Geir Dahl

Instituttleder - Matematisk institutt

$Bilde av Geir Dahl$

English version of this page

E-post geird@math.uio.no

Telefon +47 22855835

Mobiltelefon +47 90640373

Rom 1015

Brukernavn

Besøksadresse Moltke Moes vei 35 Niels Henrik Abels hus 0851 Oslo

Postadresse Postboks 1053 Blindern 0316 Oslo

Pressebilde Last ned visittkort

Research interests

Combinatorial matrix theory; so the study of classes of matrices from a combinatorial point of view, or geometric, using convexity and polyhedral theory. 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)

MAT3100 Linear optimization

MAT4120/MAT9120 Mathematical optimization

Reading course in different topics: graph theory, convexity, matrix theory

Some recent talks

Nytt Munch museum - et SKRIK etter kombinatorikk og geometri!

Emneord: Matematikk

Andrade, Enide; Ciardo, Lorenzo & Dahl, Geir (2022). Perron values and classes of trees. Linear Algebra and its Applications. ISSN 0024-3795. 639, s. 135–158. doi: 10.1016/j.laa.2022.01.005. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2021). Alternating Sign and Sign-Restricted Matrices: Representations and Partial Orders. The Electronic Journal of Linear Algebra. ISSN 1537-9582. 37. doi: 10.13001/ela.2021.6513. Fulltekst i vitenarkiv
Brualdi, Richard A. & Dahl, Geir (2021). Sign-restricted matrices of 0's, 1's, and −1's. Linear Algebra and its Applications. ISSN 0024-3795. 615, s. 77–103. doi: 10.1016/j.laa.2021.01.001. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2021). Diagonal Sums of Doubly Stochastic Matrices. Linear and multilinear algebra. ISSN 0308-1087. doi: 10.1080/03081087.2021.1901844. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2021). Convex (0,1)-Matrices and Their Epitopes, . Discrete Applied Mathematics. ISSN 0166-218X. 297, s. 21–34. doi: 10.1016/j.dam.2021.02.038. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2020). Permutation matrices, their discrete derivatives and extremal properties. Vietnam Journal of Mathematics. ISSN 2305-221X. 48, s. 719–740. doi: 10.1007/s10013-020-00392-5. Fulltekst i vitenarkiv
Ciardo, Lorenzo; Dahl, Geir & Kirkland, Steve (2020). On Kemeny's constant for trees with fixed order and diameter. Linear and multilinear algebra. ISSN 0308-1087. doi: 10.1080/03081087.2020.1796905. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2020). Alternating Sign Matrices: Extensions, König-properties, and Primary Sum-Sequences. Graphs and Combinatorics. ISSN 0911-0119. 36, s. 63–92. doi: 10.1007/s00373-019-02119-x. Fulltekst i vitenarkiv
Dahl, Geir; Guterman, Alexander & Shteyner, Pavel (2019). Majorization for (0,1)-matrices. Linear Algebra and its Applications. ISSN 0024-3795. 585, s. 147–163. doi: 10.1016/j.laa.2019.09.038. Fulltekst i vitenarkiv
Andrade, Enide; Ciardo, Lorenzo & Dahl, Geir (2019). Combinatorial Perron Parameters for Trees. Linear Algebra and its Applications. ISSN 0024-3795. 566, s. 138–166. doi: 10.1016/j.laa.2018.12.028. Fulltekst i vitenarkiv
Andrade, Enide; Dahl, Geir; Leal, Laura & Robbiano, Maria (2019). New bounds for the signless Laplacian spread. Linear Algebra and its Applications. ISSN 0024-3795. 566, s. 98–120. doi: 10.1016/j.laa.2018.12.019. Fulltekst i vitenarkiv
Dahl, Geir; Guterman, Alexander & Shteyner, Pavel (2018). Majorization for matrix classes. Linear Algebra and its Applications. ISSN 0024-3795. 555, s. 201–221. doi: 10.1016/j.laa.2018.06.003. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2018). Alternating sign matrices, related (0,1)-matrices, and the Smith normal form. Linear Algebra and its Applications. ISSN 0024-3795. s. 1–19. doi: 10.1016/j.laa.2018.03.027. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2018). The interval structure of (0,1)-matrices. Discrete Applied Mathematics. ISSN 0166-218X. doi: 10.1016/j.dam.2018.03.024. Fulltekst i vitenarkiv
Brualdi, R.A. & Dahl, Geir (2018). Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Squares. Advances in Applied Mathematics. ISSN 0196-8858. 95, s. 116–151. doi: 10.1016/j.aam.2017.11.005. Fulltekst i vitenarkiv
Agra, Agostinho; Dahl, Geir; Haufmann, Torkel Andreas & Pinheiro, Sofia (2017). The k-regular induced subgraph problem. Discrete Applied Mathematics. ISSN 0166-218X. 222, s. 14–30. doi: 10.1016/j.dam.2017.01.029. 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. 65(12), s. 2387–2405. doi: 10.1080/03081087.2016.1274363. Fulltekst i vitenarkiv
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. Fulltekst i vitenarkiv
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. Fulltekst i vitenarkiv
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. Fulltekst i vitenarkiv
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.
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.
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.
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.
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
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). doi: 10.1142/s1793830913500195. 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.
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.
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.
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 (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 & 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 (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 (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 (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; 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 & 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.
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 & Flatberg, Truls (2007). An Integer Programming Approach to Image Segmentation and Reconstruction Problems. I Hasle, Geir; Lie, Knut-Andreas & Quak, Ewald Gunther (Red.), Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF. Springer Publishing Company. ISSN 978-3-540-68782-5. s. 461–481.
Brualdi, R.A. & Dahl, Geir (2007). Constructing (0,1)-matrices with given line sums and certain fixed zeros. I Herman, Gabor & Kuba, Attila (Red.), Advances in Discrete Tomography and its Applications. Birkhäuser Verlag. ISSN 0-8176-3614-5.
Dahl, Geir & Flatberg, Truls (2007). Reconstructing (0,1)-matrices from projections using integer programming. Computational optimization and applications. ISSN 0926-6003. s. 141–154.

Se alle arbeider i Cristin

Dahl, Geir & Brualdi, R.A. (2022). Combinatorial matrix cones.
Dahl, Geir & Brualdi, R.A. (2022). The permutation and alternating sign matrix cones.
Dahl, Geir (2021). Kombinatorikk, geometri og Munch!
Dahl, Geir (2021). Doubly stochastic matrices: old and new results.
Brualdi, R.A. & Dahl, Geir (2021). Diagonal sums of doubly stochastic matrices.
Dahl, Geir; Munthe-Kaas, Antonella Zanna; Rønquist, Einar; Rypdal, Martin Wibe; Erfjord, Ingvald & Strømskag, Heidi [Vis alle 10 forfattere av denne artikkelen] (2021). Eksamen i matematikk er på ville veier. Aftenposten (morgenutg. : trykt utg.). ISSN 0804-3116.
Dahl, Geir (2019). Majorization - some recent developments in matrix theory.
Dahl, Geir; Brualdi, R.A.; Guterman, Alexander & Shteyner, Pavel (2019). Matrix covering problems.
Andrade, Enide; Dahl, Geir; Leal, Laura & Robbiano, Maria (2019). New bounds for the signless Laplacian spread.
Brualdi, R.A. & Dahl, Geir (2019). Matrix covering and A-interval matrices.
Dahl, Geir; Andrade, Enide & Ciardo, Lorenzo (2018). Combinatorial Perron Parameters and Trees.
Dahl, Geir & Brualdi, R.A. (2018). Alternating Sign Matrices, Polyhedra and Majorization.
Dahl, Geir; Ranestad, Kristian & Hole, Arne (2017). Programmering rammer dybdelæring i matematikk. Aftenposten (morgenutg. : trykt utg.). ISSN 0804-3116. s. 22–23.
Dahl, Geir (2017). Laplacian energy, threshold graphs and majorization.
Brualdi, R.A. & Dahl, Geir (2017). Alternating sign matrices and related polyhedra.
Brualdi, R.A. & Dahl, Geir (2017). Alternating sign matrices and polyhedra.
Andrade, Enide & Dahl, Geir (2016). Combinatorial Perron values.
Andrade, Enide & Dahl, Geir (2016). Combinatorial Perron values.
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.
Dahl, Geir (2016). Some Topics in Combinatorial Matrix Theory.
Dahl, Geir (2015). Combinatorial Matrix Theory and Majorization.
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). Permutation matrices, doubly stochastic matrices and their L– rays .
Dahl, Geir (2015). Majorization, (0,1)-matrices and Laplacian energy.
Dahl, Geir & Brualdi, R.A. (2014). Majorization for partially ordered sets.
Dahl, Geir (2014). Majorization and combinatorial matrix theory.
Dahl, Geir (2014). Traveling Salesman Problem: En matematisk rundtur.
Haufmann, Torkel Andreas & Dahl, Geir (2014). Optimization and classes of completely positive matrices.
Dahl, Geir (2013). Nytt Munch museum: et SKRIK etter kombinatorikk og geometri!!
Dahl, Geir (2013). An introduction to Majorization: theory and applications.
Dahl, Geir (2013). Majorization transforms and Ryser’s algorithm.
Brualdi, R.A. & Dahl, Geir (2012). An extension of the polytope of doubly stochastic matrices.
Dahl, Geir & Brualdi, R.A. (2012). Generalized Birkhoff polytopes and majorization.
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.
Dahl, Geir (2012). A taste of Szemerédi's combinatorics.
Dahl, Geir (2012). Google: hvordan man blir styrtrik på en matematisk likning!
Dahl, Geir (2012). Majorization, matrix polytopes and combinatorics.
Dahl, Geir (2012). Lineær algebra, Google og rangering av websider.
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). Majorization and network problems.
Dahl, Geir (2009). Disjoint congruence classes and an optimization problem.
Dahl, Geir (2009). Introduction to optimization and convexity.
Dahl, Geir (2008). Majorization in matrix theory: a brief introduction.
Dahl, Geir (2008). Minimum cuts: theory and algorithms.
Dahl, Geir (2008). Matematisk spillteori - analyse av Nash likevekt.
Dahl, Geir & Dahl, Kristina Rognlien (2012). Linear optimization and mathematical finance. University of Oslo. ISSN 0806-2439. Fulltekst i vitenarkiv

Se alle arbeider i Cristin

Publisert 24. okt. 2010 15:45 - Sist endret 8. mai 2020 09:50

Forskergrupper

Beregningsorientert Matematikk