prof. dr. Franc Forstnerič

Plenary speaker, 8th European Congress of Mathematics, 5-11 July 2020, Portorož, Slovenia

International Journal of Mathematics, member of the editorial board

Seminar for Complex Analysis, 1975-

Together with Barbara Drinovec Drnovšek we coordinate the Seminar for Complex Analysis at the Department of Mathematics, University of Ljubljana and Institute of Mathematics, Physics and Mechanics. The seminar was established by Josip Globevnik in 1975 and has been running continuously since then. During the academic year it meets on Tuesdays at 12:30 in room 3.06, Jadranska 21. It covers primarily topics in complex analysis, complex geometry, harmonic analysis, and partial differential equations. Here is a list of upcoming talks:
• 12.11.2019 at 12:15h: Arkadius Lewandowski, Jagiellonian University, Krakow
• 19.11.2019: Nikolay Shcherbina, University of Wuppertal
Internal instructions for application to host a guest in the seminar are available here and there.

Research interests and grants

My research interests lie primarily in complex analysis, analytic geometry, Riemann surfaces, minimal surfaces, and holomorphic contact geometry. I have introduced in the literature the class of Oka Manifolds, named after Kiyoshi Oka; 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 and 2017). More recently, I have been interested in applications of Oka theory techniques in the classical theory of minimal surfaces and in holomorphic contact geometry.

I am coordinating the research program P1-0291 Analysis and Geometry (2015-20) and the grant J1-9104 (2018-2021) financed by ARRS, Republic of Slovenia. Research activities of members of project teams cover a wide array of topics in complex analysis and geometry, global analysis, minimal surfaces, harmonic analysis, spectral theory of operators, partial differential equation, special functions, integrable systems, and numerical analysis. A list of my past grants is available here.

Information for prospective PhD students

Stein Manifolds and Holomorphic Mappings 2018, Ljubljana, 17-21 September 2018 Photos

Books

• 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. Second Edition. Cham: Springer Internat. (ISBN 978-3-319-61057-3/hbk; 978-3-319-61058-0/ebook). xiv+562 p. (2017). MR3700709 Zbl06737283 Errata, 30 October 2019
• Stein Manifolds and Holomorphic Mappings. The homotopy principle in complex analysis. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 56. Berlin: Springer (ISBN 978-3-642-22249-8/hbk; 978-3-642-22250-4/ebook). xii, 489 p. (2011). MR2975791 Zbl 1247.32001

Preprints

• Holomorphic Legendrian curves in CP³ and superminimal surfaces in S⁴ (with A. Alarcón and F. Lárusson). arXiv.
• Immersions of open Riemann surfaces into the Riemann sphere. arXiv.
• The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends (with A. Alarcón). Rev. Mat. Iberoam., to appear. arXiv.
• H-principle for complex contact structures on Stein manifolds. J. Symplectic Geom., to appear. arXiv.
• Holomorphic Legendrian curves in projectivised cotangent bundles (with F. Lárusson). arXiv.
• Holomorphic approximation: the legacy of Weierstrass, Runge, Oka-Weil, and Mergelyan (with J. E. Fornæss and E. F. Wold). To appear in the volume "Advancements in Complex Analysis" by Springer-Verlag. arXiv.
• New complex analytic methods in the study of non-orientable minimal surfaces in Rⁿ (with A. Alarcón and F.J. López). Memoirs Amer. Math. Soc., to appear. arXiv

Online first publications

• A foliation of the ball by complete holomorphic discs (with A. Alarcón). Math. Z., to appear. arXiv.
• Runge tubes in Stein manifolds with the density property (with E. F. Wold). Proc. Amer. Math. Soc., to appear. arXiv
• Proper holomorphic immersions into Stein manifolds with the density property. J. Anal. Math., to appear. arXiv

Research and expository papers, 2013-2019

• Every meromorphic function is the Gauss map of a conformal minimal surface (with A. Alarcón and F.J. López). J. Geom. Anal., 29:4 (2019), 3011-3038. Full text view only. arXiv
• Mergelyan's and Arakelian's theorems for manifold-valued maps. Moscow Math. J., 19:3 (2019), 465-484. MR3993004 arXiv
• New complex analytic methods in the theory of minimal surfaces: a survey (with A. Alarcón). J. Aust. Math. Soc., 106:3 (2019), 287-341. MR3951461 arXiv
• The parametric h-principle for minimal surfaces in Rⁿ and null curves in Cⁿ (with F. Lárusson). Comm. Anal. Geom., 27 (2019), no. 1, 1-45. MR3951019 arXiv
• A properly embedded holomorphic disc in the ball with finite area and dense boundary curve. Math. Ann., 373 (2019) 1-2, 719-742. MR3968886 arXiv
• Darboux charts around holomorphic Legendrian curves and applications (with A. Alarcón). Internat. Math. Res. Not. (IMRN) (2019), no. 3, 893-922. MR3910477 arXiv
• Minimal surfaces in minimally convex domains (with A. Alarcón, B. Drinovec Drnovšek, and F. J. López). Trans. Amer. Math. Soc. 371 (2019), no. 3, 1735-1770. MR3894033 arXiv
• Holomorphic embeddings and immersions of Stein manifolds: a survey. In: Geometric Complex Analysis (In Honor of Kang-Tae Kim's 60th Birthday, Gyeongju, Korea, 2017), 145-169. Springer Proceedings in Mathematics and Statistics, 2018. MR3923223 arXiv
• Every conformal minimal surface in R³ is isotopic to the real part of a holomorphic null curve (with A. Alarcón). J. reine angew. Math. (Crelle's J.), 740 (2018) 77-109. MR3824784 arXiv
• Divisors defined by noncritical functions. Proc. Amer. Math. Soc., 146:7 (2018) 2985-2994. MR3787359 arXiv
• The Oka principle for holomorphic Legendrian curves in C²ⁿ⁺¹ (with F. Lárusson). Math. Z., 288 (2018) 643-663. MR3774429 arXiv
• Complete densely embedded complex lines in C² (with A. Alarcón). Proc. Amer. Math. Soc. 146:3 (2018) 1059-1067. MR3750218 arXiv
• Surjective holomorphic maps onto Oka manifolds. In: Complex and Symplectic Geometry (Proceedings of the INdAM Meeting Complex and Symplectic Geometry, Cortona, 2016), pp. 73-84. Springer INdAM Series, Vol. 21 (2017). MR3645307 arXiv
• Hyperbolic complex contact structures on C²ⁿ⁺¹. J. Geom. Anal. 27:4 (2017) 3166-3175. Full text view only MR3708010 arXiv
• Holomorphic Legendrian curves (with A. Alarcón and F. J. López). Compositio Math. 153:9 (2017) 1945-1986. MR3705282 arXiv
• A long C² without holomorphic functions (with L. Boc Thaler). Analysis & PDE 9:8 (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. 130:1 (2016) 135-150. Full text view only. MR3574650 arXiv
• Noncritical holomorphic functions on Stein spaces. J. Eur. Math. Soc. (JEMS) 18:11 (2016) 2511-2543. MR3562350 arXiv
• Embedded minimal surfaces in Rⁿ (with A. Alarcón and F. J. López). Math. Z. 283:1 (2016) 1-24. Full text view only. 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 R³ (with B. Drinovec Drnovšek). Trans. Amer. Math. Soc. 368:10 (2016) 7477-7506. MR3471098 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
• Null holomorphic curves in ℂ³ 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
• 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
• The Calabi-Yau problem, null curves, and Bryant surfaces (with A. Alarcón). Math. Ann. 363:3-4 (2015) 913-951. MR3412347 arXiv
• Fatou-Bieberbach domains in ℂⁿ\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
• Gromov's contribution to the Oka principle. 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 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 proofs can be completed by applying Lemma 3.1 in the preprint Proper holomorphic immersions into Stein manifolds with the density property (March 2017), to appear in J. Anal. Math.
• 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. MR3078344 arXiv Japanese translation
• Embeddings of infinitely connected planar domains into ℂ² (with E. F. Wold). Analysis & PDE 6:2 (2013) 499-514. MR3071396 arXiv

Publications 1986-2012. 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.

• Characterizations of projective hulls by analytic discs (with B. Drinovec Drnovšek). Illinois J. Math. 56:1 (2012) 53-65 (2013). PDF MR3117017 arXiv
• The Poletsky-Rosay theorem on singular complex spaces (with B. Drinovec Drnovšek). Indiana Univ. Math. J. 61 (2012) 1707-1423. PDF MR3085613 arXiv
• Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties (with B. Drinovec Drnovšek). Ann. Polon. Math. 106 (2012) 171-191. PDF MR2995450 arXiv
• Holomorphic families of long ℂ²'s. Proc. Amer. Math. Soc. 140 (2012) 2383-2389. PDF MR2898700 arXiv
• Survey of Oka theory (with F. Lárusson). New York J. Math., 17a (2011), 1-28. PDF MR2782726
• 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
• 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
• Oka Manifolds. C. R. Acad. Sci. Paris, Ser. I 347 (2009) 1017-1020. PDF MR2554568
• Bordered Riemann surfaces in ℂ² (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 ℂ² 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
• 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
• 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 ℂ² (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 ℂⁿ (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 ℂⁿ. J. Geom. Anal. 9 (1999) 93-118. PDF MR1760722
• Holomorphic equivalence of smooth submanifolds in ℂⁿ (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 ℂ² (with J. Globevnik and J.-P. Rosay). Ark. Mat. 34 (1996) 97-101. PDF MR1396625
• Flows on ℂ² with polynomial time one map (with P. Ahern and D. Varolin). Complex Var. Theory Appl. 29 (1996) 363-366. PDF MR1390620
• Holomorphic automorphisms of ℂⁿ: 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
• 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 ℂ² (with P. Ahern). Complex Var. Theory Appl. 27 (1995) 245-268. PDF MR1333980
• Equivalence of real submanifolds under volume preserving holomorphic automorphisms of ℂⁿ. Duke Math. J. 77 (1995) 431-445. PDF MR1321065
• Approximation by automorphisms on smooth submanifolds of ℂⁿ. 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 ℂⁿ (with J.-P. Rosay). Invent. Math. 112 (1993) 323-349. PDF MR1213106 Erratum: Invent. Math. 118 (1994) 573-574. PDF MR1296357
• 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
• 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 ℂ² 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 ℂ² (with E. L. Stout). Ark. Mat. 29 (1991) 51-62. PDF MR1115074
• A totally real three-sphere in ℂ³ 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 ℂ². Ann. Inst. Fourier 37 (1987) 1-44. PDF MR0894560
• On totally real embeddings into ℂⁿ. 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

Recent lectures at international conferences

• Mergelyan's and Arakelian's theorems for manifold-valued maps. 27th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (ICFIDCAA), Krasnoyarsk, 11--15 August 2019
• H-principle for complex contact structures on Stein manifolds. Analysis and CR geometry, ESI - Vienna, Austria, 10-14 December 2018
• Runge tubes. Holomorphic Elliptic Geometry and Group Actions, University of Bern, Switzerland, 5-7 September 2018
• Runge tubes. Hayama Symposium on Several Complex Variables XX joint with Pacific Rim Complex-Symplectic Geometry conference, Shonan Village Center, Hayama, Japan, 13-17 July 2018
• New developments in nonlinear holomorphic approximation theory. CR-Geometry and PDE's-VIII, Levico Terme, Trento, Italy, 4-8 June 2018
• Nonlinear holomorphic approximation theory. Complex Analysis and Related Topics, Euler International Mathematical Institute, St. Petersburg, 23-27 April 2018
• Runge tubes. Second Central European Complex Analysis Meeting, University of Vienna, Austria, 12-14 April 2018
• A properly embedded holomorphic disc in the ball with finite area and dense boundary curve. Complex Geometry for Serguei Ivashkovych's 60th anniversary, Lille, 23-24 November 2017
• Proper holomorphic embeddings and immersions into Stein manifolds with the density property. International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin, Steklov Mathematical Institute, Moscow, 9-10 October 2017
• Divisors defined by noncritical functions. Workshop on ∂ at NTNU Trondheim, Norway, 5-8 October 2017
• Proper holomorphic mappings of Stein manifolds. Festkolloquium Anlässlich des 80. Geburtstags von Otto Forster, Ludwig Maximilians-Universität München, 14 July 2017
• Holomorphic immersions and embeddings of Stein manifolds into Stein manifolds with the density property. The KSCV12 Symposium; The 12th Korean Conference on Several Complex Variables - in honor of Kang-Tae Kim's 60th birthday, The Kolon Hotel in Gyeong-Ju, South Korea, 3-7 July 2017
• Holomorphic Legendrian curves and Darboux charts. Complex Analysis and Geometry - XXIII, Levico Terme (Trento), Italy, 11-15 June 2017
• Holomorphic Legendrian curves. Conference on Complex Geometry, Dynamical Systems and Foliation Theory, Institute for Mathematical Sciences, National University of Singapore, 15-19 May 2017
• 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 Rⁿ. The INdAM Workshop Complex function theory, its generalizations and applications, Rome, Italy, 12-16 September 2016
• A long C² 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 Rⁿ and null curves in Cⁿ. Complex Analysis and Complex Geometry, Banff International Research Station, Banff, Canada, 1-6 May 2016
• Non-orientable minimal surfaces in Rⁿ. 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 Rⁿ. NORDAN 2015, University of Iceland, Reykjavik, Iceland, 25-26 April 2015
• Minimal hulls of compact sets in R³. Norwegian-Spanish Workshop in Complex Variables and Applications, Complutense University of Madrid, Spain, 19-20 February 2015
• Minimal hulls of compact sets in R³. 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 ℂ². 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 ℂ². 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

• Frontiers in Elliptic Holomorphic Geometry, Jevnaker, Norway, 10-14 October 2016
• 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), 2009-2016
• Several Complex Variables and Connections with PDEs and Geometry, Fribourg, Switzerland, 7-11 July 2008
• The International Summer School in Several Complex Variables, Szczyrk, Poland, 19-23 June 2006
• A Symposium in Complex Analysis - Slovenia 2006, Kranjska Gora, Slovenia, 7-10 June 2006
• Conference on Complex Analysis}, University of Wisconsin, Madison, USA, 16-19 March 2006
• Seattle Symposium on Complex Analysis, University of Washington, Seattle, USA, March 1998
• Geometric and analytic methods in several complex variables (Special session), AMS regional meeting, Iowa City, USA, March 1996
• Midwest several complex variables seminar, University of Wisconsin, Madison, USA, April 1995

Beamer files of invited lectures:

• Runge tubes. Geometria Complessa e Geometria Differenziale, Dipartimento di Matematica, Università degli Studi di Firenze, Italia, 24 Maggio 2018
• Runge tubes. Istanbul Analysis Seminars, Sabanci University, Istanbul, Turkey, 16 March 2018
• A properly embedded holomorphic disc in the ball with finite area and dense boundary curve. Geometry Seminar, University of Granada, Spain, 9 February 2018
• Holomorphic Legendrian curves. Differential Geometry Seminar, University of Adelaide, 26 May 2017
• Complete bounded submanifolds in different geometries. Dublin Mathematics Colloquium, Trinity College, Dublin, 30 March 2017
• Every meromorphic function is the Gauss map of a conformal minimal surface. Geometry Seminar, 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. Geometry Seminar, University of Granada, Spain, 18 March 2016
• A long C² without holomorphic functions. Differential Geometry Seminar, University of Adelaide, 29 January 2016.
• Oka manifolds and minimal surfaces. Geometry Seminar, University of Granada, Spain, 13 November 2015

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):

• Analiza na mnogoterostih
• Riemannove ploskve
• Kompleksna analiza
• Analiza 4: Uvod v parcialne diferencialne enačbe
• Dinamični sistemi
• Zveza med Chernovo ukrivljenostjo in q-konveksnostjo

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 2 3 4 5 6 7 8 9 10

Eva's art

2015-1 2015-2 2015-3 2015-4 2015-5 2015-6 2015-7 2015-8

Events

Spirito by Dolfo Vina