Dr. Peter N. Malkin

Postdoctoral Researcher and Lecturer

Department of Mathematics and Graduate School of Management
University of California, Davis


Office: 3141 MSB

Telephone: (530) 754-9368

Email: m a l k i n (at) m a t h . u c d a v i s . e d u

Research Interests: operations research, integer programming, combinatorial optimization, computational commutative algebra, and polyhedral computation.


Research Articles

Hilbert's Nullstellensatz and an Algorithm for Proving Combinatorial Infeasibility with J.A. De Loera, Jon Lee and Susan Margulies, Proceedings of ISSAC 2008, July 20–23, 2008, Hagenberg, Austria, pages 197--206.

Computing generating sets of lattice ideals with Raymond Hemmecke, Journal of Symbolic Computation, Volume 44, issue 10, October 2009, pp 1493-1476.

Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization with J.A. De Loera and P.A. Parrilo, submitted to the Institute for Mathematics and its Applications Volume on Mixed Integer Non-Linear Programming.

Computing Infeasibility Certificates for Combinatorial Problems through Hilbert’s Nullstellensatz, with J.A. De Leora, J. Lee and S. Margulies, submitted to the Journal of Symbolic Computation.

Working Papers

Iterative Algebraic Algorithms for the Recognition of Combinatorial Properties and Integer Hull Descriptions with J.A. De Loera, C. Hillar, and M. Omar.

Truncated Markov bases and Gröbner bases for integer programming.

Computing extreme rays of cones revisited.

Software

4ti2 : A software package for algebraic, geometric and combinatorial problems on linear spaces, available at www.4ti2.de.


Lecturing

Fall 2009: Decision Making and Management Science MGP206 at the Graduate School of Management.
Fall 2009: Decision Making and Management Science MGT206 at the Graduate School of Management.
Fall 2008: Short Calculus Math 16C Section 1 at the Department of Mathematics
Spring 2008: Short Calculus Math 16C Section 2 at the Department of Mathematics
Fall 2007: Short Calculus Math 16C Section 1 at the Department of Mathematics


PhD. Thesis

Computing Markov bases, Gröbner bases, and extreme rays, Université catholique de Louvain, 2007.