# 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.
- Low-Density Parity-Check Codes Creation of good LDPC codes using basic number theory.
- 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.

Decoding algorithms that generalize the Berlekamp-Massey algorithm.

Interpolation decoding using Groebner basis techniques following Sudan's list-decoding breakthrough.

Analysis of the sum-product algorithm.

My thesis was on divisor classes on normal cubic surfaces.

### Research Grants

- 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).
- 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).
- Korea Research Foundation, Postdoctoral Foreign Study Grant, PI M. E. O'Sullivan. Supported one-year postdoctoral position for Kwankyu Lee (7/2005-6/2006).
- 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.
- 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).
- 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).
- 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

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