Contact
Département de mathématiquesUniversité de Fribourg
Chemin du Musée 23
1700 Fribourg
Switzerland
Email: maths (at) matthiaslenz (dot) eu (dot)
About me
From September 2015 to September 2017, I was a member of the Combinatorics group at the Université de Fribourg.
From 20122015, 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
2019
 Workshop on Applied Algebra, 89 June, TU Braunschweig
2017
 Meeting on matroids over hyperfields, 2829 August 2017, Fribourg
 FPSAC 2017, 913 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, 1317 March 2017, Novi Sad, Serbia
2016
 Einstein Workshop on Lattice Polytopes, 1215 December 2016, Berlin
 CUSO Graduate Colloquium, 1516 September 2016, Fribourg (president of the jury for the Birkhäuser prize for the best talk)
 77ème Séminaire Lotharingien de Combinatoire, 1114 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, 1822 July 2016, Berlin
I have organised a Minisymposium on Matroid Theory jointly with Felipe Rincón  Symposium Diskrete Mathematik, 1516 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), 1324 June 2016, Medellín, Colombia (short talk in open problems session)
 ToGA (Topology and Geometry of Arrangements), 68 June 2016, Fribourg
 Arrangements: topology, combinatorics and stability, 36 February 2016, Pisa
 Algebra Seminar, Queen Mary University of London, 7 March 2016 (talk)
 Seminar on Matroids in Algebra, Representation Theory and Topology, 2429 January 2016, Les Diablerets, Switzerland
Publications
Preprints

StanleyReisner rings for quasiarithmetic matroids,
[arXiv]
September 2017 
Computing the poset of layers of a toric arrangement,
[arXiv]
August 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

Representations of weakly multiplicative arithmetic matroids are unique,
[arXiv]
[journal pdf]
Annals of Combinatorics 23 (June 2019), no. 2, 335–346
DOI: 10.1007/s0002601900424z
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/s1080101506212
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 fvector of a representablematroid complex is logconcave
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 logconcavity [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. 7984. 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. 4960 [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. 417426 [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. 623634 [Link]
Other
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