Enumerative and algebraic combinatorics; in particular, permutation statistics, permutation patterns and partially ordered sets

- Professor, University of Iceland, from 2016
- Senior Lecturer, University of Strathclyde, 2011–2015
- Associate Professor, Reykjavík University, 2009–2010
- Assistant Professor, Reykjavík University, 2006–2009
- Lecturer, University of Kalmar (Linnéuniversitetet), 2005–2006
- Postdoc at Institut Mittag-Leffler (The Royal Swedish Academy of Sciences), Spring 2005
- Lecturer, University of Kalmar (Linnéuniversitetet), Autumn 2004
- Graduate student, Chalmers University of Technology, 1998–2004

- Chalmers University of Technology, Doctor of Philosophy, 1998–2004. Thesis:
*Permutation patterns, continued fractions, and a group determined by an ordered set*(ISBN 0346-718x). Advisor: Professor Einar Steingrímsson. Defense: February 27, 2004. Opponent: Mireille Bousquet-Mélou, director of research at LaBRI, Université Bordeaux 1 - Chalmers University of Technology, Licentiate of Philosophy, 1998–2001. Thesis:
*Generalised Pattern Avoidance* - Göteborg University, Bachelor of Science in Mathematics, 1994–1998. (Including one year of studies at University of Strathclyde, Glasgow)

Completed the course “Supervising post graduate research” at Strathclyde University (2012). This course qualifies me as first advisor for doctoral students in the UK.

- Plenary/Invited talk at the Scottish Combinatorics Meeting in St Andrews,
*Counting with sign-reversing involutions*, April 2017 - Plenary/Invited talk at Permutation Patterns 2016 in Washington DC,
*Interval orders and their interpretations in terms of permutations*, June 2016 - Permutation Patterns 2018 at Dartmouth College,
*Enumerating permutations sortable by \(k\) passes through a pop-stack*, July 2018 - Permutation Patterns 2015 in London,
*An exponential formula for counting subsets, subwords and permutation patterns*, June 2015 - NORCOM—The 11th Nordic Combinatorial Conference, KTH (Sweden),
*Upper bounds for the Stanley-Wilf limit of layered patterns*, June 2013 - Invited talk in a Special Session on Permutations at the AMS-MAA Joint Mathematics Meeting in San Diego,
*Upper bounds for the Stanley-Wilf limit of 1324*, January 2013 - Permutation Patterns 2011 at California Polytechnic State Unviersity,
*1324-avoiders with few inversions*June 2011 - Aurora Borealis Combinatorics Workshop, Abisko (Sweden),
*Mesh Patterns*, December 2010 - Invited talk in a Special Session on Permutations at the AMS-MAA Joint Mathematics Meeting in San Francisco,
*\(n!\) matchings, \(n!\) posets*, January 2010 - FPSAC—International Conference on Formal Power Series and Algebraic Combinatorics, San Francisco,
*\(n!\) matchings, \(n!\) posets*, August 2010 - Permutation Patterns 2010 at Dartmouth College,
*Expanding permutation statistics as sums of permutation patterns*, August 2010 - FPSAC—International Conference on Formal Power Series and Algebraic Combinatorics,
*Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations*, July 2009 - 24th Nordic and 1st Franco-Nordic Congress of Mathematicians, Reykjavik,
*Permutations in new guises*, Iceland, January 2005 - FPSAC—International Conference on Formal Power Series and Algebraic Combinatorics, Arizona State University,
*Generalised pattern avoidance*, May 2001

- DIMAI Dipartimento di Matematica e Informatica ‘Ulisse Dini’, Università degli Studi di Firenze (University of Florence),
*Conway’s napkin problem*, December 2018. - The Icelandic Mathematical Society, University of Iceland,
*An introduction to combinatorial species*, November 2018 - The Icelandic Mathematical Society, University of Iceland,
*Conway’s napkin problem*, May 2017 - Math Colloquium, University of Iceland,
*Interval orders via combinatorial species and ballot matrices*, February 2016 - Combinatorics seminar at KTH (Royal Institute of Technology, Stockholm),
*Interval orders via combinatorial species and ballot matrices*, November 2015 - Reykjavik University, ICE-TCS, Research Seminar Series,
*Pascal’s matrix and incidence algebras*, April 2015 - Colloquium at The Open University,
*The monotonicity of principal pattern classes with respect to inversions*, Milton Keynes, February 2014 - Reykjavik University, ICE-TCS, Research Seminar Series,
*Interval orders can be viewed as pairs of permutations*, April 2014 - Computer Science and Information Science Seminars, University of Otago,
*Conway’s Napkin Problem*, March 2010 - CISeminar, University of Strathclyde,
*New directions in permutation patterns*, September 2010 - University of Iceland,
*Permutations in two new guises*, October 2010 - Combinatorics seminar at KTH (Royal Institute of Technology, Stockholm),
*(2+2)-free posets, ascent sequences and pattern avoiding permutations*, April 2009 - Combinatorics Seminar at Reykjavik University,
*Factors in binary strings*,February 2009 - Undergraduate Mathematics Seminar Series, Reykjavik University,
*Conway’s Napkin Problem*, November 2009 - Budapesti Műszaki és Gazdaságtudományi Egyetem (BME),
*Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations*, October 2008 - Combinatorics seminar at KTH (Royal Institute of Technology, Stockholm),
*Stack sorting, trees and pattern avoidance*, December 2007 - Reykjavik University, ICE-TCS, Research Seminar Series,
*Stack sorting, trees and pattern avoidance*, October 2007 - Reykjavik University, ICE-TCS, Research Seminar Series,
*The generating power of continued fractions*, March 2007 - University of Iceland,
*The generating power of continued fractions*, April 2007 - Combinatorics seminar at KTH (Royal Institute of Technology, Stockholm),
*Conway’s napkin problem*, December 2006 - ICE-TCS Theory Day, Reykjavik University,
*An introduction to permutation patterns*, June 2006 - Reykjavik University, ICE-TCS, Research Seminar Series, May 2006
- Reykjavik University, ICE-TCS, Research Seminar Series,
*Conway’s Napkin Problem*, March 2006 - The Icelandic Mathematical Society, University of Iceland,
*Continued Fractions and Increasing Subsequences in Permutations*, October 2006 - University of Iceland, October 2006
- The Icelandic Mathematical Society,
*The art of bijections and the science of generating functions*, August 2006 - Mathematics Seminar at the University of Karlstad,
*Conways servettproblem*, December 2005 - Combinatorics Seminar at Chalmers University of Technology,
*Conways servettproblem*, November 2005 - Kalmars Matematiska Kollokvium,
*En permutationsgrupp betämd av pomängd*, October 2005 - Kalmars Matematiska Kollokvium,
*Conways servettproblem*, September 2005 - Kalmars Matematiska Kollokvium,
*Vad kedjebråk och Pascals triangel har med mönster i permutationer att göra*, June 2004 - Kalmars Matematiska Kollokvium,
*Permutationsmönster*, October 2004 - Summer School on Combinatorics of Groups and Algebras, CIRM, Luminy,
*Permutation patterns and Catalan continued fractions*, July 2004 - Combinatorics Seminar at Chalmers University of Technology,
*Gröbner bases*, March 2003 - Tutte Colloquium, University of Waterloo, May 2002
- Combinatorics Seminar at LaBRI, Université Bordeaux 1,
*Generalised Pattern Avoidance*, February 2001 - Combinatorics Seminar at Chalmers University of Technology,
*Permutations, Patterns, and Binary Trees*, September 2001 - Combinatorics Seminar at Chalmers University of Technology,
*The Coding of Permutations and Set Partitions by Labelled Motzkin Paths*, April 2001 - Combinatorics Seminar at Chalmers University of Technology,
*Rook Theory*, February 2001

- 30th International Conference on Formal Power Series & Algebraic Combinatorics (FPSAC 2018), Dartmouth College,
*Enumerating permutations sortable by \(k\) passes through a pop-stack*, July 2018 - 24th International Conference on Formal Power Series & Algebraic Combinatorics (FPSAC 2012), Nagoya,
*Sorting and preimages of pattern classes*, with Henning Úlfarsson, August 2012 - 23rd International Conference on Formal Power Series & Algebraic Combinatorics (FPSAC 2011), Reykjavík,
*Partition and composition matrices: two matrix analogues of set partitions*, with Mark Dukes and Martina Kubitzke, June 2011 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010),
*Pattern avoidance in partial permutations*, with Vit Jelínek, Eva Jelínková, Sergey Kitaev, August 2010 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), San Francisco State University,
*n! matchings, n! posets*, with Svante Linusson, August 2010 - 20th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008),
*Classification of bijections between 321- and 132-avoiding permutations*, with Sergey Kitaev, June 2008

- Co-recipient of a project grant: Finding structure in sets of permutations, Iceland Research Fund, 2014–2016. Grant reference: 141761051

Amount: 9,790,000 ISK - University of Strathclyde Faculty of Science Starter Grant. 2011–2012

Amount: 11,000 GBP - Co-recipient of a Grant for Excellence: Combinatorics on Words and Permutations, Iceland Research Fund, 2009–2011. Grant reference: 90038011, 90038012, 90038013

Amount: 67,609,000 ISK - Postdoc grant as a part of a Grant of Excellence: Permutation patterns, Iceland Research Fund, 2006–2008. Grant reference: 60005011, 60005012, 60005013

Amount: 24,886,000 ISK

- Member of the board of Institut Mittag-Leffler (from 2019).
- Member of the scientific committee for GASCom 2020 (Conference on Random and Exhaustive Generation of Combinatorial Structures).
- Editor (with Mark Dukes, Sergey Kitaev, David Manlove and Kitty Meeks), Surveys in Combinatorics 2017, Cambridge University Press 440.
- Guest editor, Pure Mathematics and Applications, special issue devoted to Permutation Patterns 2012
- Referee work for Journals: Journal of Combinatorial Theory Series A, Advances of Applied Mathematics, Transactions of the American Mathematical Society, European Journal of Combinatorics, Electronic Journal of Combinatorics, Discrete Mathematics, Theoretical Computer Science, Séminaire Lotharingien de Combinatoire, Annals of Combinatorics, Journal of Integer Sequences, Discrete Applied Mathematics, Pure Mathematics and Applications, The Australasian Journal of Combinatorics, The Journal of Combinatorial Mathematics and Combinatorial Computing, Discrete Mathematics & Theoretical Computer Science.
- Referee work for Conferences: PP13–The eleventh conference on Permutation Patterns, PP10–The eighth conference on Permutation Patterns, PP09–The seventh conference on Permutation Patterns, SOFSEM09—35th International Conference on Current Trends in Theory and Practice of Computer Science, FPSAC09–21st International Conference on Formal Power Series & Algebraic Combinatorics, PP07—The fifth conference on Permutation Patterns, LICS—IEEE Symposium on Logic in Computer Science
- Book reviewer for Taylor & Francis
- Referee for QNRF (Qatar National Research Fund), 2012
- Referee for NSA (National Security Agency) / NSF (National Science Foundation), 2011, 2016.
- Member of the Organizing Committee for BCC 2017
- Member of the Organizing Committee for PP 2017
- Member of the Organizing Committee for PP 2012
- Member of the Organizing Committee for FPSAC 2011
- Member of the Organizing Committee for the 10th Nordic Combinatorial Conference (NORCOM 2010)
- Organizer of the Math Colloquium at the University of Iceland, 2016–2018
- Organizer of the combinatorics seminar at Reykjavik University, 2006–2010
- Member of the hiring committee (RU) for postdoc positions in 2008
- Member of the hiring committee (RU) for postdoc positions in 2009
- Member of the hiring committee (Strathclyde) for postdoc positions in 2014
- Member of the hiring committee (Strathclyde) for postdoc positions in 2015
- Member of the International Student Recruitment Group at Strathclyde, 2012–2015
- PhD selector / admissions officer at CIS Strathclyde, 2011–2015

- Supervisor for Bjarki Ágúst Guðmundsson, “Formalizing the translation method in Agda”, Reykjavik University, MSc June 2017

- Second supervisor for Christian Bean, Reykjavik University, PhD June 2018.
- Supervisor for Stuart Hannah, University of Strathclyde, “Interval order enumeration”, PhD May 2015.
- Second supervisor for Jason Smith, University of Strathclyde, PhD September 2015.

The following are honours degree (4th year) projects that I have supervised at Strathclyde.

- Wojciech Jesiotr,
*Sorting by shifts on a torus*, 2014 - Graeme Hutchinson,
*A “Read it later” program*, 2014 - Scott McCullagh,
*Password manager*, 2014 - Connor Galligan,
*talk 3000*, 2014 - Kit Yiu Raymond Leung,
*A sorting game played on a square*, 2013 - Mark Graham,
*A distributed password manager*, 2013 - Ricky Dalziel,
*A sorting game played on a square*, 2012 - Stuart Paton,
*Catalan structures and bijections*, 2012 - Ross Herbertson,
*Sorting with primitive devices*, 2012 - Michael Wilson,
*Guess a Formula from a Sequence of Numbers*, 2011 - Ramadan Khadeir,
*Binary Strings Avoiding a Given Substring as a Factor*, 2011 - Jordan Haldane,
*A Web Program for the 8-Tile Game*, 2011 - Kenneth Chan,
*Guess a Formula from a Sequence of Numbers*, 2011

- Examiner for Arnar Bjarni Arnarson (Reykjavik University), MSc,
*Substitution decomposition for permutation classes with infinitely many simple permutations*, 2019 - Examiner for Unnar Freyr Erlendsson (Reykjavik University), MSc,
*Effective enumeration of permutation classes and their juxtapositions*, 2019 - Examiner for Tómas Ken Magnússon (Reykjavik University), MSc,
*Forced permutation patterns and applications to coincidence classification of mesh patterns and enumeration of permutation classes*, 2018 - Opponent for Murray Tannock (Reykjavik University), MSc,
*Equivalence classes of mesh patterns with a dominating pattern*, 2016 - Internal examiner for Adam Gundry (Strathclyde), PhD,
*Type Inference, Haskell and Dependent Types*, 2013 - Convener for Pierre-Evariste Dagand (Strathclyde), PhD,
*Reusability and Dependent Types*, 2013 - Opponent for Lína Viðarsdóttir (Reykjavik University), MSc,
*Isomorphisms between consecutive pattern classes*, 2014 - Opponent for Hjalti Magnússon (Reykjavik University), MSc,
*Sorting Operators and Their Preimages*, 2013

Spring | 2019: | STÆ402G - Mathematical Seminar |

Autumn | 2018: | STÆ533M - Combinatorics |

Autumn | 2018: | STÆ303G - Algebra I |

Autumn | 2018: | STÆ532M - Cryptocurrency |

Spring | 2018: | STÆ403M - Algebra III |

Spring | 2018: | STÆ402G - Mathematical Seminar |

Autumn | 2017: | STÆ303M - Algebra I |

Spring | 2017: | STÆ401M - Algebra II |

Spring | 2017: | STÆ402G - Mathematical Seminar |

Autumn | 2016: | STÆ303G - Algebra I |

Spring | 2016: | STÆ402G - Mathematical Seminar |

Lecturer in, and responsible for, the following courses: CS101–Topics in Computing 1 (2011–2012); CS103–Machines, Languages and Computation (2012–2015); CS203–Topics in Computing 2 (2011–2013); CS316–Functional Programming (2011–2015); CS411–Theory of Computation (2013–2015).

*Master students*: Coadvisor for two master students: Marteinn T. Hardarson and Bergsteinn Einarsson

*New courses*: Developed and taught a master level course in Generating Functions as well as an undergraduate course in Mathematics by Computer.

*Existing courses*: Responsible for several undergraduate courses: Number theory and abstract algebra; Financial Mathematics; Calculus for teachers; Calculus for computer scientists; Elementary Number Theory; Linear Algebra; Graph Theory (shared responsibility); Coding Theory

*Extracurricular*: Trained the Icelandic math olympiad team in 2007 and 2009. Referee for The Baltic Way mathematical contest in 2010.

Developed and taught a new course in Discrete Mathematics. Lecturer in, and responsible for, six courses: Calculus I, Calculus II, Discrete Mathematics, Linear Algebra, Graph Theory, and Mathematics for Economists. Teaching assistant in Algebra and Calculus

Lecturer in, and responsible for, two courses: Elementary Number Theory, and Discrete Mathematics. Teaching assistant in a variety of courses, such as: Calculus, Basic Algebra, Linear Algebra, Mathematical Logic, Absolute Geometry, and Discrete Mathematics.