Geir Dahl

Instituttleder - Matematisk institutt
Bilde av Geir Dahl
English version of this page
Telefon +47-22855835
Rom 1029
Brukernavn
Besøksadresse Moltke Moes vei 35 Niels Henrik Abels hus 0851 OSLO
Postadresse Postboks 1053 Blindern 0316 OSLO

Research interests

Combinatorial matrix theory and optimization, in particular combinatorial optimization and relations to convex polyhedra (polyhedral combinatorics). Recent focused activities include majorization order and polytopes, classes of (0,1)-matrices with given line sums, doubly stochastic matrices, interval polytopes, matrix ranking methods in tennis(!) , Birkhoff polytopes, spectral graph theory etc.. My CV is here.

Teaching

MAT1120 Linear algebra  (I often lecture together with Erik Bedos)

MAT-INF3100 Linear optimization

MAT-INF4110/MAT-INF9110 Mathematical optimization

Some recent talks

Nytt Munch museum - et SKRIK etter kombinatorikk og geometri!

 

Emneord: Matematikk, Centre of Mathematics for Applications - CMA

Publikasjoner

  • Agra, Agostinho; Dahl, Geir; Haufmann, Torkel Andreas & Pinheiro, Sofia (2017). The k-regular induced subgraph problem. Discrete Applied Mathematics.  ISSN 0166-218X. Fulltekst i vitenarkiv
  • Brualdi, R.A. & Dahl, Geir (2017). Alternating sign matrices, extensions and related cones. Advances in Applied Mathematics.  ISSN 0196-8858.  86, s 19- 49 . doi: 10.1016/j.aam.2016.12.001 Fulltekst i vitenarkiv
  • Andrade, Enide & Dahl, Geir (2016). Combinatorial Perron values of trees and bottleneck matrices. Linear and multilinear algebra.  ISSN 0308-1087. . doi: 10.1080/03081087.2016.1274363
  • Barragan, Luis A.; Dahl, Geir; Dominguez, Alberto & Otin, Arantxa (2016). Zero sum sign-central matrices and applications. Linear Algebra and its Applications.  ISSN 0024-3795.  505, s 109- 125 . doi: 10.1016/j.laa.2016.04.034
  • Brualdi, Richard A.; Dahl, Geir & Fritscher, Eliseu (2016). Doubly Stochastic Matrices and the Bruhat Order. Czechoslovak Mathematical Journal.  ISSN 0011-4642.  66(3), s 681- 700 . doi: 10.1007/s10587-016-0286-6
  • Dahl, Geir & Haufmann, Torkel Andreas (2016). Zero-one completely positive matrices and the A(R, S) classes. Special Matrices.  ISSN 2300-7451.  4(1), s 296- 304 . doi: 10.1515/spma-2016-0024
  • Brualdi, Richard A. & Dahl, Geir (2015). Strict Sign-Central Matrices. SIAM Journal on Matrix Analysis and Applications.  ISSN 0895-4798.  36(3), s 1202- 1220 . doi: 10.1137/140995428
  • Dahl, Geir (2015). L-rays of permutation matrices and doubly stochastic matrices. Linear Algebra and its Applications.  ISSN 0024-3795.  480, s 127- 143 . doi: 10.1016/j.laa.2015.04.033
  • Abreu, Nair; Costa, Liliana; Dahl, Geir & Martins, Enide (2014). The skeleton of acyclic Birkhoff polytopes. Linear Algebra and its Applications.  ISSN 0024-3795.  457, s 29- 48 . doi: 10.1016/j.laa.2014.05.021
  • Charina, Maria & Dahl, Geir (2014). Subdivision schemes, network flows and linear optimization. Advances in Computational Mathematics.  ISSN 1019-7168.  41, s 507- 528 . doi: 10.1007/s10444-014-9371-2
  • Dahl, Geir (2014). The Laplacian energy of threshold graphs and majorization. Linear Algebra and its Applications.  ISSN 0024-3795.  469, s 518- 530 . doi: 10.1016/j.laa.2014.12.002
  • Brualdi, Richard A. & Dahl, Geir (2013). An extension of the polytope of doubly stochastic matrices. Linear and multilinear algebra.  ISSN 0308-1087.  61(3), s 393- 408 . doi: 10.1080/03081087.2012.689980 Fulltekst i vitenarkiv
  • Brualdi, Richard A. & Dahl, Geir (2013). Majorization for partially ordered sets. Discrete Mathematics.  ISSN 0012-365X.  313(22), s 2592- 2601 . doi: 10.1016/j.disc.2013.08.003
  • Dahl, Geir (2013). A note on majorization transforms and Ryser’s algorithm. Special Matrices.  ISSN 2300-7451.  1, s 17- 24 . doi: 10.2478/spma-2013-0004
  • Dahl, Geir & Zhang, Fuzhen (2013). Integral majorization polytopes. Discrete Mathematics, Algorithms and Applications (DMAA).  ISSN 1793-8309.  5(3) Fulltekst i vitenarkiv
  • Benth, Fred Espen; Dahl, Geir & Mannino, Carlo (2012). Computing Optimal Recovery Policies for Financial Markets. Operations Research.  ISSN 0030-364X.  60(6), s 1373- 1388 . doi: 10.1287/opre.1120.1112
  • Brualdi, R.A. & Dahl, Geir (2012). Majorization classes of integral matrices. Linear Algebra and its Applications.  ISSN 0024-3795.  436(4), s 802- 813 . doi: 10.1016/j.laa.2010.11.036
  • Dahl, Geir (2012). A matrix-based ranking method with application to tennis. Linear Algebra and its Applications.  ISSN 0024-3795.  437(1), s 26- 36 . doi: 10.1016/j.laa.2012.02.002
  • Dahl, Geir (2012). Martingale matrix classes and polytopes. Linear Algebra and its Applications.  ISSN 0024-3795.  437(7), s 1722- 1733 . doi: 10.1016/j.laa.2012.04.042
  • Dahl, Geir (2011). Polytopes related to interval vectors and incidence matrices. Linear Algebra and its Applications.  ISSN 0024-3795.  435(11), s 2955- 2960 . doi: 10.1016/j.laa.2011.05.026
  • Dahl, Geir (2010). Majorization permutahedra and (0,1)-matrices. Linear Algebra and its Applications.  ISSN 0024-3795.  432(12), s 3265- 3271 . doi: 10.1016/j.laa.2010.01.024
  • Dahl, Geir & Minken, Harald (2010). A note on permutations and rank aggregation. Mathematical and computer modelling.  ISSN 0895-7177.  52(1-2), s 380- 385 . doi: 10.1016/j.mcm.2010.02.052
  • Dahl, Geir (2009). Disjoint congruence classes and a timetabling application. Discrete Applied Mathematics.  ISSN 0166-218X.  157(8), s 1702- 1710 . doi: 10.1016/j.dam.2008.11.015 Fulltekst i vitenarkiv
  • Dahl, Geir (2009). Permutation matrices related to Sudoku. Linear Algebra and its Applications.  ISSN 0024-3795.  430(8-9), s 2457- 2463 . doi: 10.1016/j.laa.2008.12.023
  • Dahl, Geir; Ball, Michael & Vossen, Thomas (2009). Matchings in Connection with Ground Delay Program Planning . Networks.  ISSN 0028-3045.  53(3), s 293- 306 . doi: 10.1002/net.20272
  • Dahl, Geir & Flatberg, Truls (2009). Reconstructing (0,1)-matrices from projections using integer programming. Computational optimization and applications.  ISSN 0926-6003.  42(1), s 141- 154 . doi: 10.1007/s10589-007-9116-y
  • Dahl, Geir (2008). Transportation matrices with staircase patterns and majorization. Linear Algebra and its Applications.  ISSN 0024-3795.  429(7), s 1840- 1850
  • Dahl, Geir & Minken, Harald (2008). Methods based on discrete optimization for finding road network rehabilitation strategies . Computers & Operations Research.  ISSN 0305-0548.  35(7), s 2193- 2208 . doi: 10.1016/j.cor.2006.10.015
  • Brualdi, R.A. & Dahl, Geir (2007). Constructing (0,1)-matrices with given line sums and certain fixed zeros , In Gabor Herman & Attila Kuba (ed.),  Advances in Discrete Tomography and its Applications.  Birkhäuser Verlag.  ISBN 0-8176-3614-5.  6.
  • Dahl, Geir (2007). A note on a parameter relating traffic equilibria and system optimal routing. Applied Mathematics and Computation.  ISSN 0096-3003.  191, s 445- 450
  • Dahl, Geir (2007). Combinatorial properties of Fourier-Motzkin elimination . The Electronic Journal of Linear Algebra.  ISSN 1081-3810.  16, s 334- 346
  • Dahl, Geir (2007). Majorization and distances in trees . Networks.  ISSN 0028-3045.  50(4)
  • Dahl, Geir & Flatberg, Truls (2007). An Integer Programming Approach to Image Segmentation and Reconstruction Problems , In Geir Hasle; Knut-Andreas Lie & Ewald Gunther Quak (ed.),  Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF.  Springer Publishing Company.  ISBN 978-3-540-68782-5.  Part III Optimization.  s 461 - 481
  • Dahl, Geir & Flatberg, Truls (2007). Reconstructing (0,1)-matrices from projections using integer programming . Computational optimization and applications.  ISSN 0926-6003.  s 141- 154
  • Dahl, Geir; Leinaas, Jon Magne; Myrheim, Jan & Ovrum, Eirik (2007). A tensor product matrix approximation problem in quantum physics. Linear Algebra and its Applications.  ISSN 0024-3795.  420(2-3), s 711- 725 . doi: 10.1016/j.laa.2006.08.026
  • Dahl, Geir & Brualdi, R.A. (2006). The Bruhat shadow of a permutation matrix, In Olga Azenhas; Antonio Duarte; Joao Queiro & Ana Santana (ed.),  Mathematical papers in honour of Eduardo Marques de Sa.  Textos de Matematica, Departamento de Matematica.  ISBN 978-972-8564-43-8.  kapittel.  s 25 - 38
  • Dahl, Geir & Foldnes, Njål (2006). LP based heuristics for the multiple knapsack problem with assignment restrictions. Annals of Operations Research.  ISSN 0254-5330.  146(1), s 91- 104 Fulltekst i vitenarkiv
  • Dahl, Geir; Gouveia, Luis & Requejo, Christina (2006). On formulations and methods for the hop-constrained minimum spanning tree problem, In Mauricio Resende & Panos Pardalos (ed.),  Handbook of Optimization in Telecommunications.  Springer Publishing Company.  ISBN 0-387-30662-5.  19.
  • Dahl, Geir; Huygens, David; Mahjoub, A. Ridha & Pesneau, Pierre (2006). On the k edge-disjoint 2-hop-constrained paths polytope. Operations Research Letters.  ISSN 0167-6377.  34(5), s 577- 582
  • Dahl, Geir & Brualdi, R.A. (2005). Matrices of zeros and ones with given line sums and a zero block. Electronic Notes in Discrete Mathematics.  ISSN 1571-0653.  403, s 207- 215
  • Dahl, Geir & Flatberg, Truls (2005). A remark concerning graphical sequences. Discrete Mathematics.  ISSN 0012-365X.  304(1-3), s 62- 64
  • Dahl, Geir & Flatberg, Truls (2005). Optimization and Reconstruction of hv-convex (0,1)-matrices. Discrete Applied Mathematics.  ISSN 0166-218X.  151, s 93- 105
  • Dahl, Geir (2005). A method for approximating symmetrically reciprocal matrices by transitive matrices. Linear Algebra and its Applications.  ISSN 0024-3795.  403, s 207- 215
  • Dahl, Geir (2004). On the directed hop-constrained shortest path problem. Operations Research Letters.  ISSN 0167-6377.  32, s 15- 22
  • Dahl, Geir (2004). Tridiagonal doubly stochastic matrices. Linear Algebra and its Applications.  ISSN 0024-3795.  390, s 197- 208 Fulltekst i vitenarkiv
  • Dahl, Geir & Flatberg, Truls (2004). Some constrained partitioning problems and majorization. European Journal of Operational Research.  ISSN 0377-2217.  158(2), s 434- 443
  • Dahl, Geir; Foldnes, Njål & Gouveia, Luis (2004). A note on hop-constrained walk polytopes. Operations Research Letters.  ISSN 0167-6377.  32, s 345- 349
  • Dahl, Geir & Johannessen, B (2004). The 2-path network problem. Networks.  ISSN 0028-3045.  43, s 190- 199
  • Dahl, Geir (2003). A note on linear discrepancy. The Electronic Journal of Linear Algebra.  ISSN 1081-3810.  10
  • Dahl, Geir (2003). Matrices of zeros and ones with given line sums and a zero block. Linear Algebra and its Applications.  ISSN 0024-3795.  371, s 191- 207

Se alle arbeider i Cristin

  • Brualdi, R.A. & Dahl, Geir (2017). Alternating sign matrices and polyhedra.
  • Brualdi, R.A. & Dahl, Geir (2017). Alternating sign matrices and related polyhedra.
  • Andrade, Enide & Dahl, Geir (2016). Combinatorial Perron values.
  • Andrade, Enide & Dahl, Geir (2016). Combinatorial Perron values.
  • Dahl, Geir (2016). Some Topics in Combinatorial Matrix Theory.
  • Dahl, Geir & Brualdi, R.A. (2016). Doubly stochastic matrices and the Bruhat order.
  • Dahl, Geir & Haufmann, Torkel Andreas (2016). Zero-one completely positive matrices and the A(R,S )matrix classes.
  • Haufmann, Torkel Andreas; Agra, Agostinho; Dahl, Geir & Pinheiro, Sofia (2016). The k-regular induced subgraph problem.
  • Agra, Agostinho; Dahl, Geir; Haufmann, Torkel Andreas & Pinheiro, Sofia (2015). Maximal induced k-regular subgraphs.
  • Agra, Agostinho; Dahl, Geir; Haufmann, Torkel Andreas & Pinheiro, Sofia (2015). The k-regular induced subgraph problem for k=1,2.
  • Dahl, Geir (2015). Combinatorial Matrix Theory and Majorization.
  • Dahl, Geir (2015). Majorization, (0,1)-matrices and Laplacian energy..
  • Dahl, Geir (2015). Permutation matrices, doubly stochastic matrices and their L– rays.
  • Dahl, Geir (2014). Majorization and combinatorial matrix theory.
  • Dahl, Geir (2014). Traveling Salesman Problem: En matematisk rundtur.
  • Dahl, Geir & Brualdi, R.A. (2014). Majorization for partially ordered sets.
  • Haufmann, Torkel Andreas & Dahl, Geir (2014). Optimization and classes of completely positive matrices.
  • Dahl, Geir (2013). An introduction to Majorization: theory and applications.
  • Dahl, Geir (2013). Majorization transforms and Ryser’s algorithm.
  • Dahl, Geir (2013). Nytt Munch museum: et SKRIK etter kombinatorikk og geometri!!.
  • Bebiano, Natália; Dahl, Geir; da Silva, José Dias & da Fonseca, Carlos M. (2012). Preface to the Proceedings of the Coimbra Meeting on 0-1 Matrix Theory and Related Topics. Linear Algebra and its Applications.  ISSN 0024-3795.  436(4), s 789- 790 . doi: 10.1016/j.laa.2011.09.028
  • Brualdi, R.A. & Dahl, Geir (2012). An extension of the polytope of doubly stochastic matrices.
  • Dahl, Geir (2012). A taste of Szemerédi's combinatorics.
  • Dahl, Geir (2012). Google: hvordan man blir styrtrik på en matematisk likning!.
  • Dahl, Geir (2012). Lineær algebra, Google og rangering av websider.
  • Dahl, Geir (2012). Majorization, matrix polytopes and combinatorics.
  • Dahl, Geir & Brualdi, R.A. (2012). Generalized Birkhoff polytopes and majorization.
  • Dahl, Geir & Dahl, Kristina Rognlien (2012). Linear optimization and mathematical finance. Fulltekst i vitenarkiv
  • Dahl, Geir (2011). Kombinatorikk på roterommet!.
  • Dahl, Geir (2011). Majorization in matrix theory: a brief introduction and some recent progress.
  • Dahl, Geir (2011). Martingale matrix classes.
  • Dahl, Geir (2010). Majorization and related combinatorial matrix classes.
  • Dahl, Geir (2010). Majorization permutahedra and (0,1)-matrices.
  • Dahl, Geir (2010). Majorization, A(R,S) and related matrix classes.
  • Dahl, Geir (2009). Disjoint congruence classes and an optimization problem.
  • Dahl, Geir (2009). Introduction to optimization and convexity.
  • Dahl, Geir (2009). Majorization and network problems.
  • Dahl, Geir (2008). Majorization in matrix theory: a brief introduction.
  • Dahl, Geir (2008). Matematisk spillteori - analyse av Nash likevekt.
  • Dahl, Geir (2008). Minimum cuts: theory and algorithms.
  • Dahl, Geir (2007). Matematikk og økonomi: fra John Nash ("A Beautiful Mind") til analyse av trafikk i nettverk.
  • Dahl, Geir & Brualdi, R.A. (2007). Some Combinatorial Matrix Problems and Discrete Tomography.
  • Dahl, Geir & Brualdi, R.A. (2007). Some Combinatorial Matrix Problems and Discrete Tomography.
  • Dahl, Geir & Brualdi, R.A. (2006). Constructing (0,1)-matrices with given line sums and certain fixed zeros.
  • Dahl, Geir & Flatberg, Truls (2006). An integer programming approach to image segmentation and reconstruction problems.
  • Dahl, Geir; Flatberg, Truls; Foldnes, Njål & Gouveia, Luis (2006). The Jump Formulation for the Hop-Constrained Minimum Spanning Tree Problem.
  • Dahl, Geir; Leinaas, Jon Magne; Myrheim, Jan & Ovrum, Eirik (2006). A tensor product matrix approximation problem in quantum physics.
  • Dahl, Geir; Ovrum, Eirik; Leinaas, Jon Magne & Myrheim, Jan (2006). A tensor product matrix approximation problem in quantum physics.
  • Dahl, Geir & Brualdi, R.A. (2005). Matrices of zeros and ones and a zero block.
  • Dahl, Geir (2004). A method for approximating symmetrically reciprocal matrices by transitive matrices.

Se alle arbeider i Cristin

Publisert 24. okt. 2010 15:45 - Sist endret 14. feb. 2017 14:27