• Real Analysis and Potential Theory
• PDE
• Fluid Mechanics and Mathematical Physics
• Sub-Riemannian and Sub-Lorentzian geometry

 

 

Vitenskapelig artikkel

• Langøen, René; Markina, Irina; Solynin, Alexander (2024). Stokes Graphs of the Rabi Problem with Real Parameters. (ekstern lenke)
• Jurdjevic, V.; Markina, Irina; Silva Leite, Leite (2023). Symmetric Spaces Rolling on Flat Spaces. (ekstern lenke)
• Schlarb, Markus; Hüper, Knut; Markina, Irina et al. (2023). Rolling Stiefel Manifolds Equipped with α-Metrics. (ekstern lenke)
• Franchi, Bruno; Markina, Irina (2023). Exceptional families of measures on Carnot groups. (ekstern lenke)
• Grong, Erlend; Markina, Irina (2023). Harmonic maps into sub-Riemannian Lie groups. (ekstern lenke)
• Furutani, Kenro; Markina, Irina (2021). Automorphism groups of pseudo H-type algebras. (ekstern lenke)
• Hüper, Knut; Markina, Irina; Leite, Fátima Silva (2021). A lagrangian approach to extremal curves on stiefel manifolds. (ekstern lenke)
• Hüper, Knut; Markina, Irina; Silva Leite, Fátima (2021). An extrinsic approach to sub-riemannian geodesics on the orthogonal group. (ekstern lenke)
• Godoy Molina, Mauricio; Markina, Irina (2021). Sub-riemannian geodesics on nested principal bundles. (ekstern lenke)
• Bauer, Wolfram; Froehly, André; Markina, Irina (2020). Fundamental solutions of a class of ultra-hyperbolic operators on pseudo H-type groups. (ekstern lenke)
• Jurdjevic, Velimir; Markina, Irina; Silva Leite, F (2019). Extremal Curves on Stiefel and Grassmann Manifolds. (ekstern lenke)
• Markina, Irina; Raffaelli, Matteo (2019). Flat approximations of hypersurfaces along curves. (ekstern lenke)
• Furutani, Kenro; Markina, Irina (2019). Complete classification of pseudo H-type algebras: II. (ekstern lenke)
• Godoy Molina, Mauricio; Grong, Erlend; Markina, Irina (2019). Submersions and curves of constant geodesic curvature. (ekstern lenke)
• Chang, Der-Chen; Markina, Irina; Wang, Wei (2019). The Laguerre calculus on the nilpotent Lie groups of step two. (ekstern lenke)
• Markina, Irina; Godoy Molina, Mauricio; Furutani, Kenro et al. (2018). Lie algebras attached to Clifford modules and simple graded Lie algebras. (ekstern lenke)
• Autenried, Christian; Furutani, Kenro; Markina, Irina et al. (2018). Pseudo-metric 2-step nilpotent Lie algebras. (ekstern lenke)
• Markina, Irina (2017). Sub-riemannian geometry and hypoelliptic operators. (ekstern lenke)
• Furutani, Kenro; Markina, Irina (2017). Complete classification of pseudo H-type Lie algebras: I. (ekstern lenke)
• Godoy Molina, Mauricio; Kruglikov, Boris; Markina, Irina et al. (2017). Rigidity of 2-step carnot groups. (ekstern lenke)
• Brakalova, Melkana A.; Markina, Irina; Vasil'ev, Alexander (2017). Extremal functions for modules of systems of measures. (ekstern lenke)
• Chang, Der-Chen; Markina, Irina; Wang, Wei (2016). On the Hodge-type decomposition and cohomology groups of k-Cauchy-Fueter complexes over domains in the quaternionic space. (ekstern lenke)
• Brakalova, Melkana A.; Markina, Irina; Vasiliev, Alexander (2016). Modules of systems of measures on polarizable Carnot groups. (ekstern lenke)
• Markina, Irina; Vasiliev, Alexander (2016). Evolution of smooth shapes and integrable systems. (ekstern lenke)
• Markina, Irina; Leite, Fátima Silva (2016). Introduction to the intrinsic rolling with indefinite metric. (ekstern lenke)
• Grong, Erlend; Markina, Irina; Vasiliev, Alexander (2015). Sub-Riemannian Geometry on Infinite-Dimensional Manifolds. (ekstern lenke)
• Chitour, Yacine; Godoy Molina, Mauricio; Kokkonen, Petri et al. (2015). Rolling against a sphere: the non-transitive case. (ekstern lenke)
• Furutani, Kenro; Markina, Irina; Vasiliev, Alexander (2015). Free nilpotent and H-type Lie algebras. Combinatorial and orthogonal designs. (ekstern lenke)
• Khajeh Salehani, Mahdi; Markina, Irina (2014). Controllability on Infinite-Dimensional Manifolds: A Chow-Rashevsky Theorem. (ekstern lenke)
• Autenried, Christian; Markina, Irina (2014). Sub-Riemannian geometry of Stiefel manifolds. (ekstern lenke)
• Furutani, Kenro; Markina, Irina (2014). Existence of lattices on general H-type groups. (ekstern lenke)
• Chang, Der-Chen; Markina, Irina; Wang, Wei (2013). On the Cauchy-Szegö kernel for quaternion siegel upper half-space. (ekstern lenke)
• Godoy Molina, Mauricio; Korolko, Anna; Markina, Irina (2013). Sub-semi-Riemannian geometry of general H-type groups. (ekstern lenke)
• Godoy Molina, Mauricio; Grong, Erlend; Markina, Irina et al. (2012). An intrinsic formulation of the problem on rolling manifolds. (ekstern lenke)
• Markina, Irina; Godoy Molina, Mauricio (2012). Sub-Riemannian geodesics and heat operator on odd dimensional spheres. (ekstern lenke)
• Chang, Der-chen; Markina, Irina; Vasiliev, Alexander (2011). Hopf fibration: Geodesics and distances. (ekstern lenke)
• Markina, Irina; Godoy Molina, Mauricio (2011). Sub-Riemannian geometry of parallelizable spheres. (ekstern lenke)
• Korolko, Anna; Markina, Irina (2011). SEMI-RIEMANNIAN GEOMETRY WITH NONHOLONOMIC CONSTRAINTS. (ekstern lenke)
• Chang, Der-chen; Markina, Irina; Vasiliev, Alexander (2010). Modified action and differential operators on the 3-D sub-Riemannian sphere. (ekstern lenke)
• Markina, Irina; Vasiliev, Alexander (2010). Virasoro algebra and dynamics in the space of univalent functions. (ekstern lenke)
• Korolko, Anna; Markina, Irina (2010). Geodesics on H-type Quaternion Groups with Sub-Lorentzian Metric and Their Physical Interpretation. (ekstern lenke)
• Chang, Der-Chen; Markina, Irina; Vasiliev, Alexander (2009). Sub-Riemannian geodesics on the 3-D sphere. (ekstern lenke)
• Calin, Ovidiu; Chang, Der-chen; Markina, Irina (2009). SubRiemannian Geometry on the Sphere S-3. (ekstern lenke)
• Calin, Ovidiu; Chang, Der-chen; Markina, Irina (2009). Geometric analysis on H-type groups related to division algebras. (ekstern lenke)
• Korolko, Anna; Markina, Irina (2009). Nonholonomic lorentzian geometry on some H-type groups. (ekstern lenke)
• Chang, Der-chen; Markina, Irina; Vasiliev, Alexander (2008). Sub-Lorentzian geometry on anti-de Sitter space. (ekstern lenke)
• Chang, Der-chen; Markina, Irina (2008). Quaternion H-type group and differential operator Delta(lambda). (ekstern lenke)
• Chang, Der-Chen; Markina, Irina (2008). Geometric analysis on quaternion anisotropic Carnot groups. (ekstern lenke)
• Markina, Irina; Prokhorov, Dmitri; Vasiliev, Alexander (2007). Sub-Riemannian geometry of the coefficients of univalent functions. (ekstern lenke)
• Hidalgo, Ruben; Markina, Irina; Vasiliev, Alexander (2007). Finite dimensional grading of the Virasoro algebra. (ekstern lenke)
• Chang, Der-chen; Markina, Irina (2007). Anisotropic quaternion carnot groups: Geometric analysis and green function. (ekstern lenke)
• Markina, Irina; Meneses, Rodrigo; Vasiliev, Alexander (2007). On a Saffman-Taylor problem in an infinite wedge. (ekstern lenke)
• Chang, Der-Chen; Markina, Irina (2006). Geometric analysis on quaternion H-type groups. (ekstern lenke)
• Markina, Irina; Vodopyanov, Sergey (2006). On value distribution for quasimeromorphic mappings on H-type Carnot groups. (ekstern lenke)

Vitenskapelig foredrag

• Langøen, René; Markina, Irina; Solynin, Alexander (2023). Stokes graphs of the Rabi problem with real parameters. (ekstern lenke)

Vitenskapelig antologi/Konferanseserie

• Hervik, Sigbjørn; Kruglikov, Boris; Markina, Irina et al. (2022). Geometry, Lie Theory and Applications: The Abel Symposium 2019. (ekstern lenke)

Forord

• Hervik, Sigbjørn; Kruglikov, Boris; Markina, Irina et al. (2022). Geometry, Lie Theory and Applications: The Abel Symposium 2019. (ekstern lenke)

Doktorgradsavhandling

• Frolova, Anastasia; Markina, Irina (2017). Analytical, combinatorial and topological properties of quadratic differentials and their applications. (ekstern lenke)
• Molina, Mauricio Godoy; Markina, Irina (2011). Sub-Riemannian geometry of spheres and rolling of manifolds. (ekstern lenke)

Vitenskapelig Kapittel/Artikkel/Konferanseartikkel

• Markina, Irina (2016). Geodesics in Geometry With Constraints and Applications. (ekstern lenke)
• Markina, Irina; Vasiliev, Alexander (2013). Löwner-Kufarev Evolution in the Segal-Wilson Grassmannian. (ekstern lenke)
• Grong, Erlend; Markina, Irina; Vasiliev, Alexander (2012). Sub-Riermannian structures corresponding to Kählerian metrics on the universal Teichmüller space and curve. (ekstern lenke)
• Molina, Mauricio Godoy; Grong, Erlend; Leite, Fátima Silva et al. (2011). Rolling manifolds : an intrinsic perspective. (ekstern lenke)
• Korolko, Anna; Markina, Irina (2011). Nonholonomic semi-Riemannian geometry with examples on H-type groups. (ekstern lenke)
• Calin, Ovidiu; Chang, Der-chen; Markina, Irina (2009). Generalized Hamilton-jacobi Equation and Heat kernel. (ekstern lenke)

Se en full oversikt over publikasjoner i Cristin

1. I.Markina: The change of variable that preserves the differential properties of Functions. Sibirsk. Mat. Zh. 31 (1990), no. 3, 73-84; translation in Siberian Math. J. 31 (1990), no. 3, 422-432.
2. I.Markina: The multiplier space M(Hpm->Hq1). Applications of functional analysis to problems of mathematical physics, 106-120; Akad Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1990.
3. I.Markina, S.K.Vodop'yanov: Exceptional sets for solutions of subelliptic equations. Sibirsk. Mat. Zh. 36 (1995), no. 4, 805-818; translation in Siberian Math. J. 36 (1995), no. 4, 694-706.
4. I.Markina, S.K.Vodop'yanov: Fundamentals of the nonlinear potential theory for subelliptic equations. Sobolev spaces and related problems of analysis, 100-160; Trudy Inst. Mat., 31, Izdat. Ross. Akad. Nauk Sib. Otd.Inst. Mat., Novosibirsk, 1996.
5. I.Markina: Classification of sub-Riemannian manifolds.- Algebra,geometry, analysis and mathematical physics (Novosibirsk, 1996), 176-178; Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 1997.
6. I.Markina, S.K.Vodop'yanov: Fundamentals of the nonlinear potential theory for subelliptic equations. I. Siberian Adv. Math. 7 (1997), no. 1, 32-62.
7. I.Markina, S.K.Vodop'yanov: Fundamentals of the nonlinear potential theory for subelliptic equations. II.- Siberian Adv. Math. 7 (1997), no. 2, 18-63.
8. I.Markina, S.K.Vodop'yanov: Foundations of the nonlinear potential theory of subelliptic equations. Dokl. Acad. Sci. Rus. 359 (1998), no. 2, 155-158.
9. I.Markina, S.K.Vodop'yanov: Classification of sub-Riemannian manifolds. Sibirsk. Mat. Zh. 39 (1998), no. 6, 1271-1289; translation in Siberian Math. J. 39 (1998), no. 6, 1096-1111.
10. I.Markina, S.K.Vodop'yanov: Local estimates of change of mappings with bounded s-distortion on the Carnot groups.- Proceedings of the 11-th Siberian school: Algebra, geometry, analysis and mathematical physics. (Novosibirsk, August 1-9, 1998) Novosibirsk. 1999, 28-53.
11. I.Markina: On the coincidence p-module of a family of curves and p-capacity of a condenser in the metric space with controlled geometry. Proceedings of the 11-th Siberian school: Algebra, geometry, analysis and mathematical physics. (Novosibirsk, August 1-9, 1998) Novosibirsk, 1999, 83 - 92.
12. I.Markina: On local homeomorphism of mappings with bounded distortion with the coefficient of distortion close to identity. Sci. Ser. A Math. Sci. (N.S.) 8 (2002), 21-42.
13. I.Markina: On coincidence of p-module of a family of curves and p-capacity on the Carnot group.- Rev. Mat. Iberoamericana 19 (2003), no. 1, 143-160.
14. I.Markina, A.Vasil'ev: On the geometry of Hele-Shaw flows with small surface tension. Interfaces Free Boundaries 5 (2003), no. 2, 183-192.
15. I.Markina: Extremal lengths for mappings with bounded s-distortion on Carnot groups. Bol. Soc. Mat. Mexicana (3) 9 (2003), no. 1, 89-108.
16. I.Markina: Hausdorff measure of the singular set of quasiregular maps on Carnot groups.  Int. J. Math. Math. Sci. 35 (2003), 2203-2220.
17. I.Markina: Extremal length for quasiregular mappings on Heisenberg groups. J.Math. Anal. Appl. 284 (2003), no. 2, 532-547.
18. I.Markina, A.Vasil'ev: Long-pin perturbations of the trivial solution for Hele-Shaw corner flows. Sci. Ser. A Math.  Sci. (N.S.) 9 (2003), 33-43.
19. I.Markina: Extremal widths on homogeneous groups. Complex Variables 48 (2003), no. 11, 947 - 960.
20. I.Markina: P-module of vector measures in domains with intrinsic metric on Carnot groups. Tohoku Math.  J. 54 (2004), no. 4, 553-569.
21. I.Markina, A.Vasil’ev: Explicit solutions for the Hele-Shaw corner flows. Euro. J. Appl. Math. 15, (2004), no. 6, 781-789.
22. I.Markina, S.Vodop´yanov: On value distribution for quasimeromorphic mappings on polarizable Carnot groups. Dokl. Acad. Sci. Rus.  403 (2005), no. 3, 300-304.
23. I.Markina: Module of vector measures on the Heisenberg group. Contemp. Math., 382 (2005), 291-304.
24. I.Markina: Singularities of quasiregular mappings on Carnot groups. Sc. Ser. A Math.  Sci. (N.S.) 11, (2005), 69-81.
25. I.Markina, D.Ch.Chang: Geometric analysis on quaternion $H$-type groups. J. Geom. Anal. 16, (2006), no. 2, 265-294.
26. I.Markina, S.Vodop´yanov: On value distribution for quasimeromorphic mappings on H-type Carnot groups. Bull. Sci. math. 130 (2006), 467-523.
27. I.Markina, R.Meneses, A.Vasil’ev: Generalizations of Kadanoff's solution of the Saffman-Taylor problem in a wedge. Appl. Anal. 86 (2007), no 2, 239-250.
28. I.Markina, V.D.Prokhorov, A.Vasil’ev: Sub-Riemannian geometry of the coefficients of univalent functions. J. Func. Anal. 245 (2007), 475-492.
29. I.Markina, R.Hidalgo, A.Vasil’ev: Finite dimensional grading on the Virasoro algebra. Georgian Mathematical Journal 14 (2007), no. 3, 419-434.
30. I.Markina, D.Ch.Chang: Anisotropic quaternion Carnot groups: geometric analysis and Green’s function. Adv. Appl. Math. 39 (2007), 345-394.
31. I.Markina, D.Ch.Chang: Geometric analysis on anisotropic quaternion Carnot groups. Dokl. Acad. Sci. Rus. 77 (2008), no. 1, 124-129.
32. I.Markina, D.Ch.Chang: Quaternion H-type group and differential operator ∆_l. Science in China Ser. A. Mathematics. 51 (2008), no. 4,  523-540.
33. I.Markina, D.Ch.Chang, A. Vasiliev. Sub-Lorentzian geometry on anti-de Sitter space.  J. Math. Pures Appl. (9) 90 (2008), no. 1,  82-110.
34. I.Markina, D.Ch.Chang, A.Vasiliev: Sub-Riemannian geodesics on 3-D sphere. Complex Anal. Oper. Theory. 3 (2) (2008), 361-377
35. I.Markina, D.Ch.Chang, O. Calin: Geometric analysis on H-type groups related to division algebras. Math. Nach.  282 (2009), no. 1, 44-68
36. I.Markina, D.Ch.Chang, O. Calin: Generalized Hamilton - Jacobi equation and heat kernel on  step two nilpotent Lie groups. Proceedings of the conference”Harmonic and complex analysis and its applications” Anal. Math. Phys. Trends in Math. (2009), 49-76
37. I.Markina, D.Ch.Chang, O. Calin: Sub-Riemannian geometry on the sphere S^3. Can. J. Math. 61 (4) 2009, 721-739

 

 

RESEARCH NETWORK “ANALYSIS and APPLICATIONS”

Irina Markina is the Principal coordinator of the NordForsk Research Network “Analysis and Applications”. The purpose of the network is to promote mobility and cooperation between analysts in the Nordic countries. About 2/3 of the funding is for workshops, seminars and similar events, the rest is for mobility scholarships. The network “Analysis and Applications” is open for researchers and students in analysis in the Nordic countries, Estonia and Northern-West Russia (St. Petersburg). Read more on the research network web-site.

 

GRANTS:

 

• 2008: Grant of NordForsk for Research Groups Network “Analysis and Applications”, Norway.
• 2007: Grant NFR – Bilat USA-Norway. (Norwegian Research Council) #180275/D15, Norway.
• 2005:  Grant FONDECYT # 7050181 –International cooperation, Chile.
• 2004:  Grant FONDECYT # 7040027 –International cooperation, Chile.
• 2004-2007: Grant FONDECYT # 1040333– Council for the Development of Science and Technology of Chile, Chile.
• 2003: Grant FONDECYT # 7030010 –International cooperation, Chile.
• 2002-2003: Grant FONDECYT # 1020067– Council for the Development in Science and Technology of Chile, Chile.
• 1996-1997: Grant of Russian Ministry of Superior Education for participation of young researchers in International Conferences, Novosibirsk State University, Novosibirsk, Russia.

 

 

Education:

Graduated from Novosibirsk State University in 1986

Degrees:

• M.Sci., June 3, 1986, in the Novosibirsk State University, Special studies in Advanced Mathematics. Thesis title: "Change-variable formula for functional spaces with fractional derivatives", 45 pp., supervisor Prof. S.K. Vodopyanov.
• Ph.D., November 15, 1995, in the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University (Candidate in Physics and Mathematics) Thesis title: "Nonlinear potential theory of subelliptic equations", 180 pp. supervisor Prof. S.K. Vodopyanov

 

Employment:

• 2008-present: Professor, University of Bergen, Norway.
• 2008: Associate Professor, University of Bergen, Norway.
• 2007-2008: Researcher, UNIFOB AS v/ Unifob petroleum (temporary position), University of Bergen, Bergen, Norway.
• 2006: Associate Professor (temporary position), University of Bergen, Bergen, Norway.
• 2005: Full Professor, University of Valparaiso, Valparaiso, Chile.
• 2001-2005: Visiting Professor, Department of Mathematics of Technical University Federico Santa Maria, Valparaiso, Chile.
• 2000: Research Fellow, The Mittag-Leffler Institute, Stockholm, Sweden.
• 1999-2000: Associate Professor, Department of Mathematics, Siberian State University of Telecommunication and Information, Novosibirsk, Russia.
• 1996-1999: Assistant Professor, Department of Mathematics, Novosibirsk State University, Russia.
• 1991-1996: Assistant Professor, College of Informatics, Novosibirsk State University, Russia.
• 1986-1991: Post-graduate course, Sobolev Institute of Mathematics, of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia.

 

Languages:

Russian, English, Spanish, Norwegian

 

Professional Membership:

• American Mathematical Society, since 2001
• Mathematical Society of Chile, 2001-2006

 

Other Professional Activities:

• 2009: Main organizer of the "Norwegian Fall School in Analysis for PhD Students and Young Researchers" Trondheim, September 10-13.
• 2008-2011: Principal coordinator of the NordForsk Research Network “Analysis and Application”
• 2003-2005: Responsible for the Department’s Mathematical Colloquium, Technical University Federico Santa Maria, Valparaiso, Chile.
• 1996-2000: Administrative assistant, Division of Mathematical Analysis, Department of Mathematics, Novosibirsk State University, Russia.
• 1992-1995: Administrative assistant at the College of Informatics, Novosibirsk State University, Russia.