Kristian Ranestad

• Ranestad, Kristian; Kapustka, Grzegorz; Kapustka, Michal ; Stillman, Michael; Schenck, Henry & Yuan, Beihui (2021). Quaternary quartic forms and Gorenstein rings. http://arxiv.org/archive/math.
• Piene, Ragni; Kohn, Kathlén; Ranestad, Kristian; Rydell, Felix; Shapiro, Boris & Sinn, Rainer [Vis alle 8 forfattere av denne artikkelen] (2021). Adjoints and canonical forms of polypols. arXiv.org. ISSN 2331-8422. Vis sammendrag

  Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an algebro-geometric perspective. We relate planar polypols to positive geometries introduced originally in particle physics, and identify the adjoint curve of a planar polypol with the numerator of the canonical differential form associated with the positive geometry. We settle several cases of a conjecture by Wachspress claiming that the adjoint curve of a regular planar polypol does not intersect its interior. In particular, we provide a complete characterization of the real topology of the adjoint curve for arbitrary convex polygons. Finally, we determine all types of planar polypols such that the rational map sending a polypol to its adjoint is finite, and explore connections of our topic with algebraic statistics

• Helsø, Martin & Ranestad, Kristian (2021). Rational Quartic Spectrahedra. Mathematica Scandinavica. ISSN 0025-5521. doi: 10.7146/math.scand.a-121456. 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. Fulltekst i vitenarkiv
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Ciliberto, Ciro; Cueto, Maria Angelica; Mella, Massimiliano; Ranestad, Kristian & Zwiernik, Piotr (2017). Cremona Linearizations of Some Classical Varieties. I Casnati, Gianfranco; Conte, Alberto; Gatto, Letterio; Giacardi, Livia; Marchisio, Marina & Verra, Alessandro (Red.), From Classical to Modern Algebraic Geometry: Corrado Segre's Mastership and Legacy. Birkhäuser Verlag. ISSN 978-3-319-32992-5. s. 375–408. doi: 10.1007/978-3-319-32994-9_9.
• 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
• 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
• 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. I Lasserre, Jean-Bernard & Anjos, Miguel (Red.), Handbook on Semidefinite, Conic and Polynomial Optimization. Springer. ISSN 978-1461407683. s. 61–76. doi: 10.1007/978-1-4614-0769-0_3.
• Ranestad, Kristian & Sturmfels, Bernd (2011). The Convex Hull of a Variety. I Branden, Petter; Passare, Mikael & Putinar, Mihai (Red.), Notions of Positivity and the Geometry of Polynomials. Springer. ISSN 978-3-0348-0141-6. s. 331–344. doi: 10.1007/978-3-0348-0142-3_18.
• 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.
• Hansen, Johan P.; Johnsen, Trygve & Ranestad, Kristian (2010). Grassmann codes and Schubert unions. I Rodier, Francois & Vladut, Sergei (Red.), Arithmetic, Geometry and Coding Theory (ACCT 2005). Soc. Math. France Paris. ISSN 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.
• 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.
• 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.

Se alle arbeider i Cristin

• Christophersen, Jan Arthur & Ranestad, Kristian (2018). Geometry of Moduli. Abelsymposium 2017. Springer. ISBN 978-3-319-94880-5. 326 s.
• Ranestad, Kristian (2008). The 1-2-3 of Modular Forms. Springer. ISBN 978-3-540-74117-6. 266 s.

Se alle arbeider i Cristin

• Ranestad, Kristian (2022). Betti tables and power sum varieties of quaternary quartics.
• Ranestad, Kristian (2021). Power sum varieties of quaternary quartics.
• 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 (2019). Brukerkurs og nye undervisningsformer.
• Ranestad, Kristian (2019). Bruker kurs og nye undervisningsformer.
• 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.
• Ranestad, Kristian (2018). Apolarity and powersum varieties, old and new results.
• 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). Symmetric and skew symmetric degeneracy loci and constructions of hyperkähler manifolds.
• 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 (2016). Rational Quartic Spectrahedra.
• Ranestad, Kristian (2016). Geometri og algebra-arven etter Euklid og Descartes.
• 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 (2016). Kummer surfaces and hyperkähler fourfolds, as degeneracy loci.
• 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). Cactus varieties of homogeneous forms.
• Ranestad, Kristian (2015). Algebra og Geometri-arven etter Euclid og Descartes.
• Ranestad, Kristian (2015). Varieties of sums of powers of bihomogeneous 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 (2014). Quartic Spectrahedra.
• Ranestad, Kristian (2014). Cactus varieties of cubic forms.
• Ranestad, Kristian (2014). Apolarity and decomposition of homogeneous forms.
• Ranestad, Kristian (2014). Apolarity and decompositions of homogeneous forms.
• Ranestad, Kristian (2014). Varieties of sums of powers of cubic fourfolds.
• Ranestad, Kristian (2014). Quartic Spectrahedra.
• Ranestad, Kristian (2013). Symmetric Tensor Decompositions.
• 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 (2013). On the rank and decompositions of symmetric tensors.
• Ranestad, Kristian (2013). Symmetric tensors, rank versus cactus rank.
• Ranestad, Kristian (2013). Symmetric tensors, rank versus cactus rank.
• Ranestad, Kristian (2013). On the rank and decompositions of symmetric tensors.
• Ranestad, Kristian (2012). Om å lese i matematikk.
• Ranestad, Kristian (2012). Decompositions of symmetric tensors.
• Ranestad, Kristian (2012). The variety of polar simplices and beyond.
• Ranestad, Kristian (2012). The variety of polar simplices and beyond.
• Ranestad, Kristian (2011). Symmetric tensor decompositions.
• Ranestad, Kristian (2011). Algebraic boundaries of Hilbert's SOS cones.
• Ranestad, Kristian (2011). Polare trekanter.
• Ranestad, Kristian (2010). The convex hull of a variety.
• Ranestad, Kristian (2010). The convex hull of a variety.
• 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). Bevis i geometri.
• Stedøy-Johansen, Ingvill; Maugesten, Marianne; Dalvang, Tone; Pedersen, Vivi & Ranestad, Kristian (2009). Veiledning til Kunnskapsløftet, matematikk. Vis sammendrag

  Nettsiden er en veiledning til den gjennomgående delen av matematikkfaget. Viktige elementer er vurdering, tilpasset opplæring, grunnleggende ferdigheter og oppdeling av kompetansemålene i læringsmål på trinn.

• 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.
• Ranestad, Kristian & Johansen, Nils Voje (2008). Matematikklærerkompetanse i skolen. Lektorbladet. ISSN 1503-027X. s. 17–18.
• Ranestad, Kristian (2008). Torisk polare Cremonatransformasjoner.
• Borge, Inger Christin; Sanne, Anders; Nortvedt, Guri A.; Meistad, Jens Arne; Skrindo, Knut & Ranestad, Kristian [Vis alle 9 forfattere av denne artikkelen] (2014). Matematikk i norsk skole anno 2014. Utdanningsdirektoratet.
• Moe, Torgunn Karoline; Piene, Ragni & Ranestad, Kristian (2013). Cuspidal curves on Hirzebruch surfaces. Akademika forlag.
• Ranestad, Kristian; Graf von Bothmer, Hans Christian & Sottile, Frank (2008). Linear precision for toric surface patches. arxiv.org.
• Ranestad, Kristian & Nie, Jiawang (2008). Algebraic Degree of Polynomial Optimization. arxiv.org.

Se alle arbeider i Cristin