News and upcoming events

• Current/Upcoming: Workshop on Convex Polytopes (Kyoto, July 2012), ISMP 2012 (Berlin, Aug. 2012)

• Mixed Integer Programming 2012 at UC Davis, July 16–19, 2012
  

• I am forming an Interest Group in Optimization at UC Davis, which crosses department boundaries -- you are invited to join. Subscribe to the mailing list for information on optimization-related events at UC Davis.

• Current classes and seminars at UC Davis (Winter 2012):
  • Teaching MAT 21B "Calculus"
  • Teaching MAT 258B "Discrete and Mixed Integer Optimization"

• New LattE integrale software

• MSRI lecture notes on Geometry of Numbers and Short Rational Generating Function Techniques from my MSRI Summer Graduate Workshop Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2-13, 2010.

• more...

Research

My research interests are mathematical optimization (integer programming) and computational discrete mathematics.

• Projects

  • High-performance computations with rational generating functions (NSF, Computational Mathematics program, 2009-2012)

• Selected Publications, Theses and Preprints
  • A Primal All-Integer Algorithm Based on Irreducible Solutions (the paper on the Integral Basis Method; with U.-U. Haus and R. Weismantel, 2001).
  • On the Way to Perfection: Primal Operations for Stable Sets in Graphs (with C. Gentile, U.-U. Haus, G. Rinaldi, and R. Weismantel, 2002).
  • Extended Formulations for Gomory Corner Polyhedra (with Q. Louveaux, R. Weismantel, and L. Wolsey, 2004)
  • A primal Barvinok algorithm based on irrational decompositions (2006)
  • Integer Minkowski Programs and the Design of Survivable Networks (with E. Eisenschmidt and A. Laugier, 2006)
  • FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension (with J. A. De Loera, R. Hemmecke, and R. Weismantel, 2007)
  • Ehrhart Polynomials of Matroid Polytopes and Polymatroids (with J. A. De Loera and D. C. Haws, 2007)
  • How to Integrate a Polynomial over a Simplex (with V. Baldoni, N. Berline, J. A. De Loera, M. Vergne, 2008)
  • Nonlinear Integer Programming (with R. Hemmecke, J. Lee, R. Weismantel, 2009)
  • A parametric integer programming algorithm for bilevel mixed integer programs (with M. Queyranne, C. T. Ryan, 2009)
  • more...

• Recent Talks and Events
  • Participation in BADMath Day (San Francisco State), ISSAC 2011 (San Jose), IPCO 2011 (IBM Yorktown Heights), Mixed Integer Programming 2011 (Waterloo), Rocky Mountain Mathematics Consortium Summer School (U Wyoming), Discrete Geometry and Optimization (Fields Institute), Berkeley Optimization Day, SIAM Conf. on Applied Algebraic Geometry (NCSU, Raleigh, Oct. 2011), BAD Math Day (UC Davis)
  • Recent talks on primal integer programming at Arizona State University, March 29, and in the workshop Optimization in an Uncertain Environment, UC Davis, March 26
  • Research in Pairs stay at American Institute of Mathematics, Nov 8-12, 2010
  • I participated in the program Modern Trends in Optimization and Its Application at UCLA's Institute for Pure & Applied Mathematics, Sep 13-Dec 17, 2010. I co-organized Workshop III: Discrete Optimization and gave tutorials in discrete optimization.
  • Research in Pairs stay at American Institute of Mathematics, Sep 6-10, 2010
  • I participated in the Mini-Workshop: Exploiting Symmetry in Optimization, at Mathematisches Forschungsinstitut Oberwolfach, Aug 22-28, 2010
  • I co-organized (with Jiawang Nie) the MSRI Summer Graduate Workshop Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2-13, 2010. My MSRI lecture notes on Geometry of Numbers and Short Rational Generating Function Techniques are now available.
  • I co-organized Mixed Integer Programming 2010, Georgia Institute of Technology, July 26-29, 2010
  • I visited the Banff International Research Station for a Focused Research Group, July 18-25, 2010
  • Talks and sessions at SIAM Annual Meeting, Pittsburgh, July 12-17, 2010
  • Talk in the Optimization Seminar at U Washington, Seattle, Apr 13, 2010
  • Research in Pairs stay at Mathematisches Forschungsinstitut Oberwolfach, Mar 21-Apr 3, 2010

• Mathematical Software and Data
  • A program to compute the Primitive Partition Identities
  • A table of the Primitive Partition Identities up to a largest part of 27
  • Tables of the irreducible solutions to cyclic group equations (with M. Jach and R. Weismantel)
  • CPLEX-glue, an interface that makes the ILOG CPLEX Callable Library accessible from Guile (a Scheme implementation) and Allegro Common Lisp (with U.-U. Haus)
  • CDD-glue, an interface that makes Komei Fukuda's cddlib available from the Scheme implementation Guile
  • GYWOPT, an interactive system for exploring primal reformulations of integer linear programs, containing an implementation of the Integral Basis Method (with U.-U. Haus)
  • LattE macchiato, an improved version of LattE, containing new irrational primal decomposition algorithms for counting lattice points in polytopes, and more
  • 4ti2, a software package for algebraic, geometric and combinatorial problems on linear spaces (with R. Hemmecke, R. Hemmecke, P. Malkin, M. Walter)
  • Tables of matroids and the Ehrhart polynomials and h^*-vectors of their base polytopes (with J. De Loera and D. Haws)
  • Maple programs for integrating polynomials over simplices (with V. Baldoni, N. Berline, J. De Loera, and M. Vergne)
  • LattE integrale, an improved version of LattE macchiato, which adds integration and volume computation methods (with J. De Loera and B. Dutra)

Teaching

• Fall 2011: Math 258A: Numerical Optimization
• Spring 2011: Math 133: Mathematical Finance
• Spring 2011: Math 168: Optimization
• Winter 2011: Math 148: Discrete Mathematics (Combinatorial Optimization)
• Winter 2011: Math 280: Global and Mixed-Integer Nonlinear Optimization
• Spring 2010: Math 168: Optimization
• Winter 2010: Math 258B: Discrete and Mixed-Integer Optimization
• Fall 2009: Math 258A: Numerical Optimization
• earlier...

• CV information can be found here.

• Memberships: American Mathematical Society (AMS), Deutsche Mathematiker-Vereinigung (DMV), Gesellschaft für Operations Research (GOR), Institute for Operations Research and the Management Sciences (INFORMS), Mathematical Optimization Society (MOS)

• Mathematics Jobs Wiki

• (Non-math) computer programming etc.

• Ich habe versucht zusammenzutragen, woher ihr mich sonst noch kennen könntet. (in German)

• Business address, office and phone number:

  University of California, Davis           Office: MSB 3143
  Department of Mathematics
  One Shields Avenue                        Phone: +1 (530) 554-2817
  Davis, CA 95616                           Skype: mkoeppe.ucdavis
  USA
  

• Office hours for my current classes: See department page

• If you want to set up an appointment with me, you might find my Availability Calendar useful.

• Email Address:
  • mkoeppe@math.ucdavis.edu

  Mails encrypted with GnuPG (or PGP) are welcome.