Kristian Ranestad
Professor
-
Algebra, geometri og topologi

English version of this page
E-post
ranestad@math.uio.no
Telefon
+47 22855917
Mobiltelefon
+47 47811785
Rom
1111
Brukernavn
Besøksadresse
Niels Henrik Abels Hus
Blindern
0316 Oslo
Postadresse
Postboks 1053 Blindern
0316 Oslo
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)
Undervisning
Høst 2020 MAT4230
Publikasjoner
- Helsø, Martin & Ranestad, Kristian (2021). Rational Quartic Spectrahedra. Mathematica Scandinavica. ISSN 0025-5521. . doi: 10.7146/math.scand.a-121456
- Agostini, Daniele; Améndola, Carlos & Ranestad, Kristian (2020). Moment Identifiability of Homoscedastic Gaussian Mixtures. Foundations of Computational Mathematics. ISSN 1615-3375. . doi: 10.1007/s10208-020-09469-6 Fulltekst i vitenarkiv.
- Cifuentes, Diego; Ranestad, Kristian; Sturmfels, Bernd & Weinstein, Madeleine (2020). Voronoi cells of varieties. Journal of symbolic computation. ISSN 0747-7171. s 1- 16 . doi: 10.1016/j.jsc.2020.07.009
- Ranestad, Kristian & Sturmfels, Bernd (2020). Twenty-seven questions about the cubic surface. Le Mathematiche. ISSN 2037-5298. 75(2), s 411- 424 . doi: 10.4418/2020.75.2.1 Fulltekst i vitenarkiv.
- Iliev, Atanas; Kapustka, Grzegorz; Kapustka, Michal & Ranestad, Kristian (2019). EPW Cubes. Journal für die Reine und Angewandte Mathematik. ISSN 0075-4102. 2019(748), s 241- 268 . doi: 10.1515/crelle-2016-0044 Fulltekst i vitenarkiv.
- Kohn, Kathlén & Ranestad, Kristian (2019). Projective Geometry of Wachspress Coordinates. Foundations of Computational Mathematics. ISSN 1615-3375. 20, s 1135- 1173 . doi: 10.1007/s10208-019-09441-z Fulltekst i vitenarkiv.
- Amendola, Carlos; Ranestad, Kristian & Sturmfels, Bernd (2018). Algebraic Identifiability of Gaussian Mixtures. International mathematics research notices. ISSN 1073-7928. 2018(21), s 6556- 6580 . doi: 10.1093/imrn/rnx090 Fulltekst i vitenarkiv.
- Bernardi, Alessandra; Jelisiejew, Joachim; Marques, Pedro Macias & Ranestad, Kristian (2018). On polynomials with given Hilbert function and applications. Collectanea Mathematica. ISSN 0010-0757. 69(1), s 39- 64 . doi: 10.1007/s13348-016-0190-2 Fulltekst i vitenarkiv.
- Gallet, Matteo; Ranestad, Kristian & Villamizar, Nelly (2018). Varieties of apolar subschemes of toric surfaces. Arkiv för matematik. ISSN 0004-2080. 56(1), s 73- 99 . doi: 10.4310/ARKIV.2018.v56.n1.a6 Fulltekst i vitenarkiv.
- 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
- De Poi, Pietro; Faenzi, Daniele; Mezzetti, Emilia & Ranestad, Kristian (2017). Fano congruences of index 3 and alternating 3-forms. Annales de l'Institut Fourier. ISSN 0373-0956. 67(5), s 2099- 2165 . doi: 10.5802/aif.3131 Fulltekst i vitenarkiv.
- 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 & Voisin, Claire (2017). Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds. Documenta Mathematica. ISSN 1431-0635. 22, s 455- 504 Fulltekst i vitenarkiv.
- Ranestad, Kristian; Sturmfels, Bernd & Amendola, Carlos (2016). Algebraic Identifiability of Gaussian Mixtures. http://arxiv.org/archive/math. . doi: 10.1093/imrn/rnx090
- Ranestad, Kristian; Villamizar, Nelly & Gallet, Matteo (2016). Varieties of apolar subschemes of toric surfaces. arXiv.org. ISSN 2331-8422. . doi: 10.4310/arkiv.2018.v56.n1.a6
- 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 1431-0635. 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: 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
- Christophersen, Jan Arthur & Ranestad, Kristian (ed.) (2018). Geometry of Moduli. Abelsymposium 2017. Springer. ISBN 978-3-319-94880-5. 326 s.
- Ranestad, Kristian (ed.) (2008). The 1-2-3 of Modular Forms. Springer. ISBN 978-3-540-74117-6. 266 s.
- Ranestad, Kristian (2019). Bruker kurs og nye undervisningsformer.
- Ranestad, Kristian (2019). Brukerkurs og nye undervisningsformer.
- Ranestad, Kristian (2019). Divisors in the moduli space of cubic fourfolds.
- Ranestad, Kristian (2019). Projective geometry of Wachspress coordinates.
- Ranestad, Kristian (2019). Projective geometry of Wachspress coordinates.
- Ranestad, Kristian (2018). Apolarity and powersum varieties, old and new results.
- Ranestad, Kristian (2018). Apolarity and powersum varieties, old and new results.
- Ranestad, Kristian (2018). Symmetric and skew symmetric degeneracy loci and constructions of hyperkähler manifolds..
- Dahl, Geir; Ranestad, Kristian & Hole, Arne (2017). Programmering rammer dybdelæring i matematikk. Aftenposten (morgenutg. : trykt utg.). ISSN 0804-3116. s 22- 23
- 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
Publisert 24. okt. 2010 15:06
- Sist endret 13. aug. 2020 10:49