency

Committee Service

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

• 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