# Matthias Koeppe

Professor

Discrete Optimization

Ph.D., 2002, University of Magdeburg, GermanyWeb Page: http://www.math.ucdavis.edu/~mkoeppe/

Email: mkoeppe@math.ucdavis.edu

Office: MSB 3143

Phone: 530-754-0479

### Research

Matthias Köppe works in mathematical optimization and computational discrete mathematics. His specialty, integer programming, is concerned with mathematical optimization problems where variables can take only integer values and are constrained by linear inequalities. In this context it is natural to study the interaction of point lattices and polyhedra. To solve integer programs and related problems, Dr. Köppe has applied techniques from discrete geometry (Hilbert bases) and algorithmic enumerative combinatorics (rational generating functions).

### Selected Publications

- Utz-Uwe Haus, Matthias Köppe, and Robert Weismantel. "A primal all-integer algorithm based on irreducible solutions. Math,"
*Programming,*Series B,**96**(2):205–246, 2003. Full Text - Jesús A. De Loera, Raymond Hemmecke, Matthias Köppe, and Robert Weismantel. "Integer polynomial optimization in fixed dimension,"
*Mathematics of Operations Research*,**31**(1):147–153, 2006. math_arxiv.0410111 - Matthias Köppe. "A primal Barvinok algorithm based on irrational decompositions,"
*SIAM Journal on Discrete Mathematics,***21**(1):220–236, 2007. math_arxiv.0603308 - Winfried Bruns, Raymond Hemmecke, Bogdan Ichim, Matthias Köppe, and Christof Söger. "Challenging computations of Hilbert bases of cones associated with algebraic statistics,"
*Experimental Mathematics*,**20**(1):25-33, 2011. Full Text - Velleda Baldoni, Nicole Berline, Jesús De Loera, Matthias Köppe, and Michèle Vergne. "How to integrate a polynomial over a simplex,"
*Mathematics of Computation*,**80**(273):297-325, 2011. Full Text

### Selected Awards and Fellowships

- 1995–1999 Fellow of the German National Merit Foundation (Studienstiftung des deutschen Volkes)
- 2003 Dissertation Award of the German Operations Research Society (GOR)
- 2006–2007 Feodor Lynen Research Fellowship (short-term fellowship) of the Alexander von Humboldt Foundation

*Last updated: 2011-09-02*