Kristian Ranestad

Bilde av Kristian Ranestad
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Telefon +47-22855917
Mobiltelefon +47-47811785
Rom 615
Brukernavn
Besøksadresse Ullevål stadion Sognsveien 77 B 0855 OSLO
Postadresse Postboks 1053 Blindern 0316 OSLO
Andre tilknytninger Matematisk institutt

Faglige interesser/Research interests

  • Projective algebraic geometry (surfaces in 4-space, varieties of small codimension, homogeneous varieties, hyperkaehler varieties, abelian varieties)
  • Applications of algebraic geometry (elliptic curve cryptography, phylogeny and algebraic statistical models, semidefinite programming)

ArXiv papers

Undervisning

Høst 2017: MAT 2500

Vår 2018: MAT 2100

 

 

 

 

Emneord: Matematikk, Algebra og algebraisk geometri

Publikasjoner

  • Ciliberto, Ciro; Cueto, Maria Angelica; Mella, Massimiliano; Ranestad, Kristian & Zwiernik, Piotr (2017). Cremona Linearizations of Some Classical Varieties, In Gianfranco Casnati; Alberto Conte; Letterio Gatto; Livia Giacardi; Marina Marchisio & Alessandro Verra (ed.),  From Classical to Modern Algebraic Geometry: Corrado Segre's Mastership and Legacy.  Birkhäuser Verlag.  ISBN 978-3-319-32992-5.  Kapittel.  s 375 - 408
  • Iliev, Atanas; Kapustka, Grzegorz; Kapustka, Michal & Ranestad, Kristian (2017). Hyper-Kähler fourfolds and Kummer surfaces. Proceedings of the London Mathematical Society.  ISSN 0024-6115.  115(6), s 1276- 1316 . doi: 10.1112/plms.12063 Fulltekst i vitenarkiv.
  • Ranestad, Kristian; Bernardi, Alessandra; Jelisiejew, Joachim & Marques, Pedro Macias (2017). On polynomials with given Hilbert function and applications. Collectanea Mathematica.  ISSN 0010-0757. . doi: 10.1007/s13348-016-0190-2 Fulltekst i vitenarkiv.
  • Ranestad, Kristian; Mezzetti, Emilia; De Poi, Pietro & Faenzi, Daniele (2017). Fano congruences of index 3 and alternating 3-forms. Annales de l'Institut Fourier.  ISSN 0373-0956.  67(5), s 2099- 2165
  • Ranestad, Kristian; Sturmfels, Bernd & Amendola, Carlos (2017). Algebraic Identifiability of Gaussian Mixtures. International mathematics research notices.  ISSN 1073-7928. . doi: /10.1093/imrn/rnx090 Fulltekst i vitenarkiv.
  • Ranestad, Kristian & Voisin, Claire (2017). Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds. Documenta Mathematica.  ISSN 1431-0643.  22, s 455- 504 Fulltekst i vitenarkiv.
  • Iliev, Atanas; Kapustka, Grzegorz; Kapustka, Michal & Ranestad, Kristian (2016). EPW Cubes. Journal für die Reine und Angewandte Mathematik.  ISSN 0075-4102. . doi: 10.1515/crelle-2016-0044 Fulltekst i vitenarkiv.
  • Ranestad, Kristian; Sturmfels, Bernd & Amendola, Carlos (2016). Algebraic Identifiability of Gaussian Mixtures. http://arxiv.org/archive/math.
  • Ranestad, Kristian; Villamizar, Nelly & Gallet, Matteo (2016). Varieties of apolar subschemes of toric surfaces. arXiv.org.  ISSN 2331-8422.
  • Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd & Vinzant, Cynthia (2015). Quartic spectrahedra. Mathematical programming.  ISSN 0025-5610.  151(2), s 585- 612 . doi: 10.1007/s10107-014-0844-3 Fulltekst i vitenarkiv.
  • Bernardi, Alessandra & Ranestad, Kristian (2013). On the cactus rank of cubic forms. Journal of symbolic computation.  ISSN 0747-7171.  50, s 291- 297 . doi: 10.1016/j.jsc.2012.08.001
  • Ranestad, Kristian & Kapustka, Michal (2013). Vector bundles on Fano varieties of genus ten. Mathematische Annalen.  ISSN 0025-5831.  356(2), s 439- 467 . doi: 10.1007/s00208-012-0856-3
  • Ranestad, Kristian & Schreyer, Frank-Olaf (2013). The Variety of Polar Simplices. Documenta Mathematica.  ISSN 1431-0643.  18, s 469- 505
  • Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian & Sturmfels, Bernd (2012). Algebraic boundaries of Hilbert's SOS cones. Compositio Mathematica.  ISSN 0010-437X.  148(6), s 1717- 1735 . doi: 10.1112/S0010437X12000437 Fulltekst i vitenarkiv.
  • Ranestad, Kristian & Bernardi, Alessandra (2012). On the cactus rank of cubic forms. Journal of symbolic computation.  ISSN 0747-7171. . doi: doi.org/10.1016/j.jsc.2012.08.001
  • Ranestad, Kristian & Sturmfels, Bernd (2012). On the convex hull of a space curve. Advances in Geometry.  ISSN 1615-715X.  12(1), s 157- 178 . doi: 10.1515/ADVGEOM.2011.021
  • Ranestad, Kristian (2011). Algebraic Degree in Semidefinite and Polynomial Optimization, In Jean-Bernard Lasserre & Miguel Anjos (ed.),  Handbook on Semidefinite, Conic and Polynomial Optimization.  Springer.  ISBN 978-1461407683.  Kap. 3.  s 61 - 76
  • Ranestad, Kristian & Schreyer, Frank-Olaf (2011). On the rank of a symmetric form. Journal of Algebra.  ISSN 0021-8693.  346(1), s 340- 342 . doi: 10.1016/j.jalgebra.2011.07.032
  • Ranestad, Kristian & Sturmfels, Bernd (2011). The Convex Hull of a Variety, In Petter Branden; Mikael Passare & Mihai Putinar (ed.),  Notions of Positivity and the Geometry of Polynomials.  Springer.  ISBN 978-3-0348-0141-6.  artikkel.  s 331 - 344
  • Giuffrida, Salvatore & Ranestad, Kristian (2010). A geometric characterization of Hankel r-planes. Bulletin of the London Mathematical Society.  ISSN 0024-6093.  42, s 912- 916 . doi: 10.1112/blms/bdq047
  • Hansen, Johan P.; Johnsen, Trygve & Ranestad, Kristian (2010). Grassmann codes and Schubert unions, In Francois Rodier & Sergei Vladut (ed.),  Arithmetic, Geometry and Coding Theory (ACCT 2005).  Soc. Math. France Paris.  ISBN 978-2-85629-279-2.  -.  s 103 - 123
  • Nie, Jiawang; Ranestad, Kristian & Sturmfels, Bernd (2010). The algebraic degree of semidefinite programming. Mathematical programming.  ISSN 0025-5610.  122(2), s 379- 405 . doi: 10.1007/s10107-008-0253-6
  • von Bothmer, H.-C. Graf; Ranestad, Kristian & Sottile, Frank (2010). Linear Precision for Toric Surface Patches. Foundations of Computational Mathematics.  ISSN 1615-3375.  10(1), s 37- 66 . doi: 10.1007/s10208-009-9052-6
  • Graf von Bothmer, Hans-Christian & Ranestad, Kristian (2009). A general formula for the algebraic degree in semidefinite programming. Bulletin of the London Mathematical Society.  ISSN 0024-6093.  41(2), s 193- 197 . doi: 10.1112/blms/bdn114
  • Graf von Bothmer, Hans-Christian & Ranestad, Kristian (2009). Classification of rational surfaces of degree 11 and sectional genus 11 in P4. Mathematica Scandinavica.  ISSN 0025-5521.  104(1), s 60- 94
  • Nie, Jiawang & Ranestad, Kristian (2009). ALGEBRAIC DEGREE OF POLYNOMIAL OPTIMIZATION. SIAM Journal on Optimization.  ISSN 1052-6234.  20(1), s 485- 502 . doi: 10.1137/080716670
  • Hansen, Johan Peder; Johnsen, Trygve & Ranestad, Kristian (2007). Schubert unions in Grassmann varieties. Finite Fields and Their Applications.  ISSN 1071-5797.  13(4), s 738- 750 . doi: 10.1016/j.ffa.2007.06.003
  • Ranestad, Kristian & Iliev, Atanas (2007). Addendum to “K3-Surfaces of Genus 8 and Varieties of Sums of Powers of Cubic Fourfolds”. Comptes Rendus de l'Academie Bulgare des Sciences / Proceedings of the Bulgarian Academy of Sciences.  ISSN 1310-1331.  60(12), s 1265- 1270
  • Ranestad, Kristian & Iliev, Atanas (2007). The Abelian Fibration on the Hilbert Cube of a K3 Surface of Genus 9. International Journal of Mathematics.  ISSN 0129-167X.  18(1), s 1- 26
  • Goodman, Jacob E.; Holmsen, Andreas; Pollack, Richard; Ranestad, Kristian & Sottile, Frank (2006). Cremona convexity, frame convexity and a theorem of Santalo. Advances in Geometry.  ISSN 1615-715X.  6(2), s 301- 321 . doi: 10.1515/ADVGEOM.2006.018

Se alle arbeider i Cristin

  • Ranestad, Kristian (ed.) (2008). The 1-2-3 of Modular Forms. Springer.  ISBN 978-3-540-74117-6.  266 s.

Se alle arbeider i Cristin

  • Ranestad, Kristian (2017). Apolarity, powersum varieties and divisors in the moduli space of cubic fourfolds.
  • Ranestad, Kristian (2017). Divisors in the moduli space of cubic fourfolds.
  • Ranestad, Kristian (2017). Symmetric and Lagrangian degeneracy loci, Kummer surfaces and Hyperkähler fourfolds..
  • Ranestad, Kristian (2017). Symmetric and skew symmetric degeneracy loci and constructions of hyperkähler manifolds.
  • Ranestad, Kristian (2016). Geometri og algebra-arven etter Euklid og Descartes.
  • Ranestad, Kristian (2016). Kummer surfaces and hyperkähler fourfolds, as degeneracy loci..
  • Ranestad, Kristian (2016). Rational Quartic Spectrahedra.
  • Ranestad, Kristian (2016). Symmetric and Lagrangian degeneracy loci, Kummer surfaces and Hyperkähler fourfolds.
  • Ranestad, Kristian (2016). Tensor decompositions and cubic sections of rational surface scrolls.
  • Ranestad, Kristian (2015). Algebra og Geometri-arven etter Euclid og Descartes.
  • Ranestad, Kristian (2015). Cactus varieties of homogeneous forms.
  • Ranestad, Kristian (2015). From powersum varieties to cactus varieties; old and new results.
  • Ranestad, Kristian (2015). On the powersums presenting a general cubic form in 6 variables..
  • Ranestad, Kristian (2015). Quartic Spectrahedra.
  • Ranestad, Kristian (2015). The Waring problem for homogeneous and bihomogeneous forms in few variables, old and new results..
  • Ranestad, Kristian (2015). Varieties of sums of powers of bihomogeneous forms.
  • Borge, Inger Christin; Sanne, Anders; Nortvedt, Guri A.; Meistad, Jens Arne; Skrindo, Knut; Ranestad, Kristian; Maugesten, Marianne; Lindstrøm, Tom & Kristensen, Tor Espen (2014). Matematikk i norsk skole anno 2014.
  • Ranestad, Kristian (2014). Apolarity and decomposition of homogeneous forms.
  • Ranestad, Kristian (2014). Apolarity and decompositions of homogeneous forms.
  • Ranestad, Kristian (2014). Cactus varieties of cubic forms.
  • Ranestad, Kristian (2014). Quartic Spectrahedra.
  • Ranestad, Kristian (2014). Quartic Spectrahedra.
  • Ranestad, Kristian (2014). Varieties of sums of powers of cubic fourfolds.
  • Moe, Torgunn Karoline; Piene, Ragni & Ranestad, Kristian (2013). Cuspidal curves on Hirzebruch surfaces.
  • Ranestad, Kristian (2013). On the rank and decompositions of symmetric tensors.
  • Ranestad, Kristian (2013). On the rank and decompositions of symmetric tensors.
  • Ranestad, Kristian (2013). Symmetric Tensor Decompositions.
  • Ranestad, Kristian (2013). Symmetric tensors, rank versus cactus rank.
  • Ranestad, Kristian (2013). Symmetric tensors, rank versus cactus rank.
  • Ranestad, Kristian (2013). Varieties of sums of powers of a cubic 4-folds.
  • Ranestad, Kristian (2013). Varieties of sums of powers of cubic 4-folds.
  • Ranestad, Kristian (2012). Decompositions of symmetric tensors.
  • Ranestad, Kristian (2012). Om å lese i matematikk.
  • Ranestad, Kristian (2012). The variety of polar simplices and beyond.
  • Ranestad, Kristian (2012). The variety of polar simplices and beyond.
  • Ranestad, Kristian (2011). Algebraic boundaries of Hilbert's SOS cones.
  • Ranestad, Kristian (2011). Polare trekanter.
  • Ranestad, Kristian (2011). Symmetric tensor decompositions.
  • Ranestad, Kristian (2010). Bevis i geometri.
  • Ranestad, Kristian (2010). Fano fourfolds of genus ten as linear sections of G(2,7) and G(3,6).
  • Ranestad, Kristian (2010). The convex hull of a space curve.
  • Ranestad, Kristian (2010). The convex hull of a space curve.
  • Ranestad, Kristian (2010). The convex hull of a space curve.
  • Ranestad, Kristian (2010). The convex hull of a variety.
  • Ranestad, Kristian (2010). The convex hull of a variety.
  • Ranestad, Kristian (2009). Smooth rational surfaces in P^4.
  • Ranestad, Kristian (2009). The abelian fibration on the Hilbert cube of a K3 surface of genus 9.
  • Ranestad, Kristian (2009). Veiledning til læreplanen i matematikk.
  • Stedøy-Johansen, Ingvill; Maugesten, Marianne; Dalvang, Tone; Pedersen, Vivi & Ranestad, Kristian (2009). Veiledning til Kunnskapsløftet, matematikk. Vis sammendrag
  • Ranestad, Kristian (2008). Bevis i plangeometri.
  • Ranestad, Kristian (2008). Multisecants of surfaces in projective fourspace.
  • Ranestad, Kristian (2008). Symmetri.
  • Ranestad, Kristian (2008). Toric Polar Cremona Transformations.
  • Ranestad, Kristian (2008). Toric polar Cremona transformations.
  • Ranestad, Kristian (2008). Torisk polare Cremonatransformasjoner.
  • Ranestad, Kristian; Graf von Bothmer, Hans Christian & Sottile, Frank (2008). Linear precision for toric surface patches.
  • Ranestad, Kristian & Johansen, Nils Voje (2008). Matematikklærerkompetanse i skolen. Lektorbladet.  ISSN 1503-027X.  s 17- 18
  • Ranestad, Kristian & Nie, Jiawang (2008). Algebraic Degree of Polynomial Optimization.
  • Ranestad, Kristian (2007). A class formula for varieties of symmetric matrices.
  • Ranestad, Kristian (2007). Algebra, geometri og phylogeni.
  • Ranestad, Kristian (2007). Ceva's teorem og bevis i geometri.
  • Ranestad, Kristian (2007). Cremonatransformasjoner.
  • Ranestad, Kristian (2007). Den algebraiske graden til semidefinit programmering.
  • Ranestad, Kristian (2007). Nye læreplaner for programfag i matematikk i videregående skole.
  • Ranestad, Kristian (2007, 01. mars). Superstreng 64. [Radio].  Radio 24.
  • Ranestad, Kristian (2007). Tall og koder.
  • Ranestad, Kristian (2007). The algebraic degree in semidefinite programming.
  • Ranestad, Kristian (2007). The algebraic degree in semidefinite programming and varieties of symmetric matrices.
  • Ranestad, Kristian (2006). Abelian Fibrations on Hilbertschemes of K3-Surfaces.

Se alle arbeider i Cristin

Publisert 24. okt. 2010 15:06 - Sist endret 5. des. 2017 10:25