Office : Room 4A3d in Realfagbygget
Address : Allegaten 41, 4 etg. nord
Email : email@example.com
Tel. work : +47 55 58 28 40
- Resolutions over polynomial rings
- Coherent sheaves on projective spaces and their homological invariants
- Combinatorial commutative algebra
- Interactions with representation theory
I belong to the
algebra group in Bergen.
- Associative algebras, Koszul algebras and Koszul duality
- Algebraic operads
- Pre- and post-Lie algebras
- Interactions with computational mathematics
Autumn 2020 I teach
MAT221 Discrete mathematics . The syllabus is from:
- Ian Anderson : A first course in discrete mathematics
- Gunnar Fløystad : Kompendium i tallteori
Spring 2021 I teach
MAT230 Non-linear differential equations . The syllabus is from:
- Strogatz: Nonlinear dynamical systems, and Bush: Perturbation theory
- Henning Lohne, 2013 :
- Square-free modules and ideals: Brill-Noether theory, polarization, and deformations.
- Amin Nematbakhsh, IPM Teheran (external advisor), 2017:
- Algebraic and Geometric Properties of Ideals of Poset Homomorphisms
Visiting Ph.D. :
- Alessio D'Ali, Spring/Fall 2015
- Ayah Almousa, Spring 2019
- Milo Ohrlich, Spring 2020
- Andreas østhus: Combinatorial Hopf algebras and Loday-Ronco Hopf algebra of trees, 2020.
- Theo Brønstad: Volume preservation of formal series in aromatic trees, 2019
- Nils Petter Storset: En studie av letterplace og co-letterplace idealer over et poset P, med
|P| = 2,3, 2017
- Kristine Njøs Slinde: Gröbner bases and photogrammetry, 2016
- Tobias Friedl: Projective Hibi varieties, 2013
- Bjørn Møller Greve: Degenerations of determinantal ideals
to generalized Hibi ideals, 2013.
My recent scientific papers.
Partitions of vertices and facets in trees and stacked simplicial complexes
, preprint 2022, 18p.
- Triangulations of polygons and stacked simplicial complexes: separating their Stanley-Reisner ideals
, preprint, 26p.
- Shift modules, strongly stable ideals, and their dualities
, preprint 2021, 44p.
- Profunctors between posets and Alexander duality
, preprint 2021, 31p.
- The universal pre-Lie-Rinehart algebras of aromatic trees
, Springer Proceedings of Mathematics and Statistics, 366, (2021), p.137-159.
- Polarizations of powers of graded maximal ideals
, Journal of Pure and Applied Algebra, 226, no.5, (2022), 33p.
- Solving non-linear Boolean equation systems
by variable eliminiation
, Applicable algebra in Engineering, Communication and Computation, (2021)
- Poset ideals of P-partitions and generalized
letterplace and determinantal ideals,
Acta Mathematica Vietnamica, 44 (2019), no. 1, p.213-241, special issue on Commutative Algebra
- Pre- and post-Lie algebras: The algebro-geometric view,
Proceedings Abel Symposium 2016, 36p.
- Rigid ideals by deforming quadratic
Journal of Algebra, 510 (2018), p.413-457
- The Chow Form of the Essential
Variety in Computer Vision
, Journal of Symbolic Compuation 86 (2018), p.97-119.
- Resolutions of co-letterplace
ideals and generalizations of Bier spheres
, Transactions of the American Mathematical Society, 371 (2019), no.12, p.8733-8753.
- Resolutions of letterplace
ideals of posets , Journal of Algebraic Combinatorics, (2017), no.3, p.911-930.
- Three themes on syzygies,
Bulletin of the American Mathematical Society, 53 (2016), no.3, pp.415-435.
- Letterplace and co-letterplace
ideals of posets , journal article:
Journal of Pure and Applied Algebra 221, no.5 (2017), 1218-1241 .
- P-partitions, letterplace ideals and
triangulated spheres , youtube-video on recent research
The exterior algebra and central notions in mathematics ,
Notices of the American Mathematical Society 62 (2015), no 4, p.364-371.
Here is the Arxiv version of the same paper.
Ideals and guidelines for writing mathematical papers , 12 pages.
Idealer og retningslinjer når man skriver matematiske artikler , 12 sider.
- Stanley-Reisner theory and letterplace ideals of posets , slides April 2016, elementary version of the following slides.
- Letterplace ideals of posets: A large class of ideals with
unusually nice properties , slides March 2016.
- Beyond pure resolutions and vector bundles with supernatural cohomology: Complexes
associated to triplets of degree sequences , slides November 2012 and February 2013.
- Macaulay2 files to compute the dual ideals of strongly stable ideals. Package authored by
Emily Carrick, McGill University:
Last updated July 4'th, 2022.