Homepage of Jan Snellman

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

+46 (0)13 28 1444

jan.snellman@liu.se

• Jan Snellman
• Matematiska Institutionen
• Linköpings Universitet
• 581 83 Linköping
• Sweden

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.

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.

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!

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.

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

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

• 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.

• 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.

• Michael Paulsen, Enumerativa egenskaper för konkava partitioner av heltal, 2003. Parts of the candidate thesis published as Enumeration of concave integer partitions, J. Integer Seq. 7(1), 2004
• 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
• Albin Jaldevik A study on Poset Probability, 2022

1. “Chaos complexes” in analogy with order complexes.
2. “Algebraic number theory” in particular, maximal orders in number fields
3. “Poset probability” in particular for partition posets.
4. “Tropical difference equations” or linear reccurence equations involving max (or min) of (affine) linear forms
5. “Properties of the ternary convolution” A novel convolution product on arithmetical functions
6. Multivariate continued fractions and Diophantine approximation, exploring the work by Labbe, using his code repo.

7. Continued fractions for Gaussian integers, as in

   “Geodesic Gaussian Integer Continued Fractions.” Michigan Math. J. 69 (2) 297 - 322, May 2020. https://doi.org/10.1307/mmj/1576033219

8. Hilbert series of monomial modules over the exterior algebra has been classified by Amata and Crupi. To understand their result better, it would be interesting to mimic the work of Kozlov and calculate the vertices of the polytope of the convex hull of those Hilbert series (viewed as integer vectors). See Aliaksandra Kupreyeva, Simplices of f-vectors, for more references.
9. The investigation of enumerative and multiplicative properties of “concave partitions”, i.e. artinian integrally closed monomial ideals, can be attempted in 3 variables, extending the two variable case by Veronica Crispin Quinonez in her PhD thesis (showing that in two variables such monomial ideals enjoy unique factorization, not true for 3 vars) and Paulsen and Snellman (enumeration using generating functions, see Enumeration of concave integer partitions, J. Integer Seq. 7(1), 2004)