Matthias Lenz

Contact

Département de mathématiques
Université de Fribourg
Chemin du Musée 23
1700 Fribourg
Switzerland


Email: matthias.lenz (at) unifr (dot) ch (dot)

Office: 2.109


photo

About me

In September 2015, I joined the Combinatorics group at the Université de Fribourg.

From 2012-2015, I was a Junior Research Fellow at Merton College and a member of the Combinatorics Group at University of Oxford.

Before that, I was a graduate student at TU Berlin and Berlin Mathematical School. My advisor was Olga Holtz (UC Berkeley, TU Berlin, IMDb).

My research is on combinatorial and algebraic structures, including (arithmetic) matroids, splines, vector partition functions, hyperplane arrangements and toric arrangements.

Here is my entry in the Mathematics Genealogy Project. My ancestors include Isaac Newton and Galileo Galilei.

Activities

Recent and upcoming activities

2017

2016

Previous activities

Publications

Preprints

  • Representations of weakly multiplicative arithmetic matroids are unique, [arXiv]
    April 2017
  • On powers of Plücker coordinates and representability of arithmetic matroids, [arXiv]
    March 2017
  • with Spencer Backman, A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures, [arXiv], [Poster]
    February 2016

Journal articles

  • Zonotopal algebra and forward exchange matroids [arXiv]
    Advances in Mathematics 294 (May 2016), 819–852
    DOI: 10.1016/j.aim.2016.03.005
    The journal version and the arXiv version are identical (up to layout).
  • Splines, lattice points, and arithmetic matroids [arXiv] [pdf]
    Journal of Algebraic Combinatorics 43 (March 2016), no. 2, 277–324
    DOI: 10.1007/s10801-015-0621-2
    The best version is the pdf provided on this website.
  • Lattice points in polytopes, box splines, and Todd operators
    [arXiv] [journal pdf] [journal html]
    International Mathematics Research Notices 2015 (2015), no. 14, 5289–5310
    DOI: 10.1093/imrn/rnu095
    The journal version is more recent than the arXiv version and incorporates a few improvements suggested by the referee.
  • Interpolation, box splines, and lattice points in zonotopes
    [arXiv] [journal pdf] [journal html] [Poster]
    International Mathematics Research Notices 2014 (2014), no. 20, 5697–5712,
    DOI: 10.1093/imrn/rnt142
    The journal version contains in Section 4 a few more details than the arXiv version.
  • The f-vector of a representable-matroid complex is log-concave
    Advances in Applied Mathematics 51 (2013), no. 5, 543–545,
    DOI: 10.1016/j.aam.2013.07.001
    This is an abridged version of the preprint Matroids and log-concavity [arXiv]
  • Hierarchical zonotopal power ideals [arXiv]
    European Journal of Combinatorics 33 (2012), no. 6, 1120–1141,
    DOI: 10.1016/j.ejc.2012.01.004
    The journal version and the arXiv version are equal up to the layout and a few small changes made by the copy editor.

Conference proceedings

  • A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures, in Proceedings of 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2017), to appear
  • On a conjecture of Holtz and Ron concerning interpolation, box splines, and zonotopes in Combinatorial methods in topology and algebra. Based on the presentations at the INdAM conference, CoMeTa 2013, Cortona, Italy, September 2013, Springer INdAM Series 12, pp. 79-84. Springer, 2015.
  • Splines, lattice points, and (arithmetic) matroids in Proceedings of 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings, Nancy, France, pp. 49-60 [Link] [Slides]
  • Interpolation, box splines, and lattice points in zonotopes in Proceedings of 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings, Nancy, France, pp. 417-426 [Link]
  • Hierarchical zonotopal power ideals in Proceedings of 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings, Nancy, France, pp. 623-634 [Link]

Other

  • My thesis
  • Matroids and log-concavity [arXiv]
    June 2013
    This is an extended version of the paper The f-vector of a representable-matroid complex is log-concave

Teaching