Homepage of Jan Snellman

How to reach me

Office

Room 659, corridor A, floor 1, house B.

Office phone

+46 (0)13 28 1444

e-mail

jan.snellman@liu.se

Regular mail

Jan Snellman
Matematiska Institutionen
Linköpings Universitet
581 83 Linköping
Sweden

Career

PhD studies

I was a PhD student at Stockholm University under the supervision of Jörgen Backelin. I was also advised and tutored by Jan-Erik Roos and Ralf Fröberg.

Other professors that helped broaden my horizons were Clas Löfwall and Torsten Ekedahl.

Fellow PhD-students in the commutative algebra group were Emil Sköldberg, Kristina Crona, and Freyja Hreinsdóttir.

I shared office with fellow PhD-students Ozan Öktem and Leif Johansson, and took many courses together with them and Andreas Nilsson and Erik Backelin.

I graduated in february 1998, with the thesis A graded subring of an inverse limit of polynomial rings. In brief, my thesis is about Gröbner bases of generic ideals, in “the ring of generalized polynomials”. I studied how initial ideals of sequences of ideals in polynomial rings with ever more variables stabilizes.

Work at the “radio facility”

Before finishing my PhD I worked for about a year at a goverment agency doing cryptography. I have, sadly, forgotten most of what I learned there.

Post-doc

I was a post-doc at Laboratoire GAGE at Ecole Polytechnique, Palaiseau, Paris, France, from 1998-10-01 to 1999-09-01. I was funded by grants from Centre International des Etudiants et Stagiaires and Svenska Institutet. Laboratoire GAGE was a CNRS-funded “laboratory” with about 10 reserchers and 5 phd students. It has since been absorbed by Laboratoire X.

During the period 1999-10-11 to 2000-07-05 I was at the School of Informatics at the University of Wales, Bangor, supported by grants from KVA and Svenska Institutet. The school of Informatics has since then been dismantled.

I do not think it is more than a strange coincidence that every department where I was a post-doc has ceased to exist!

Temporary work at Linköping

The autumn of 2000, and the spring of 2001, and the first half of the autumn of 2001 I taught at the department of mathematics at Linköping University.

Reserch position at Stockholm

From the autumn of 2002 to the summer of 2005 I held a position as a “forskarassistent” at Stockholm University.

Permanent teaching position at Linköping

From october 2005 and onwards, I am an assistant professor (swedish “universitetslektor”) at Linköping.

Research

Areas of interest

Articles and preprints

Articles

2005
1. A conjecture on the Poincaré-Betti series of modules of differential operators on a generic hyperplane arrangement, Experimental Mathematics, vol 14 (2005), no 4, pp 445-456 math.AC/0408437
2004
1. Standard paths in another composition poset The electronic journal of combinatorics, volume 11(1) 2004, R76 math.CO/0309458
2. The ring of arithmetical functions with unitary convolution: Divisorial and topological properties, Archivum Mathematicum (Brno), tomus 40, 2004/2, pp 161-179. math.RA/0201082, Research Reports in Mathematics 2002/4.
3. Enumeration of concave integer partitions, joint work with Michael Paulsen, Journal of Integer Sequences, Vol. 7 (2004), Article 04.1.3, math.CO/0309065
2003
1. Truncations of the ring of arithmetical functions with unitary convolution, International Journal of Mathematics, Game Theory, and Algebra, 13 (2003), no. 6, 485–519. math.RA/0208183 and math.RA/0205242.
2. Lifting Gröbner bases from the exterior algebra, Communications in Algebra, vol 31, issue 12, 2003. Joint work with Andreas Nilsson, Paris-Sud, Tokyo, KTH. math.RA/0010117
3. The maximal spectral radius of a digraph with (m+1)² - s edges, Electronic Journal of Linear Algebra, volume 10 (2003), pp 179-189. math.CA/0210365
2002
1. Factorisation in topological monoids, International Journal of Mathematics, Game Theory, and Algebra, volume 12, no 4, 2002, pp 313-324. math.GN/9902137
2. Some conjectures on the Hilbert series of generic ideals in the exterior algebra, Homology, homotopy and applications, volume 4, no 2, 2002, pages 409-426, math.RA/0007089, joint work with Guillermo Moreno Socías, Versailles.
2001
1. On the degrees of minimal generators of homogeneous ideals in the exterior algebra, joint work with Guillermo Moreno Socías, Versailles. Communications in Algebra, Vol. 29,#11 (Nov. 2001), pages 5155–5170. MR 1 856 949. ZB pre01690505. Postscript
2. A poset classifying non-commutative term orders. Discrete mathematics and theoretical computer science procedings AA (DM-CCG) 2001, pp 301-314. math.CO/0201083, MR 1 88 781. See also the slides from my talk.
2000
1. Non-homogeneous ideals in a graded subring of the power series ring on a countably infinite number of variables over a field International Journal of Mathematics, Game Theory, and Algebra, volume 10, no 5, 2000, pp 391-404. Postscript. MR CMP 1 763 032.
2. Truncations of the ring of number-theoretic functions, Homology, homotopy and applications, volume 2, 2000, pages 17-27, math.NT/9904143, MR 1 750 379
3. *On some partial orders associated to generic initial ideals*, Séminaire Lotharingien de Combinatoire, B43h, 2000, math.CO/9811095, MR 1 756 409
1999
1. *Topological properties of inverse limits of free abelian monoids, with an application to inverse limits of UFDs*. Semigroup Forum volume 59, pp 418-434, 1999. Also available as Postscript. ZB pre990.63115 CMP1847656
  
  Some (minor) errors corrected in Correction of two errors in: “Topological properties of inverse limits of free abelian monoids, with an application to inverse limits of UFDs”. Semigroup Forum 64 (2002), no. 3, 489–490. MR 1 896 383.
2. Some topological properties of a subring of the power series ring on a countably infinite number of variables over a field International Journal of Mathematics, Game Theory, and Algebra, volume 8, no 4, 1999. Postscript. MR CMP1680346. ZB 928.13015
1998
1. Generalized Hilbert numerators Communications in Algebra, volume 27, no 1, 1998. Postscript. MR 99m:13033. ZB 929.13009
2. Reverse lexicographic initial ideals of generic ideals are finitely generated In Gröbner Bases and Applications: Proceedings of the Conference 33 years of Gröbner Bases, ed Buchberger, B. and Winkler, F., London Mathematical Society Lecture Notes Series, vol 251, 1998. PostScript. ZB 980.34387 MR CMP 1 708 900.
3. Initial ideals of truncated homogeneous ideals Communications in Algebra, 1998, volume 26, number 3. Postscript. MR 99k:13030. ZB 915.13013
4. Gröbner bases and normal forms in a subring of the power series ring on countably many variables over a field, Journal of Symbolic Computation 1998, vol 25, number 3, pp 315-328. Postscript. MR99h:13035. Available from IDEAL. ZB 980.49971

Preprints

Generating functions for borders, arXiv:0710.5415
On the number of plane partitions and non isomorphic subgroup towers of abelian groups, joint work with Johan Andersson, arXiv:math/0607698
Laplacians on shifted multicomplexes, math.CO/0606104
Infinite Minkowski sums of lattice polyhedra, math.AC/0508092
Saturated Chains in Composition Posets, Report no 11, 2004/2005,spring,Institut Mittag-Leffler, math.CO/0505262.
Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functions, math.CO/0211201
Bounds for the entropy of graded algebras, math.RA/0209080,
Generalised Hilbert Numerators II, math.RA/0003097

PhD Thesis

A graded subring of an inverse limit of polynomial rings, consists of the articles GBN, IIT, RLI, GHN, STP, NHI. Slightly modified version (errata added)

Lectures

Mittag-Leffler talk on posets of termorders
colloqium talk 2006-03-15
docentföreläsning 2006-11-21 on lattice points in cones (in swedish)
talk 2008-12-12 on term orders (in swedish)
non-commutative term orders
Laplacians on multicomplexes talk 2009-06-12 at the conference in honor of Ralf Fröbergs 65’th birthday.
f-vectors of simplicial complexes, talk at Algebra seminar at Linköping, 2023-12-07.

Supervision

PhD students

I was the main supervisor for Jonna Gill, who defended her PhD thesis The k-assignment polytope, phylogenetic trees, and permutation patterns in 2013. For the first half of her studies, Jonna had Svante Linusson as her advisor.
I was the secondary advisor for Mikael Hansson, who defended his PhD thesis Combinatorics and topology related to involutions in Coxeter groups. Axel Hultman was the main advisor.
I was similarly the secondary advisor for Vincent Umutabazi, who defended his thesis Boolean complexes of involutions and smooth intervals in Coxeter groups in 2022. Axel Hultman was the main advisor.

Masters and candidate exams

Elin Gawell, Rings of arithmetic functions with regular convolutions, 2005, Stockholm University
Kåre Krig, Methods for phylogenetic analysis 2010.
Olle Abrahamsson, A Gröbner basis algorithm for fast encoding of Reed-Müller codes, 2016
Ludwig Rahm, Generating functions and regular languages of walks with modular restrictions in graphs, 2017
Aliaksandra Kupreyeva, Simplices of f-vectors, 2019