Research and Grants

Research Interests (roughly in reverse chronologically)

  • Algebraic Statistics: This is my current passion.
    • The geometry of the space of entropy vectors for n random variables (the entropic polymatroids).
    • The combinatorics of probabilistic models: graphoids, semigraphoids and such.
    • Bayesian Reasoning on directed acyclic graphs, and generalizations to other probablistic models.
  • Algebraic Geometry Codes and Decoding
    • Dimension and minimum distance for codes from curves and other varieties.
    Decoding algorithms that generalize the Berlekamp-Massey algorithm.
    Interpolation decoding using Groebner basis techniques following Sudan's list-decoding breakthrough.
  • Low-Density Parity-Check Codes
    • Creation of good LDPC codes using basic number theory.
    Analysis of the sum-product algorithm.
  • Ring-linear Codes
    • Bounds for ring-linear codes generalizing MacWilliams work.
  • Algebraic Curves and Surfaces
    • Graduate studies on linkage theory and generalized divisors on Gorenstein curves.
    My thesis was on divisor classes on normal cubic surfaces.

Research Grants

  1. National Science Foundation, Directorate for Computer and Information Science and Engineering, "Decoding of Algebraic Geometry Codes: Theoretical Analysis, Efficient Algorithms, Practical Implementation," PI: M. E. O'Sullivan (7/2009).
  2. National Science Foundation, Directorate for Computer and Information Science and Engineering, "Collaborative Research: Improving Low-Density Parity-Check Codes Through Algebraic Analysis of the Sum-Product Algorithm," PIs: M. E. O'Sullivan, J. Brevik (CSULB), R. Wolski (UCSB) (2/2007).
  3. Korea Research Foundation, Postdoctoral Foreign Study Grant, PI M. E. O'Sullivan. Supported one-year postdoctoral position for Kwankyu Lee (7/2005-6/2006).
  4. National Science Foundation, Division of Networking and Communication Research and Infrastructure: "High-Performance Decoding of Algebraic Codes beyond their Packing Radii," PI R. Blahut (UIUC) (8/2000-7/2003). I was an investigator.
  5. National Science Foundation, Division of Networking and Communication Research and Infrastructure grant, "Implementation and Applications of Practical Codes on Curves," PI R. Blahut (UIUC), Co-PI M. E. O'Sullivan, (7/1998-6/2000).
  6. National Science Foundation, Small Business Innovations Research Grant, "Construction of a Decoder for an Algebraic Geometry Code," PI M. E. O'Sullivan. Phase I (2/1993-10/1993) and Phase II (7/1994-9/1996).
  7. Department of Energy, Small Business Cooperative Research and Development Grant (9/1994-12/1994): Joint work with the Computer Research Group at the Lawrence Livermore National Laboratory.

Educational Grants

  1. SDSU President's Leadership Fund, "A Discrete Mathematics Problem Library for Online Homework," PI: M. E. O'Sullivan, CoPI: Tom Schmidt (2012).
  2. SDSU President's Leadership Fund, "Incorporating Computational Software into Mathematics Courses," PI: M. E. O'Sullivan, coPI: David Monarres (2009).
  3. SDSU Travel grant, "Research Collaboration in Applied Algebra with the National University of Ireland." (5-6/2004).