Department of Mathematical Sciences

Applicable and Computational Algebra Lab

Applicable and Computational Algebra Lab at Clemson University studies a wide spectrum of topics in algebra, number theory and their applications in coding theory, cryptogrpahy, computational biology, and symbolic computation. This is a multidisciplinary area of research lying at the cross roads of mathematics, computer science, engineerings and sciences. Faculty research interests and selected research topics are outlined below. Potenial students are expected to have a strong background in algebra and number theory as well as a strong desire to solve important problems in sciences and engineerings. Visitors and potential students are welcome to contact any of the faculty members for further details.

Main Research Areas

Coding theory
Computational biology
Computational algebra
Computational number theory
Research Topics
ADM Seminar

Faculty Members and Their Research Interests

Elena Dimitrova
Associate Professor

Finite deterministic and stochastic dynamical systems, Groebner bases, systems biology, reverse engineering of biochemical regulatory systems.
Shuhong Gao

Algorithmic number theory, computational algebra, finite fields, cryptography, coding theory and compressive sensing, computational biology. Dr. Gao coauthored with Menezes et al. a book Applications of Finite Fields and is on the Editorial Board of the international journal Finite Fields and Their Applications.
Matthew Macauley
Assistant Professor

Systems and discrete mathematical biology, combinatorial aspects of Coxeter groups, discrete dynamical systems.
Gretchen Matthews

Applications of algebraic geometry to coding theory:how to best define algebraic geometry (AG) codes and how to make these codes more suitable for implementation; iterative decoding algorithms for linear codes, in particular low-density parity-check codes.

Past Faculty Members

Joel Brawley (Alumni Distinguished Professor of Mathematical Sciences): Professor Brawley's main research interest is in finite field theory and applications. He has over 60 publications, and has coauthored with Schnibben a book Infinite Algebraic Extensions of Finite Fields. He has been a consultant for National Security Agency since 1975. His honors include Clemson University Board of Trustees Award of Excellence (1999, 2000), Mathematical Association of America Deborah and Franklin Tepper Haimo Award (1999), South Carolina Governor's Distinguished Professor (1995-96), and Clemson "Class of '39 Award for Excellence" (1989).

Jennifer D. Key (Professor Emeritus of Mathematical Sciences): Professor Key's main research interests include finite geometry, combinatorial designs, error-correcting codes, and groups. She has over 90 publications, and has coauthored with Assmus a book Designs and Their Codes. She is an Editor in Chief for the international journal Designs, Codes and Cryptography.  Please visit her personal web page for more information.

Hiren Maharaj (Associate Professor): Number theory, algebraic function fields, algebraic-geometric codes.

Current Students

Sara Anderson, PhD
(Advisor: Dr. Matthews)

Nate Black, PhD
(Advisor: Dr. Gao)

Juliane Capaverde, PhD
(Advisor: Dr. Gao)

Shih-Wei Chao, PhD
(Advisor: Dr. Macauley)

Michael Dowling, PhD
(Advisor: Dr. Gao)

Qijun He, MS
(Advisor: Dr. Macauley)

Fiona Knoll, MS
(Advisor: Dr. Gao)

Yue Mao, PhD
(Advisor: Dr. Gao)

Abhishek Pandey, PhD
(Advisor: Dr. Dimitrova)

Past PhD Students and Their Theses

Justin Peachey (PhD, December 2011, Advisor: Dr. Matthews). Explicit bases for Riemann-Roch spaces of function fields with many rational places and applications. (Initial position: Visiting Assistant Professor, Davidson College.)

Wittawat Kositwattanarer (PhD 2011, Advisor: Dr. Matthews). Pseudocodewords of parity-check codes. (Initial position: Postdoctoral Research Fellow, Nanyang Technological University, Singapore.)

Lori Layne (PhD 2011, Advisor: Dr. Dimitrova). Properties and applications of nested and partially nested canalyzing functions. (Initial position: Technical Staff, MIT Lincoln Laboratory.)

Frank Volny (PhD 2011, Advisor: Dr. Gao). New Algorithms for Computing Gobner Bases. (Initial position: National Security Agency.)

Nathan Drake (PhD, December 2009, Advisor: Dr. Matthews) Decoding of multipoint algebraic geometry codes via lists. (Initial position: Assistant Professor, North Greenville University.)

Raymond Heindl (PhD 2009, Advisor: Dr. Gao). New Directions in Multivariate Public Key Cryptography. (Initial position: National Security Agency.)

Mingfu Zhu (PhD 2009, Advisor: Dr. Gao). Modelling HIV Drug Resistance. (Initial position: Postdoctoral Fellow, Institute for Genome Sciences and Policy, Duke University.)

Genhua Guan (PhD 2009, Advisor: Dr. Gao). Factoring Polynomials and Groebner Bases. (Initial position: ??)

Jang-Woo Park (PhD 2009, Advisor: Dr. Gao). Discrete Dynamics over Finite Fields. (Initial position: Visiting Assistant Professor, Clemson University.)

Todd Mateer (PhD 2008, Advisor: Dr. Gao). Fast Fourier Transform Algorithms with Applications. (Initial position: National Security Agency.)

Padmapani Seneviratne (PhD 2007, Advisor: Dr. Key). Permutation decoding of codes from graphs and designs. (Initial position: Assistant Professor, American University of Sharjah, UAE.)

Prasit Limbupasiriporn (PhD 2005, Advisor: Dr. Gao). Hidden subgroup problem in quantum computing. (Initial position: faculty member, Department of Mathematics, Silpakorn University, Thailand.)

Jirapha Limbupasiriporn (PhD 2005, Advisor: Dr. Key). Partial permutation decoding for codes from designs and finite geometries. (Initial position: faculty member, Department of Mathematics, Silpakorn University, Thailand.)

Virginia Rodrigues (PhD 2003, Advisor: Dr. Gao). Multivariate polynomials : irreducibility and Groebner bases. (Initial position: Faculty member, PUCRS, Faculdade de Matematica, Brazil.)

Jeffrey Farr (PhD 2003 Advisor: Dr. Gao). Computing Groebner bases, with applications to Pade approximation and algebraic coding theory. (Initial position: Postdoctoral Fellow, Department of Mathematics, Simon Fraser University, Canada; now at National Security Agency.)

Peng Ding (PhD 2000, Advisor: Dr. Key). Minimum-weight generators for generalized Reed-Muller codes. (Initial position: Financial Analyst, Fair Issac, California.)

Kelle Clark (PhD 2000 Advisor: Dr. Key). Bounds for the minimum weight of the dual codes of some classes of designs. (Initial position: Queen's College, Charllote, NC.)

Don Mills (PhD 1999, Advisors: Drs. Brawley and Gao). Root-based polynomial compositions over finite fields. (Initial position: Davies Fellow, NCR/ARL/USMA, Amy Research Lab, West Point, NY.)

F. D. Shobe (PhD 1997, Advisor: Dr. Key). On a class of Steiner systems. (Initial position: ??)

Laurel Carpenter (PhD 1996, Advisor: Dr. Key). Designs and codes from hyperovals. (Initial position: ??)

Past MS Students

Kaitlin Woskoff (MS, May 2012, Advisor: Dr. Dimitrova)
Margaux Evans (MS, May 2012, Advisor: Dr. Dimitrova)
Ryan Harper (MS, May 2012, Advisor: Dr. Dimitrova)
Indranil Mitra (MS, Dec 2009, Advisor: Dr. Dimitrova)
Sarah Edwards (MS, May 2008, Dr. Dimitrova)
Lori Layne (MS, Dec 2007, Advisor: Dr. Dimitrova)
J. Hyde-Volpe (MS, Aug 2010, Advisor: Dr. Matthews)
J. Peachey (MS, May 2009, Advisor: Dr. Matthews)
B. Hicks (MS, May 2009, Advisor: Dr. Matthews)
R. Thomas (MS, May 2008, Advisor: Dr. Matthews)
J. Marshall (MS, May 2007, Advisor: Dr. Matthews)
S. Graham (MS, May 2005, Advisor: Dr. Matthews)
N. Drake (MS, May 2004, Advisor: Dr. Matthews)
T. Michel (MS, May 2004, Advisor: Dr. Matthews)
K. Durham (MS, May 2003, Advisor: Dr. Matthews)
Sarah Anderson (MS, May 2011, Advisor: Dr. Maharaj)
Jeannie Friedel (MS, May 2011, Advisor: Dr. Maharaj)
Grady Thomas ((MS, May 2012, Advisor: Macauley)
Nate Black (MS, May 2010, Advisor: Dr. Gao)
Yue Mao (MS, May 2010, Advisor: Dr. Gao)
Raymond Heindl (MS, May 2005, Advisor: Dr. Gao)
Mingfu Zhu (MS, May 2005, Advisor: Dr. Gao)
Mark Liu (MS, May 2004, Advisors: Drs. Gao and Maharaj)
Chris Woodard (MS, May 2000, Advisor: Dr. Gao)
Chris Seawright (MS, August 1998, Advisor: Dr. Gao)
Jason Howell (MS, May 1998, Advisor: Dr. Gao)
Jill Cuneaz (MS, May 1997, Advisor: Dr. Gao)
F. Ngwane (MS, 2006, Advisor: Dr. Key)
Padmapani Seneviratne (MS, 2003, Advisor: Dr. Key)
Caroline Lucheta (MS, April 1997, Advisor: Dr. Key)
H. Dubose-Schmidt (MS, 1994, Advisor: Dr. Key)
D. Mouritzen (MS, 1993, Advisor: Dr. Key)
Andrea McMakin (MS, 2000, Advisor: Dr. Brawley)
Research Topics
ADM Seminar