Herwig Hauser
Fakultät für Mathematik
Universität Wien
Nordbergstraße 15
A-1090 Wien
Österreich
Tel.:(+43)-1-4277-50781
Fax: (+43)-1-4277-9506
Herwig.Hauser@univie.ac.at |
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Artin Approximation (with G. Rond), Manuscript 2013, 67 pp. PDF
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Blowups and resolution, Manuscript 2013, 60 pp. PDF
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Multivariate linear recurrences and power series division (with C. Koutschan), Discrete Math. 312 (2012), 3553-3560. PDF
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Effective algebraic power series (with M.E. Alonso, F.J. Castro-Jiménez), Manuscript 2012, 32 pp. PDF
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A game for the resolution of singularities (with J. Schicho), Proc. London Math. Soc. 105 (2012), 1149-1182. PDF
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Forty Questions on Singularities (with J. Schicho), Asian J. Math. 15 (2011), 417-436 PDF
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Wild Singularities and Kangaroo Points for the Resolution in Positive Characteristic, Manuscript, 2010, 31 pp. PDF
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Arcs, Cords and Felts: Six Instances of the Linearization Principle (with C. Bruschek); Amer. J. Math., 132 (2010), 941-986. PDF
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Platonic Stars (with A. Fritz), Math. Intelligencer, 32 (2010), 22-36. PDF
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On the Problem of Resolution of Singularities in Positive Characteristic (Or: A proof we are still waiting for), Bull. Amer. Math. Soc. 47 (2010),1-30. PDF
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Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces (with E. Faber), Bull. Amer. Math. Soc. 47 (2010), 373-417. PDF
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Division Theorems and Infinite Dimensional Geometry
| Perfect bases for differential equations (with Sebastian Gann). Journal of Symbolic Computation 40 (2005), 979-997.
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Three power series techniques. Proc. London Math. Soc. 88 (2004), 1-24.
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Continuous division for differential operators (with L. Narváez). Ann. Inst. Fourier 51 (2001), 769-778. PDF
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Comparing modules of differential operators by their evaluation on polynomials. Compos. Math. 69, 295-307 (1989). PDF
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A rank theorem for analytic maps between power series spaces (with G. Müller). Publ. Math. I.H.E.S. 80 (1994), 95-115.
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Semi-universal unfoldings and orbits of the contact group (with. G. Müller). Abh. Math. Sem. Hamburg 66 (1996), 1-9. PS
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Analytic curves in power series rings (with G. Müller). Compos. Math. 76 (1990), 197-201.PDF
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Automorphsim groups in local analytic geometry, infinite dimensional Theorem and Lie groups (with G. Müller). Comptes Rendus Acad. Sci. 313, série I, (1991) 751-756.
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Sur la construction de la déformation semi-universelle dún germe déspace analytique. Ann. Éc. Norm. Sup. Paris 18, 1-56 (1985).PDF
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An algorithm of construction of the semi-universal deformation of an isolated singularity. Proc. Symp. Pure Appl. Math. Amer. Math. Soc. 40, 567-573 (1983).
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Sur la déformation semi-universelle d'une singularitée isolée. Thése de Troisiéme Cycle, Université Paris-Sud, Orsay, 1980.
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Resolution of Singularities
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Two alternative Invariants for the Embedded Resolution of Surface Singularities in Positive Characteristic (with D. Wagner), Manuscript, 2009, 35 pp. PDF
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Resolution Principles. Proceedings of Clay Research Conference 2009 PDF
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Plain Varieties (with G. Bodnár, J. Schicho, O. Villamayor), Bull. London Math. Soc. 40 (2008), 965-971. PDF
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Desingularization of ideals and varieties, In: Singularity Theory, Marseille 2005 (ed. Anne Pichon), pp. 33-69. World Sci. Publ. 2007
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Seven short stories on blowups and resolution. Proceedings Gökova Conference on Geometry and Topology 2005 (ed. Selman Akbulut),
International Press 2006, 1-48
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Explizite Auflösung von ebenen Kurvensingularitäten in beliebiger Charakteristik (with G. Regensburger). L'Enseign. Math. 50 (2004), 305-353.
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| Why the characteristic zero proof of resolution of singularities fails in positive characteristic. Manuscript 2003. 51pp
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The Hironaka Theorem on resolution of singularities (Or: A proof that we always wanted to understand). Bull. Amer. Math. Soc. 40 (2003), 323-403.
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Strong resolution of singularities in characteristic zero (with S. Encinas). Commentarii Math. Helvetici 77 (2002), 421-445.
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Excellent surfaces and their taut resolution. In: Resolution of Singularities, Progress in Math. 181, Birkhäuser (2000).
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Resolution of singularities 1860-1999. In: Resolution of Singularities, Progress in Math. 181, Birkhäuser (2000).
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Seventeen obstacles for resolution of singularities. In: The Brieskorn anniversary volume 1996 (ed. V.I. Arnol'd, G.-M. Greuel, J. Steenbrink). Progress in Math. 162, Birkhäuser (1997). PDF
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Blowup-Algebra. Contribution to the Encyclopaedia of Mathematics. Kluwer (1997).
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Vector Fields in Algebraic Geometry
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The reduced Bautin index of planar vector fields (with J.-J. Risler, B. Teissier). Duke J. Math. 100 (2000), 425-446.
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Dérivations et idéaux réels invariants (with J.-J. Risler). Publ. RIMS, Kyoto Univ. 35 (1999), 585 - 598.
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Lie algebras of polynomial vector fields and the Jacobian conjecture (with G. Müller). Monatshefte 126 (1998), 211-213.
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On the Lie algebra Θ(X) of vector fields on a singularity (with G. Müller). J. Math. Sci. Univ. Tokyo 1 (1994), 239-250.
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Affine varieties and Lie algebras of vector fields (with G. Müller). Manuscr. Math. 80 (1993), 309-337.
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Analytic varieties versus integral varieties of Lie algebras of vector fields (with G. Müller). Bull. Amer. Math. Soc. 26 (1992), 276-279.
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Frobenius type theorems and the Gröbner correspondence (with G. Müller). In: Congrès Singularités, Lille 1991 (ed. J.-P. Brasselet), IRMA, Université de Lille.
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The Lie algebras I D X, Θ(X), and D(X) of a variety (with G. Müller). In: Workshop on Lie algebras of vector fields, Mainz 1993.
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Singularities in Complex Analytic Geometry
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The cancellation property for direct products of analytic space germs (with G. Müller). 60th anniversary of Hans Grauert, Math. Ann. 286 (1990), 209-223. PDF
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The trivial locus of an analytic map germ (with G. Müller). Ann. Inst. Fourier 39 (1989), 831-844. PDF
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Automorphisms of direct products of algebroid spaces (with G. Müller). Singularity Theory and its Applications. Warwick 1989, Part I (Eds.: D. Mond, J. Montaldi).
Springer Lecture Notes in Mathematics 1462 (1991).
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Algebraic singularities have maximal reductive automorphism groups (with G. Müller). Nagoya Math. J. 113 (1989), 181-186.
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Characterizing complex analytic functions. In: Géometrie algébraique et applications (ed.: Aroca et al.), II. Singularités et géometrie
complexe, 133-139. Travaux en cours, Hermann, Paris 1987.
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| Harmonic and dissonant singularities (with G. Müller). In: Proc. Conf. Algebraic Geometry (ed.: Kurke et al.), Berlin 1985, 123-134. Teubner-Texte Bd. 92, Leipzig 1986.
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Characterizing singularities of varieties and of mappings (with T. Gaffney). Invent. math. 79, (1985) 427-447. PDF
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On the singular subspace of an analytic variety. Adv. Studies Pure Math. 8 (1986), 125-134.
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Simplification et factorisation unique des germes d'espaces analytiques complexes (with G. Müller). Comptes Rendus Acad. Sci. 309, série I (1989),
617-619.
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Algebra & Geometrie, 2013, Universität Wien.
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Kombinatorik. Vorlesungsskriptum und Proseminar 2003, Universität Innsbruck.
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Proseminar PDF
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| Funktionalanalysis. Vorlesungsskriptum 2002, Universität Innsbruck.
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Ideals, blowups and resolution. Vorlesungsskriptum 2001, Universität Innsbruck.
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Der Satz von Frobenius in der Kontrolltheorie. Vorlesungsskriptum 1997, Universität Innsbruck.
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FWF-Project P-15551 "Explicit Resolution and Related Methods in Algebraic Geometry and Number Theory" 2002-2006; with J. Schicho
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FWF-Project P-18992 "Solving Algebraic Equations" 2006-2009; with J. Schicho
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FWF-Project P-21461 "Solving Algebraic Equations II" 2009-2013; with J. Schicho
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FWF-ANR-Project "Approximation Theorems in algebra and Cauchy-Riemann geometry:
When Michael Artin meets Henri Poincaré" 2010-2014; with B. Lamel, N. Mir
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Clay Summer School 2012 "Resolution of Singularities", Obergurgl June 2012
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FWF-Project P-25652 "Resolution of Singularities", 2013-2016
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1956 Born in Innsbruck, Austria. Austrian citizen. Married, three children
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1974 - 80 Studies at the Universities of Innsbruck and Paris
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PhD 1980 in Paris with Teissier and Douady on the semi-universal deformation of singularities
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1980 - 88 Assistent professor at the University of Innsbruck
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1982 - 84 Visiting Brandeis and Northeastern University
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1988 Habilitation in singularity theory
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1988 - 2007 Associate Professor at the University of Innsbruck
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1992 - 94 Visiting Professor at the Universidad Autónoma de Madrid
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2006 Presentation of the movie "ZEROSET - I spy with my little eye" at the ICM at Madrid
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2007 - Professor at the University of Vienna, on extended leave from the University of Innsbruck
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2008 Exposition series "IMAGINARY" organized by Mathem. Forschungsinstitut
Oberwolfach
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2011 Organization of the special program "Algebraic versus Analytic Geometry" at the Erwin-Schrödinger-Institute, Vienna
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2012 Organization of the Clay Summer School on Resolution of Singularities, Obergurgl, Austria
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Diploma/Master Theses:
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Christopher Chiu, ongoing, on Noether normalization and Zariski's Main Theorem
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Markus Müller, ongoing, on the Rogers-Ramanujan identity
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Alexandra Fritz, Diploma 2010, on platonic stars and invariant theory, thesis
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Matthias Schiechtl, Diploma 2008, on zero dimensional algebraic varieties, thesis
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Martin Kreidl, Diploma 2007, on methods of commutative algebra in positive characteristic, thesis
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Eleonore Faber, Diploma 2007, on tame ideals and blowups, thesis
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Dominique Wagner, Diploma 2005, on algebraic power series and division theorems, thesis
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Clemens Bruschek, Diploma 2005, on mappings between formal power series spaces, thesis
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Andreas Hochenegger, Diploma 2004, on Bernstein's theorem, thesis
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PhD. Theses:
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Stefan Perlega, ongoing, on resolution of singularities
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Eleonore Faber, PhD 2011, on normal crossings in singularity theory
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Clemens Bruschek, PhD 2009, on infinite dimensional algebraic geometry and arc spaces
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Dominique Wagner, PhD 2009, on resolution of singularities in positive
characteristic
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Sebastian Gann, PhD 2005, on polynomial solutions of differential
equations
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Dominik Zeillinger, PhD 2005, on resolution of singularities
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