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Allen Broughton

Professor of Mathematics

Dr. Allen Broughton's areas of expertise include topology and differential geometry, singularity theory, algebra, and imaging science. He has co-authored two textbooks, The Science of Nanotechnology: An Introductory Text and Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing. Dr. Broughton directs the Tilings undergraduate research project, which received grants from the National Science Foundation, and Rose-Hulman's Summer Undergraduate Research Program, which provides opportunities for students to engage in a full-time mentored summer research experience. Check out his personal web page.

Teaching Interests

  • Calculus
  • Differential equations
  • Discrete mathematics
  • Linear algebra
  • Probability and statistics
  • Advanced parallel computing
  • Mathematics of image processing

Research Interests

  • Topology /differential geometry
  • Automorphisms of Riemann surfaces
  • Singularity theory
  • Algebra
  • Imaging science
  • Nanotechnology

Select Publications & Presentations

  • Broughton, S. A. and Bryan, K. M., “Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing,” Wiley Publishers, Hoboken, New Jersey
  • “Riemann Surfaces: A Playground for Analysis, Topology, Geometry, Group Theory, and Galois Theory,“ Department of Mathematics Colloquium, University of Linkoping, Sweden, 2016
  • “Quasi-Platonic Actions of Some Simple Groups on Riemann Surfaces and their Dessins d'enfant,” Joint Mathematics Meetings, Seattle, 2016
  •  “Quasi-Platonic PSL(2,q)-actions on Closed Riemann Surfaces,” Albanian Journal of Mathematics,  9, 31 – 61, 2015
  • “Symmetric Surfaces with Quasi-Platonic PSL(2,q) Action,” American Mathematics Society Regional Conference, Chicago, 2015
  • “Exceptional Automorphisms of (Generalized) Super Elliptic Surfaces,” Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces, Contemporary Mathematics Series #629, American Mathematics Society, 2014
  • “Superelliptic Surfaces as p-gonal Surfaces,” Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces, Contemporary Mathematics Series #629, American Mathematics Society, 2014
  • Broughton, S. A. and Judge, C., “Ellipses in Translation Surfaces,” Geometriae Dedicata, 47, 2011
  • Tilstra, L., Broughton, S. A., Tanke, R. S., Jelski, D., Zhang, G. P., French, V., Popov, A., The Science of Nanotechnology: An Introductory Text, Nova Publishers, Hauppauge, New York, 2007

Academic Degrees

  • PhD, Queen's University at Kingston, 1982
  • MSc, Queen's University at Kingston, 1978
  • BSc, University of Windsor, 1975