prof. dr. Franc Forstnerič
University of Ljubljana,
Faculty of Mathematics and Physics Institute of Mathematics, Physics and Mechanics, Ljubljana office: 424, Jadranska 21 phone: +386 (0)1 4766 556 e-mail: franc.forstneric at fmf.uni-lj.si Member of Slovenian Academy of Sciences and Arts |
CV Publications MathSciNet Zentralblatt arXiv CRIS
Editorial board
Seminar for Complex Analysis, 1975-
Together with Josip Globevnik we are coordinating the Seminar for Complex Analysis at the Department of Mathematics, University of Ljubljana and Institute of Mathematics, Physics and Mechanics. During the academic year the seminar meets on Tuesdays at 12:30. It covers primarily topics in complex analysis, geometry, harmonic analysis, and partial differential equations. Here is a list of upcoming talks:
- 28. 03. 2017: Gian Maria Dall'Ara, University of Vienna
- 04. 04. 2017: Rafael Andrist, University of Wuppertal
- 25. 04. 2017: Adam Osękowski, University of Warszaw
- 09. 05. 2017: Polona Durcik, University of Bonn
- 11. 05. 2017: Laszlo Lempert, Purdue University (Colloquium lecture)
- 16. 05. 2017: Joris Roos, University of Bonn
Research interests
My research interests lie primarily in complex analysis, analytic geometry, Riemann surfaces, global analysis and related areas of Mathematics. I have introduced in the literature the class of Oka Manifolds, named after Kiyoshi Oka, one of the pioneers of complex analysis in several variables; see the introductory note by Finnur Lárusson, What is...an Oka manifold? The class of Oka manifolds is in a precise homotopy-theoretic sense dual to the class of Stein manifolds and is opposite to the class of hyperbolic manifolds. Oka theory is the main subject of my monograph Stein Manifolds and Holomorphic Mappings (Springer 2011). In collaboration with Antonio Alarcón, Barbara Drinovec Drnovšek and Francisco J. López we developed new applications of Oka theory to the classical theory of conformal minimal surface in R^{n}.
Research grants
I am coordinating the 6-year research program Analysis and Geometry (2015-20) and the 3-year grant J1-7256 (2016-18) financed by ARRS, Republic of Slovenia. The research activities of members of project teams cover a wide array of topics in complex analysis and geometry, global analysis, the theory of minimal surfaces, harmonic analysis, partial differential equation, integrable systems, numerical analysis, and algebra.
CAS Fellow
During 2016-17, I am a Fellow of Centre for Advanced Study in Oslo, Norway, where I am participating in the research program Several Complex Variables and Complex Dynamics.
E-SCV Consortium and TSIMF
Together with John Erik Fornæss from the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway, I am coordinating activities of the European Several Complex Variables Consortium, E-SCV. The Consortium seeks to foster the development of Several Complex Variables (SCV) and related areas of Mathematics among its European member groups, to stimulate bilateral exchanges with the SCV groups in Greater China, and to promote organization of joint international conferences and PhD schools by member groups. I am a member of the Steering Committee of the Tsingua Sanya International Mathematics Forum (director Prof. Shing-Tung Yau), a conference center associated to the Tsinghua University and located in Sanya, Hainan, China.
Book
- Stein Manifolds and Holomorphic Mappings. The homotopy principle in complex analysis. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 56. Springer, Heidelberg, 2011. MR2975791
Preprints
- Proper holomorphic immersions into Stein manifolds with the density property. Preprint (2017). arXiv
- Complete densely embedded complex lines in C^{2} (with A. Alarcón). arXiv
- Darboux charts around holomorphic Legendrian curves and applications (with A. Alarcón). arXiv
- The Oka principle for holomorphic Legendrian curves in C^{2n+1} (with F. Lárusson). Math. Z., in press. arXiv
- Surjective holomorphic maps onto Oka manifolds. Proceedings of the INdAM Meeting Complex and Symplectic Geometry (Cortona, 2016). Springer INdAM Series, in press. arXiv
- Hyperbolic complex contact structures on C^{2n+1}. J. Geom. Anal., in press. arXiv
- Holomorphic Legendrian curves (with A. Alarcón and F. J. López). arXiv
- Every meromorphic function is the Gauss map of a conformal minimal surface (with A. Alarcón and F.J. López). arXiv
- New complex analytic methods in the study of non-orientable minimal surfaces in R^{n} (with A. Alarcón and F.J. López). arXiv
- The parametric h-principle for minimal surfaces in R^{n} and null curves in C^{n} (with F. Lárusson). Comm. Anal. Geom., in press. arXiv
- Minimal surfaces in minimally convex domains (with A. Alarcón, B. Drinovec Drnovšek, and F. J. López). arXiv
- Every conformal minimal surface in R^{3} is isotopic to the real part of a holomorphic null curve (with A. Alarcón). J. reine angew. Math. (Crelle's J.), in press. arXiv
Publications 2012-2017
- A long C^{2} without holomorphic functions (with L. Boc Thaler). Analysis & PDE 9 (2016) 2031-2050. MR3599525 arXiv
- Proper holomorphic embeddings into Stein manifolds with the density property (with R. Andrist, T. Ritter, and E. F. Wold). J. Anal. Math. 130 (2016) 135-150. MR3574650 arXiv
- Noncritical holomorphic functions on Stein spaces. J. Eur. Math. Soc. (JEMS) 18 (2016) 2511-2543. MR3562350 arXiv
- Embedded minimal surfaces in R^{n} (with A. Alarcón and F. J. López). Math. Z. 283(1) (2016) 1-24 MR3489056 arXiv
- On the Hodge conjecture for q-complete manifolds (with J. Smrekar and A. Sukhov). Geom. & Topol. 20(1) (2016), 353-388. MR3470716 arXiv
- Minimal hulls of compact sets in R^{3} (with B. Drinovec Drnovšek). Trans. Amer. Math. Soc. 368(10) (2016) 7477-7506. MR3471098 arXiv
- The Calabi-Yau problem, null curves, and Bryant surfaces (with A. Alarcón). Math. Ann. 363 (2015) 913-951. MR3412347 arXiv
- Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves (with A. Alarcón, B. Drinovec Drnovšek, and F. J. López). Proc. London Math. Soc. (3) 111(4) (2015) 851-886. MR3407187 arXiv
- Fatou-Bieberbach domains in ℂ^{n}\R^{k} (with E. F. Wold). Ark. Mat. 53(2) (2015) 259-270. MR3391171 arXiv
- A complex surface admitting a strongly plurisubharmonic function but no holomorphic functions. J. Geom. Anal. 25(1) (2015) 329-335. MR3299284 arXiv
- Oka properties of groups of holomorphic and algebraic automorphisms of complex affine space (with F. Lárusson). Math. Res. Lett. 21(5) (2014) 1047-1067. MR3294562 arXiv
- Holomorphic flexibility properties of compact complex surfaces (with F. Lárusson). Int. Math. Res. Not. IMRN 13 (2014) 3714-3734. MR3229766 arXiv
- Oka properties of ball complements (with T. Ritter). Math. Z. 277(1) (2014) 325-338. MR3205776 arXiv Notice: the published version essentially coincides with v5 posted on the arXiv. The proofs of Theorem 1, Corollary 2 and Theorem 15 given in the paper are incomplete in the special case when the set L is polynomially convex and the real dimension of X equals n. However, these results are correct as stated, and the proofs can be completed by applying Lemma 3.1 in the preprint Proper holomorphic immersions into Stein manifolds with the density property (March 2017).
- Null curves and directed immersions of open Riemann surfaces (with A. Alarcón). Inventiones Math. 196(3) (2014) 733-771. MR3211044 arXiv
- Every bordered Riemann surface is a complete proper curve in a ball (with A. Alarcón). Math. Ann. 357(3) (2013) 1049-1070. MR3118624 arXiv
- Gunning-Narasimhan's theorem with a growth condition (with T. Ohsawa). J. Geom. Anal. 23(3) (2013) 1078-1084. 3078344 MR3078344 arXiv
- Embeddings of infinitely connected planar domains into ℂ^{2} (with E. F. Wold). Analysis & PDE 6(2) (2013) 499-514. MR3071396 arXiv
- Characterizations of projective hulls by analytic discs (with B. Drinovec Drnovšek). Illinois J. Math. 56(1) (2012) 53-65 (2013). MR3117017 arXiv
- The Poletsky-Rosay theorem on singular complex spaces (with B. Drinovec Drnovšek). Indiana Univ. Math. J. 61 (2012) 1707-1423. MR3085613 arXiv
- Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties (with B. Drinovec Drnovšek). Ann. Polon. Math. 106 (2012) 171-191. MR2995450 arXiv
- Holomorphic families of long ℂ^{2}'s. Proc. Amer. Math. Soc. 140 (2012) 2383-2389. MR2898700 arXiv
Publications 1986-2011. These files are provided for non-commercial, personal, academic use of individual researchers. Any other use requires explicit permission from the publisher since the papers are protected by copyright.
- Invariance of the parametric Oka property. Complex Analysis, 125-144. Trends in Math., Birkhäuser (2010). PDF MR2885112
- The Oka principle for sections of stratified fiber bundles. Pure Appl. Math. Quarterly 6 (2010) 843-874. PDF MR2677316
- Strongly pseudoconvex Stein domains as subvarieties of complex manifolds (with B. Drinovec Drnovšek). Amer. J. Math. 132 (2010) 331-360. PDF MR2654777
- Oka Maps. C. R. Acad. Sci. Paris Ser. I 348 (2010) 145-148. PDF MR2600066
- Fibrations and Stein neighborhoods (with E.F. Wold). Proc. Amer. Math. Soc. 138 (2010) 2037-2042. PDF MR2596039
- Oka Manifolds. C. R. Acad. Sci. Paris, Ser. I 347 (2009) 1017-1020. PDF MR2554568
- Bordered Riemann surfaces in ℂ^{2} (with E. F. Wold). J. Math. Pures Appl. 91 (2009) 100-114. PDF MR2487902
- Approximation of holomorphic mappings on strongly pseudoconvex domains (with B. Drinovec Drnovšek). Forum Math. 20 (2008) 817-840. PDF MR2445119
- Stein compacts in Levi-flat hypersurfaces (with C. Laurent-Thiébaut). Trans. Amer. Math. Soc. 360 (2008) 307-329. PDF MR2342004
- Holomorphic curves in complex spaces (with B. Drinovec Drnovšek). Duke Math. J. 139 (2007) 203-254. PDF MR2352132
- Deformations of Stein structures and extensions of holomorphic mappings (with M. Slapar). Math. Res. Lett. 14 (2007) 343-357. PDF MR2318630
- An interpolation theorem for proper holomorphic embeddings (with B. Ivarsson, F. Kutzschebauch and J. Prezelj). Math. Ann. 338 (2007) 545-554. PDF MR2317930
- Manifolds of holomorphic mappings from strongly pseudoconvex domains. Asian J. Math. 11 (2007) 113-126. PDF MR2304585
- Stein structures and holomorphic mappings (with M. Slapar). Math. Z. 256 (2007) 615-646. PDF MR2299574
- A contractible Levi-flat hypersurface in ℂ^{2} which is a determining set for pluriharmonic functions. Ark. Math. 44 (2006) 87-91 PDF MR2237212
- Runge approximation on convex sets implies Oka's property. Ann. of Math. (2) 163 (2006) 689-707. PDF MR2199229
- Holomorphic flexibility properties of complex manifolds. Amer. J. Math. 128 (2006) 239-270. PDF MR2197073
- Holomorphic discs with dense images (with J. Winkelmann). Math. Res. Lett. 12 (2005) 265-268. PDF MR2150882
- Extending holomorphic mappings from subvarieties in Stein manifolds. Ann. Inst. Fourier 55 (2005) 733-751. PDF MR2149401
- Holomorphic submersions from Stein manifolds. Ann. Inst. Fourier 54 (2004) 1913-1942. PDF MR2134229
- Most real analytic Cauchy-Riemann manifolds are nonalgebraizable. Manuscripta Math. 115 (2004) 489-494. PDF MR2103663
- Noncritical holomorphic functions on Stein manifolds. Acta Math. 191 (2003) 143-189. PDF MR2051397
- Strongly pseudoconvex handlebodies (with J. Kozak). J. Korean Math. Soc. 40 (2003) 727-745. PDF MR1995074
- Stein domains in complex surfaces. J. Geom. Anal. 13 (2003) 77-94. PDF MR1967038
- The Oka principle for multivalued sections of ramified mappings. Forum Math. 15 (2003) 309-328. PDF MR1956971
- Embedding some bordered Riemann surfaces in the affine plane (with M. Černe). Math. Res. Lett. 9 (2002) 683-696. PDF MR1906070
- The Oka principle for sections of subelliptic submersions. Math. Z. 241 (2002) 527-551. PDF MR1938703
- Oka's principle for holomorphic submersions with sprays (with J. Prezelj). Math. Ann. 322 (2002) 633-666. PDF MR1905108
- Solving the d- and dibar-equations in thin tubes and applications to mappings (with E. Løw and N. Øvrelid). Michigan Math. J. 49 (2001) 369-416. PDF MR1852309
- Proper holomorphic discs in ℂ^{2} (with J. Globevnik) Math. Res. Lett. 8 (2001) 257-274. PDF MR1839476
- On complete intersections. Ann. Inst. Fourier 51 (2001) 497-512. PDF MR1824962
- Extending holomorphic sections from complex subvarieties (with J. Prezelj). Math. Z. 236 (2001) 43-68. PDF MR1812449
- An interpolation theorem for holomorphic automorphisms of ℂ^{n} (with G. Buzzard). J. Geom. Anal. 10 (2000) 101-108. PDF MR1758584
- Oka's principle for holomorphic fiber bundles with sprays (with J. Prezelj). Math. Ann. 317 (2000) 117-154. PDF MR1760671
- Interpolation by holomorphic automorphisms and embeddings in ℂ^{n}. J. Geom. Anal. 9 (1999) 93-118. PDF MR1760722
- Holomorphic equivalence of smooth submanifolds in ℂ^{n} (with E. Løw). Indiana Univ. Math. J. 46 (1997) 133-153. PDF MR1462799
- A Carleman type theorem for proper holomorphic embeddings (with G. Buzzard). Ark. Mat. 35 (1997) 157-169. PDF MR1443039
- Actions of (R,+) and (C,+) on complex manifolds. Math. Z. 223 (1996) 123-153. PDF MR1408866
- Embedding holomorphic discs through discrete sets (with J. Globevnik and B. Stensønes). Math. Ann. 305 (1996) 559-569. PDF MR1397436
- Non straightenable complex lines in ℂ^{2} (with J. Globevnik and J.-P. Rosay). Ark. Mat. 34 (1996) 97-101. PDF MR1396625
- Flows on ℂ^{2} with polynomial time one map (with P. Ahern and D. Varolin). Complex Var. Theory Appl. 29 (1996) 363-366. PDF MR1390620
- A theorem in complex symplectic geometry. J. Geom. Anal. 5 (1995) 379-393. PDF MR1360826
- Limits of complete holomorphic vector fields. Math. Res. Lett. 2 (1995) 401-414. PDF MR1355704
- One parameter automorphism groups on ℂ^{2} (with P. Ahern). Complex Var. Theory Appl. 27 (1995) 245-268. PDF MR1333980
- Equivalence of real submanifolds under volume preserving holomorphic automorphisms of ℂ^{n}. Duke Math. J. 77 (1995) 431-445. PDF MR1321065
- Approximation by automorphisms on smooth submanifolds of ℂ^{n}. Math. Ann. 300 (1994) 719-738. PDF MR1314745
- Complements of Runge domains and holomorphic hulls. Michigan Math. J. 41 (1994) 297-308. PDF MR1278436
- Intersections of totally real and holomorphic discs (with T. Duchamp). Publ. Mat. 37 (1993) 3-17. PDF MR1240927
- A reflection principle on strongly pseudoconvex domains with generic corners. Math. Z. 213 (1993) 49-64. PDF MR1217670
- Approximation of biholomorphic mappings by automorphisms of ℂ^{n} (with J.-P. Rosay). Invent. Math. 112 (1993) 323-349. PDF MR1213106 Erratum: Invent. Math. 118 (1994) 573-574. PDF MR1296357
- Intersections of analytic and smooth discs. In: The Madison Symposium on Complex Analysis, Madison, Wisconsin, 1991, pp. 235-244. Contemp. Math. 137. Amer. Math. Soc., Providence (1992) PDF MR1190985
- Complex tangents of real surfaces in complex surfaces. Duke Math. J. 67 (1992) 353-376. PDF MR1177310
- The length of a set in the sphere whose polynomial hull contains the origin. Indag. Math. (N.S.) 3 (1992) 169-172. PDF MR1168343
- An elementary proof of Fefferman's theorem. Expo. Math. 10 (1992) 135-150. PDF MR1164529
- Discs in pseudoconvex domains (with J. Globevnik). Comment. Math. Helv. 67 (1992) 129-145. PDF MR1144617
- Mappings of quadric Cauchy-Riemann manifolds. Math. Ann. 292 (1992) 163-180. PDF MR1141791
- A smooth holomorphically convex disc in ℂ^{2} that is not locally rationally convex. Proc. Amer. Math. Soc. 116 (1992) 411-415. PDF MR1101982
- Admissible boundary values of bounded holomorphic functions in wedges. Trans. Amer. Math. Soc. 332 (1992) 583-593. PDF MR1087055
- Mappings of strongly pseudoconvex Cauchy-Riemann manifolds. Several complex variables and complex geometry, Santa Cruz, 1989, Proc. Symp. Pure Math. 52, Part 1, 59-92. Amer. Math. Soc., Providence (1991). PDF MR1128516
- A new class of polynomially convex sets in ℂ^{2} (with E. L. Stout). Ark. Mat. 29 (1991) 51-62. PDF MR1115074
- A totally real three-sphere in ℂ^{3} bounding a family of analytic discs. Proc. Amer. Math. Soc. 108 (1990) 887-892. PDF MR1038758
- Extending proper holomorphic mappings of positive codimension. Invent. Math. 95 (1989) 31-62. PDF MR0969413
- Polynomial hulls of sets fibered over the circle. Indiana Univ. Math. J. 37 (1988) 869-889. PDF MR0982834
- Regularity of varieties in strictly pseudoconvex domains. Publ. Mat. 32 (1988) 145-150. PDF MR0939779
- Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings (with J.-P. Rosay). Math. Ann. 279 (1987) 239-252. PDF MR0919504
- Analytic disks with boundaries in a maximal real submanifold of ℂ^{2}. Ann. Inst. Fourier 37 (1987) 1-44. PDF MR0894560
- On totally real embeddings into ℂ^{n}. Exposition. Math. 4 (1986) 243-255. PDF MR0880125
- Polynomially convex hulls with piecewise smooth boundaries. Math. Ann. 276 (1986) 97-104. PDF MR0863710
- On the boundary regularity of proper holomorphic mappings. Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 13 (1986) 109-128. PDF MR0863637
- Proper holomorphic maps from balls. Duke Math. J. 53 (1986) 427-441. PDF MR0850544
- Embedding strictly pseudoconvex domains into balls. Trans. Amer. Math. Soc. 295 (1986) 347-368. PDF MR0831203
- Some totally real embeddings of three-manifolds. Manuscripta Math. 55 (1986) 1-7. PDF MR0828408
- Stability of polynomial convexity of totally real sets. Proc. Amer. Math. Soc. 96 (1986) 489-494. PDF MR0822446
Research expository articles
- Null holomorphic curves in ℂ^{3} and the conformal Calabi-Yau problem (with A. Alarcón). In: Complex Geometry and Dynamics (The Abel Symposium 2013, Fornæss, J.E., Irgens, M., Wold, E.F., Eds.), 101-121. Abel Symposia, vol. 10, Springer-Verlag (2015). PDF arXiv
- The homotopy principle in complex analysis. In: A few snapshots from the work of Mikhail Gromov. Holden, H.; Piene, R., Eds., The Abel Prize 2008-2012. Springer, Heidelberg (2014), pp. 161-165. PDF MR3185030
- Oka manifolds: from Oka to Stein and back. With an appendix by F. Lárusson. Ann. Fac. Sci. Toulouse Math. (6), XXII (2013), No. 4, 747-809. PDF MR3137250 arXiv
- Survey of Oka theory (with F. Lárusson). New York J. Math., 17a (2011), 1-28. PDF MR2782726
- Abelova nagrada 2009 Mikhaelu Gromovu. (Slovenian) (The Abel prize 2009 to Mikhael Gromov.) Obzornik mat. fiz. 57 (2010) 2, 41-52. PDF MR2677126
- Princip Oka-Grauert-Gromov in uporaba v kompleksni geometriji. (Slovenian; The Oka-Grauert principle and its applications in complex geometry). Unpublished, University of Ljubljana (2010). PDF
- The homotopy principle in complex analysis: A survey. In: Explorations in Complex and Riemannian Geometry, 73-99; Contemp. Math., 332, Amer. Math. Soc., Providence, RI (2003). PDF MR2016091
- Holomorphic automorphisms of ℂ^{n}: A survey. In: Complex Analysis and Geometry (Trento, 1993), 173-199; Lecture Notes in Pure and Appl. Math., 173, Dekker, New York (1996). PDF MR1365974
- Proper holomorphic mappings: a survey. In: Several complex variables, Mittag-Leffler Institute (Stockholm, 1987-88), 297-363; Math. Notes, 38, Princeton Univ. Press, Princeton, NJ (1993). PDF MR1207867
Recent lectures at international conferences
- Complete bounded submanifolds in different geometries. Workshop su varietà reali e complesse: geometria, topologia e analisi armonica, Scuola Normale Superiore, Palazzo della Carovana, Pisa, Italy, 24-26 February 2017
- New complex analytic methods in the study of non-orientable minimal surfaces in R^{n}. The INdAM Workshop Complex function theory, its generalizations and applications, Rome, Italy, 12-16 September 2016
- A long C^{2} without holomorphic functions. CR Geometry and PDE's - VII, dedicated to the memory of Giuseppe Zampieri, Levico Terme (Trento), Italy, 26 June - 1 July 2016
- Every meromorphic function is the Gauss map of a conformal minimal surface. INdAM Meeting Complex and Symplectic Geometry, Cortona, Italy, 13-17 June 2016
- The h-principle for minimal surfaces in R^{n} and null curves in C^{n}. Complex Analysis and Complex Geometry, Banff International Research Station, Banff, Canada, 1-6 May 2016
- Non-orientable minimal surfaces in R^{n}. Several complex variables and CR geometry, Erwin Schrödinger Institute, Vienna, Austria, 3-13 November 2015
- Minimal surfaces in minimally convex domains. The Eighth Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Sāo Paulo, Brazil, 3-7 August 2015
- Minimal surfaces in minimally convex domains. Complex Analysis and Geometry - XXII, Levico Terme, Italy, 1-5 June 2015
- Complete conformal minimal surfaces with Jordan boundaries in R^{n}. NORDAN 2015, University of Iceland, Reykjavik, Iceland, 25-26 April 2015
- Minimal hulls of compact sets in R^{3}. Norwegian-Spanish Workshop in Complex Variables and Applications, Complutense University of Madrid, Spain, 19-20 February 2015
- Minimal hulls of compact sets in R^{3}. Geometric Methods of Complex Analysis, Mathematisches Forschungsinstitut Oberwolfach, Germany, 25-31 January 2015
- Noncritical holomorphic functions on Stein spaces. Analysis and geometry in several complex variables, Texas A&M University at Qatar, Doha, Qatar, 4-8 January 2015
- The Oka-Grauert principle: its first 75 years (plenary lecture). Gedenkkolloquium für Hans Grauert, University of Bonn, Germany, 27 June 2014
- The Hodge conjecture for q-complete manifolds. CR Geometry and PDE's - VI, Levico Terme, Italy, 23-27 June 2014
- Complex analysis and the conformal Calabi-Yau problem. Abel Symposium 2013, Trondheim, Norway, 2-5 July 2013
- The conformal Calabi-Yau problem. Complex Analysis and Geometry - XXI, Levico Terme (Trento), Italy, 2-7 June 2013
- Null-curves and directed immersions of Riemann surfaces. Workshop Geometric and Complex Analysis, Granada, Spain, 22-23 November 2012
- Every bordered Riemann surface is a complete proper curve in a ball. Geometric Methods in Several Complex Variables, Lille, France, 25-26 October 2012
- Embeddings of infinitely connected planar domains into ℂ^{2}. Conference on CR Geometry and PDE's - V, Levico Terme, Trento, Italy, 5-8 June 2012
- Two theorems on Riemann surfaces. Workshop in several complex variables, University of Amsterdam, The Netherlands, 12-16 December 2011
- What is an Oka manifold? Plenary lecture, OeMG-Tagung - CSASC 2011, Krems, Austria, 25-28 September 2011.
- The Poletsky-Rosay theorem on singular complex spaces. Conference on Several Complex Variables on the occasion of Professor Józef Siciak's 80th birthday, Jagielonnian University, Krakow, Poland, 4-8 July 2011
- The Poletsky-Rosay theorem on singular complex spaces. Southern California Analysis and PDE Conference, U.C. San Diego, California, 28-29 May 2011
- Embedding Riemann surfaces in ℂ^{2}. Almost complex geometry and foliations, Lille, France, 23-29 May 2010
- Recent advances in elliptic complex geometry. Recent Advances in Function Related Operator Theory, Rincón, Puerto Rico, 22-26 March 2010
Lectures at international schools
- Applications of complex analysis to minimal surfaces. Partial Differential Equations in Complex Geometry and Singular Spaces, American University in Beirut, 24-27 November 2014. Lecture 1 Lecture 2 Lecture 3
- Oka Manifolds. Komplex Analysis Winter School KAWA4, Toulouse, France, 21-24 January 2013. Lecture Notes
- Non-singular holomorphic foliations on Stein manifolds. Foliations, pseudoholomorphic curves, applications, Institut Fourier, University of Grenoble, France, 18 June - 6 July 2012
- Noncritical holomorphic functions on Stein manifolds. Variétés complexes et feuilletages, IRMA Strasbourg, France, 7-10 June 2010
Organization of international conferences and PhD schools
- Workshop in Complex Analysis - Ljubljana 2016, FMF and IMFM, Ljubljana, Slovenia, 24-26 March 2016
- Sanya School in Complex Analysis and Geometry, Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, 11-20 January 2016
- Complex Analysis, Geometry and Dynamics - School and Workshop, International Centre for Theoretical Physics (ICTP), Trieste, Italy, 21 September - 3 October 2015
- International Conference on Complex Geometry and Several Complex Variables, East China Normal University, Shanghai, China, 11-15 May 2015
- Several Complex Variables Symposium, Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, 12-16 May 2014
- Minisymposium on Several Complex Variables, CSASC, Primorska University, Koper, Slovenia, 10-12 June 2013
- Workshop Geometric and Complex Analysis, Granada, Spain, 22-23 November 2012
- Several Complex Variables - Ljubljana 2012, University of Ljubljana, Slovenia, 27-29 September 2012
- Minisymposium on Complex Analysis, OeMG-Tagung - CSASC 2011, University of Krems, Austria, 25-28 September 2011
- Member of the Scientific Committee of KAWA (a series of PhD schools and conferences), 2009-present
- Several Complex Variables and Connections with PDEs and Geometry, Fribourg, Switzerland, 7 - 11 July 2008
Beamer files of invited lectures:
- Every meromorphic function is the Gauss map of a conformal minimal surface. University of Granada, Spain, 27 January 2017
- Every meromorphic function is the Gauss map of a conformal minimal surface. Center for Advanced Study, Oslo, 17 November 2016
- The h-principle for minimal surfaces and null curves. University of Granada, Spain, 18 March 2016.
- Oka manifolds and minimal surfaces. University of Granada, Spain, 13 November 2015.
- Complex analysis and the conformal Calabi-Yau problem. Abel Symposium, Trondheim, Norway, 2013.
- What is an Oka manifold? CSASC, Krems, Austria, 2011.
- Recent advances in elliptic complex geometry. Rincon, Puerto Rico, 2010.
Lectures at international schools:
- The Beirut Lectures on minimal surfaces, AUB, Beirut, Lebanon, 2014: Lecture 1 Lecture 2 Lecture 3
- Oka Manifolds. Lectures at KAWA 4, Toulouse, France, 2013.
Lecture notes for some of my courses (in Slovenian):
Opinion articles (in Slovenian)
- Matematika in razvoj osebnosti
- Kam želijo slovenske Univerze
- Visoko šolstvo in tržna ekonomija
- Razvoj slovenskega visokošolskega prostora
A few of my favorite places
Triglav,
Triglav from Mrežce,
A late Summer evening on Uskovnica
Furkapass,
Grimselpass,
Jungfraujoch,
Jungfrau with a star
Kvarner,
Moščenička Draga,
Motovun in Istria,
Kamenjak,
On Kamenjak,
Portić,
A pine tree in Portić
Dubrovnik and Lokrum,
Dubrovnik with old port,
Mare Adriatico
Lago di Garda 1
2
3
4
5
6,
In Dolomiti 1
2
3,
Passo di Resia
Cinque Terre,
In Cinque Terre,
Monterosso,
Vernazza,
Mare Liguro
Eze 1
2
3,
Ladies of Eze 1
2
3
4
5
6
7
8
9
10
Moustiers-Sainte Marie en Provence 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Luminy - Calanque Sugiton 1
2
3
4
5
6
Granada 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Puerto Rico 1
2
3
4
5
6
7
8
Adelaide botanical garden 1
2
3,
Titan Arum 1,
2,
Sunset in Glenelg 1
2
3,
Sunset with seagull
Barossa valley 1
2,
McLaren Vale 1
2
3
4,
Australia in motion,
Southern Ocean 1
2
3
4
Heaven on Earth 1
2
3
4
5
6
7
8
9,
And yet another one 1
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Eva's art
2015-1 2015-2 2015-3 2015-4 2015-5 2015-6 2015-7 2015-8