S. Allen Broughton, Ph.D.

S. Allen Broughton Photograph
Professor Mathematics, 
Rose-Hulman Institute of Technology

Department of Mathematics 
Rose-Hulman Institute of Technology 
5500 Wabash Ave. 
Terre Haute, IN 47803 USA 
Phone: (812)-877-8179 
Fax: (812)-877-8883 
Email: brought@rose-hulman.edu

Page Contents

Professional Background
Vita (pdf)
Teaching and Undergraduate Research
Research Interests, Publications and Presentations
Programs and Links

Special Links
Discrete Fourier Analysis and Wavelets - Applications to Signal and Image Processing
Automorphisms of Rieman Surfaces/Algebraic Curves Interest Group
NSF-REU Tilings and Hyperbolic Geometry Project (www.tilings.org)
Selected Works BE Press
Rose Summer Undergraduate Research Program

Professional Background

My Education

Where I've taught

Since graduating from Queen's (actually one year before) I've taught at: before coming to Rose-Hulman Institute of Technology as head of the Mathematics Department in August 1994. In 2014 I returned to full faculty status at Rose-Hulman.

Teaching and Undergraduate Research Activities

Teaching web pages

Undergraduate Research and Other Activities

Mathematical Interests and Research

Mathematical Interests and Research Areas

Publications and Preprints (reverse chronological order)

Books and book chapters

  1. Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing with Kurt Bryan, Wiley (2008).
  2. The Science of Nanotechnology: An Introductory Text, with L. Tilstra, R. Tanke, D. Jelski, V. French, G. Zhang, A. Popov, T. George, A.Western, Nova Science Publishers, Hauppauge NY (2007).


  1. Quasi-platonic PSL(2,q)-actions on closed Riemann surfaces, Albanian Journal of Mathematics Vol. 9 (2015) p. 31 - 61. https://sites.google.com/site/albjmath/archives/vol-9-2015/2015-2
  2. Exceptional automorphisms of (generalized) super elliptic surfaces, Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces, Contemporary Mathematics series
    #629 Amer Math Soc (2014) http://dx.doi.org/10.1090/conm/629/12573
  3. Superelliptic surfaces as p-gonal surfaces, Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces, Contemporary Mathematics series #629, Amer Math Soc (2014) http://dx.doi.org/10.1090/conm/629/12570
  4. Ellipses in translation surfaces, with Chris Judge, Geometriae Dedicata, (2011), 47 pp. arXiv preprint page
  5. Cyclic n-gonal Surfaces and their Automorphism Groups- UNED Geometry Seminar, with Aaron Wootton, Disertaciones del Seminario de Matematicas Fundamentales, no. 44, UNED, Madrid, 38 pp (2010) arXiv preprint page
  6. Topologically Unique Maximal Elementary Abelian Group Actions on Compact Oriented Surfaces, with Aaron Wootton, Journal of Pure and Applied Algebra, 213 (2009) 557-572.
  7. Finite Abelian Subgroups of the Mapping Class Group, with Aaron Wootton, Algebraic & Geometric Topology 7 (2007) http://msp.warwick.ac.uk/agt/2007/07/p066.xhtml
  8. Anharmonic Vibrational Motions in C60 : A Potential Energy Surface Derived from Vibrational Self Consistent Field Calculations, D.Jelski, Laszlo Nemes, S.Allen Broughton, Journal of Cluster Science, Vol 16, No 1, March 2005.
  9. Divisible Tilings in the Hyperbolic Plane:  (with Dawn M. Haney, Lori T. McKeough, Brandy M. Smith), New York Journal of Mathematics 6 (2000), 237-283. (link to journal, link to paper)
  10. Constructing Kaleidoscopic Tiling Polygons in the Hyperbolic Plane, American Math. Monthly, October, 2000 (link to MAA summary page).
  11. Symmetries of Accola -Machlaclan and Kulkarni surfaces, (with E. Bujalance, A.F. Costa, J.M. Gamboa, G. Gromadski), Proc. AMS, 127 (3), (1999), 637-646.
  12. Symmetries of Riemann surfaces on which PSL(2,q) acts as a Hurwitz automorphism group, (with E. Bujalance, A.F. Costa, J.M. Gamboa, G. Gromadski), J. of Pure and Appl. Algebra. 106 (1996) 113.
  13. Simple group actions on hyperbolic surfaces of least area, Pacific J. of Math. 158 (1) (1993), 23-48 5.
  14. Normalizers and centralizers of elementary Abelian subgroups of the mapping class group, Topology '90, Walter de Gruyter, New York (1992), 77-89.
  15. The Gottlieb group of finite linear quotients of odd-dimensional spheres, Proceedings of the AMS 111 (4) (1991), 1195-1197.
  16. Classifying finite group actions on surfaces of low genus, J. of Pure & Appl. Algebra 69 (1990), 233-270.
  17. The equisymmetric stratification of the moduli space and the Krull dimension of the mapping class group, Topology and its Applications 37 (1990), 101-113.
  18. Milnor numbers and the topology of polynomial hypersurfaces, Invent. Math 92 (1988), 217-241.
  19. Volumes of subgroups of compact Lie groups, Algebras, Groups and Geometries 4 (1987), 325-364.
  20. The homology and higher representations of the automorphism group of a Riemann surface, Transactions AMS 300 (1) (1987), 153-158.
  21. A note on characters of algebraic groups, Proc. of the AMS 89 (1) (1983), 39-40.
  22. The height of two-dimensional cohomology classes of complex flag manifolds, (with M. Hoffman and W. Homer),Canadian Bull. Math. 26 (4) (1983), 498-502.
  23. On the topology of polynomial hypersurfaces, Proc. Symposia Pure Math., 40, Amer. Math. Soc. (1983), 167-178.
  24. A comment on unions of sigma-fields, (with B. W. Huff), Amer. Math. Monthly, 84 (7), (1977), 553-554.

MSTR Technical Reports and Preprints

  1. Quasi-platonic PSL2(q)-actions on closed Riemann surfaces, Mathematical Sciences Technical Reports (MSTR) (2015)
  2. Continuous Dependence of Solutions of Equations on Parameters, Mathematical Sciences Technical Reports (MSTR) (2014)
  3. Analytical Solution of the Symmetric Circulant Tridiagonal Linear System (with Jeffery J. Leader), Mathematical Sciences Technical Reports (MSTR) (2014)
  4. Calculation of the Killing Form of a Simple Lie Group, Mathematical Sciences Technical Reports (MSTR) (2014)
  5. Flattening a Cone, Mathematical Sciences Technical Reports (MSTR) (2009)
  6. The Barycenter of the Numerical Range of a Matrix (with Roger G. Lautzenheiser and Thomas Werne), Mathematical Sciences Technical Reports (MSTR) (2007)
  7. The Birational Isomorphism Types of Smooth Real Elliptic Curves, Mathematical Sciences Technical Reports (MSTR) (2004)
  8. Splitting Tiled Surfaces with Abelian Conformal Tiling Group, Mathematical Sciences Technical Reports (MSTR) (1999)
  9. Counting Ovals on a Symmetric Riemann Surface, Mathematical Sciences Technical Reports (MSTR) (1997)
  10. Triangular Surface Tiling Groups for Low Genus (with Robert M. Dirks, Maria Sloughter, and C. Ryan Vinroot), Mathematical Sciences Technical Reports (MSTR) (2001) .

Archived Presentations (reverse chronological order)

  1. Quasi-platonic actions of some simple groups on Riemann surfaces and their dessins d'enfant, Joint Mathematics Meetings, Seattle, WA - January 2016
  2. Symmetric surfaces with quasi-platonic PSL(2,q) action, AMS Regional Conference, Loyola, Chicago IL - October 2015.
  3. Quasi-platonic actions of PSL2(q) and their Dessins, AMS Regional Conference, Michigan State University, East Lansing MI - March 2015.
  4. Framing the Image, Rose Math Seminar, February 2015.
  5. Exceptional Automorphisms of (Generalized) Super-elliptic Curves, Riemann and Klein Surfaces, Symmetries and Moduli Spaces, Linkoping Sweden, June 2013.
  6. Pairs of Pants and the Congruence Laws of Geometry, Rose Math Seminar, Spring 2013
  7. Who painted this Painting? Rose Math Seminar, Spring 2012.
  8. Galois actions on regular dessins and Fuchsian group covers, Conference on Riemann Surfaces and Dessins d’Enfants On the Occasion of Jürgen Wolfart’s 65'th Birthday - May 2010
  9. Flat Surfaces, Teichmueller Discs, Veech Groups, and the Veech Tessellation, Session on Automorphisms of Riemann Surfaces and Related Topics, AMS Regional Conference, Pennsylvania State University, University Park, PA - October 2009.
  10. Roll-ups and Differential Geometry, Rose Math Seminar and INMAA section meeting, Fall 2009.
  11. Cyclic n-gonal surfaces - weakly malnormal actions and computational methods, joint with Aaron Wootton, 25th Nordic and 1st British-Nordic Congress of Mathematicians, June 2009.
  12. Classification of Pairs of Fuchsian Groups, Second of two talks in the UNED Geometry Seminar, March 2009
  13. Full Automorphism Groups of Cyclic n-gonal Surfaces, First of two talks in the UNED Geometry Seminar, February 2009
  14. Billiards and Flat Surfaces,Voronoi Tesselations, Delaunay Tesselations and Flat Surfaces, Rose Math Seminar, Fall 2008.
  15. The Barycenter of the Numerical Range of an Operator, ISU Math and CS Research Seminar, November 28, 2007.
  16. Elementary Abelian Group Actions on Surfaces and the Geometry of Moduli Space, IU Geometry Seminar, November 8, 2007.
  17. Classifying Pairs of Fuchsian Groups of Finite Type, AMS Regional Conference, Tucson, April 2007.
  18. Geometry from Chemistry INMAA Spring Meeting, 2007.
  19. Higher Genus Soccer Balls, ISU Math Seminar, Fall 2006.
  20. Geometry from Chemistry, Rose Math Seminar, Fall 2006.
  21. Enumeration of the Equisymmetric Strata of the Moduli Space of Surfaces of Low Genus, AMS Regional Conference, Santa Barbara, April 2005.
  22. Fostering Undergraduate Research in Mathematics, Showcase - Best Assesment Practices VII, Rose-Hulman, Arpil 2005.
  23. Equivalence of Real Elliptic Curves, Rose Math Seminar, October 2004.
  24. Are the Students Competent Users of Mathematics?,  AMS Meeting, Phoenix, January 7, 2004.
  25. Kaleidoscopic Tilings on Surfaces, This Time with the Groups, Rose Math Seminar, Spring 2003.
  26. Vanishing Cycles and Kaliedoscopic Quadrilateral Tilings, Rose Math Seminar, Winter 2002.
  27. Signals, Images, ..., What's Next in Scientific Vizualzation, Sigma Xi, Mount Holyoke College, Spring 2001.
  28. Higher Genus Soccer Balls, Mount  Holyoke Math Club Spring 2001 & Rose Math Seminar, Spring 2000.
  29. Transform Methods in Image Processing, Mathematics Faculty Seminar, Mount Holyoke College, Spring 2001.
  30. The Unreasonable Effectiveness of Mathematics,  Rose-Hulman Symposium August 25, 2000.
  31. Finite Groups, Tilings and Hyperbolic Geometry at the Rose-Hulman REU   Kanazawa Institute of Technology, July 29, 1999.
  32. Mathematical Methods of Image Processing, AMS Meeting, San Antonio, January 16, 1999.
  33. Wavelet Based Methods In Image Processing  Applied Math Seminar, Rose-Hulman, Winter Quarter 1998-99.
  34. Undergraduate Research at the Rose-Hulman REU - What Works for Us ,  AMS Meeting, Baltimore, January 8, 1998.
  35. Finite Groups, Tilings and Hyperbolic Geometry at the Rose-Hulman REU,  INMAA Meeting, Wabash College, October 18 1997.
  36. The Role of Technology in Enhancing Learning in Various Disciplines,  IHETS Conference, Purdue University, October 15,1997.

Programs and Links



This page last updated on 20 Sep 15.