Contact

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


Email: maths (at) matthiaslenz (dot) eu (dot)

Office: 2.109

About me

From September 2015 to September 2017, I was a member of 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

2019

• Workshop on Applied Algebra, 8-9 June, TU Braunschweig

2017

• Meeting on matroids over hyperfields, 28-29 August 2017, Fribourg
• FPSAC 2017, 9-13 July 2017, Queen Mary University of London (poster)
• Oberseminar Diskrete Mathematik, Geometrie und Optimierung, Goethe Universität Frankfurt, 4 July 2017 (talk)
• Forschungsseminar Diskrete Geometrie, TU Berlin, 28 June 2017 (talk)
• Spring School on Optimization and Data Science, 13-17 March 2017, Novi Sad, Serbia

2016

• Einstein Workshop on Lattice Polytopes, 12-15 December 2016, Berlin
• CUSO Graduate Colloquium, 15-16 September 2016, Fribourg (president of the jury for the Birkhäuser prize for the best talk)
• 77ème Séminaire Lotharingien de Combinatoire, 11-14 September 2016, Strobl, Austria, (talk)
• International Workshop on Enumerative, Algebraic and Geometric Aspects of Arrangements, 25 August 2016, Bremen (talk)
• 7th European Congress of Mathematics, 18-22 July 2016, Berlin
  
  I have organised a Minisymposium on Matroid Theory jointly with Felipe Rincón
• Symposium Diskrete Mathematik, 15-16 July 2016, Berlin
• Seminar of the research group on discrete methods in algebraic geometry, 13 July 2016, Freie Universität Berlin (talk)
• 5th Encuentro Colombiano de Combinatoria (ECCO 2016), 13-24 June 2016, Medellín, Colombia (short talk in open problems session)
• ToGA (Topology and Geometry of Arrangements), 6-8 June 2016, Fribourg
• Arrangements: topology, combinatorics and stability, 3-6 February 2016, Pisa
• Algebra Seminar, Queen Mary University of London, 7 March 2016 (talk)
• Seminar on Matroids in Algebra, Representation Theory and Topology, 24-29 January 2016, Les Diablerets, Switzerland

Previous activities

Publications

Preprints

• Stanley-Reisner rings for quasi-arithmetic matroids, [arXiv]
  September 2017
• Computing the poset of layers of a toric arrangement, [arXiv]
  August 2017
• with Spencer Backman, A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures, [arXiv], [Poster]
  February 2016

Journal articles

• On powers of Plücker coordinates and representability of arithmetic matroids, [arXiv]
  Advances in Applied Mathematics 111 (January 2020)
  DOI: 10.1016/j.aam.2019.04.008
• Representations of weakly multiplicative arithmetic matroids are unique, [arXiv] [journal pdf]
  Annals of Combinatorics 23 (June 2019), no. 2, 335–346
  DOI: 10.1007/s00026-019-00424-z
  The journal version is more recent than the arXiv version and incorporates a few improvements suggested by the referee. Using the link above, it can accessed without a subscription of the journal.
• 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), Séminaire Lotharingien de Combinatoire 78B (2017), 12 pp. [Link]
• 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

• Autumn term 2015: Übung für Analysis III

• Michaelmas term 2013: Tutorials at Merton for Prelims Probability and Geometry
• Trinity term 2014: Tutorials at Merton for Prelims Optimisation
• Michaelmas term 2014: Tutorials at Merton for Prelims Geometry
• Trinity term 2015: Tutorials at Merton for Part A Introduction to Manifolds