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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Resolution Principles. Proceedings of Clay Research Conference 2009, to appear. PDF
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Wild Singularities and Kangaroo Points for the Resolution in Positive Characteristic, Preprint, 2009, 18 pp. PDF
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Two new Invariants for the Resolution of Surfaces in Positive Characteristic (with D. Wagner), Preprint, 2009, 35 pp. PDF
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Arcs, Cords and Felts: Six Instances of the Linearization Principle (with C. Bruschek). to appear in American Journal of Mathematics, 2010, 38 pp. PDF
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Platonic Stars (with A. Fritz), Math. Intelligencer, to appear. 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. 2010, Vol. 47,1; p.1-30. PDF
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Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces (with E. Faber), Bull. Amer. Math. Soc. 2010, to appear. PDF
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Plain Varieties (with G. Bodnar, J. Schicho, O. Villamayor), Bull. London Math. Soc. 40 (2008), 965-971. PDF
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| Linear Recurrences and Power Series Division (with C. Koutschan). Preprint, 2008.
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Resolution of Singularities
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Desingularization of ideals and varieties, Proceedings Winter School on Resolution of Singularities, Marseille 2005 (ed. Anne Pichon), 37 pp
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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, pp 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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Three power series techniques. Proc. London Math. Soc. 88 (2004), 1-24.
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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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Division Theorems
| Perfect bases for differential equations (with Sebastian Gann). Journal of Symbolic Computation 40 (2005), 979-997
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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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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.
PS PDF
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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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DVI
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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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Infinite Dimensional Geometry and Applications to Singularity Theory
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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
DVI
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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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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, 209-223 (1990).PDF
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The trivial locus of an analytic map germ (with G. Müller). Ann. Inst. Fourier 39, 831-844 (1989).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, 181-186 (1989).
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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, 427-447 (1985). PDF
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On the singular subspace of an analytic variety. Adv. Studies Pure Math. 8, 125-134 (1986).
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Simplification et factorisation unique des germes d'espaces analytiques complexes (with G. Müller). Comptes Rendus Acad. Sci. 309, série I,
617-619 (1989).
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Miscellaneous
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Book Review on "Resolution of Curve and Surface Singularities. Algebras and Applications" by K. Kiyek, J. L. Vicente, Bull. Amer. Math. Soc. 2006
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Report on the problem session (with D. Randell). In: Singularities Iowa 1986 (ed. D. Randell), Contemporary Mathematics vol 90.
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Alemanual para matemáticos. Deutschbuch für spanische Mathematiker zur Lektüre deutscher Mathematik-Texte. Universidad Autónoma de Madrid 1994.
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Algebra 1. Vorlesungsskriptum WS2004/2005, Universität Innsbruck. Vorlesung
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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-Projekt P-15551 "Explicit Resolution and Related Methods in Algebraic Geometry and Number Theory" 2002-2006
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FWF-Projekt P-18992 "Solving Algebraic Equations" 2006-2009
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FWF-Projekt P-21461 "Solving Algebraic Equations II" 2009-2012
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FWF-ANR-project "Approximation Theorems in algebra and Cauchy-Riemann geometry:
When Michael Artin meets Henri Poincaré" (with B. Lamel, N. Mir)
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Ausstellung "IMAGINARY"
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Enzensberger Stern - Medienpreis der DMV für Hans Magnus Enzensberger, Berlin, 12/2006
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| Artikel: Algebraisches Origami - Die Schönheit der Mathematik, Frankfurter Allgemeine Zeitung online,12/2006:
faz.net
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Artikel: Formeln zum Abfeiern, Wissenschaftsteil der Frankfurter Allgemeine Zeitung am Sonntag,12/2006
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Artikel: Enzensberger Stern, iPoint Universität Innsbruck,12/2006:
iPoint
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Artikel: Jetzt wird abgerechnet, Süddeutsche Zeitung Magazin 02/2006
Süddeutsche Zeitung
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Artikel: La Recherche 02/2006: La Recherche - L'Actualité des Sciences
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| TV-Beitrag: Mathematischer Adventkalender, Tirol heute, ORF Tirol, 12/2005 |
| Artikel: Katastrophentheorie, Wissenschaftsteil Profil Nr.15/2004, 04/2004:
JPG EPS |
| Artikel: Wie man einen Knäuel
entwirrt, Die Presse online, 03/2004:
Die Presse |
| Artikel: Vereinfacht: Problem
mathematischer Singularitäten, Wissenschaftsseite des ORF,
02/2004: .
science.orf.at |
| Artikel: Auflösung von
Singularitäten, Der Standard online, 02/2004: . Der Standard |
| Artikel: Mathematiker rechnen
Un(be)rechenbares, ORF Tirol, 02/2004:
tirol.orf.at |
| Interview: Singularitäten, OE1,
Wissen aktuell, 02/2004:
MP3 |
| Artikel: Durchschlagender Erfolg
für Innsbrucker Mathematik, iPoint Universität Innsbruck,
01/2004: .
iPoint |
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1956 Born and grown up in Innsbruck, Austria. 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 Professer at the University of Innsbruck
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1992 - 94 Visiting Universidad Autónoma de Madrid
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2002 - 06 FWF-project "Explicit Resolution and Related Methods in Algebraic Geometry and Number
Theory" (with J. Schicho)
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2006 Movie "ZEROSET - I spy with my little eye" at the ICM at Madrid
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2006 - 09 FWF-project "Solving Algebraic Equations" (with J. Schicho)
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2007 - Professor at the University of Vienna
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2008 Exposition series "IMAGINARY" with Mathem. Forschungsinstitut
Oberwolfach
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2009 - 12 FWF-project "Solving Algebraic Equations II" (with J. Schicho)
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2010 - 13 FWF-ANR-project "Approximation Theorems in algebra and Cauchy-Riemann geometry:
When Michael Artin meets Henri Poincare" (with B. Lamel, N. Mir)
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PhD students:
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Dominik Zeillinger, PhD 2005, on resolution of singularities
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Sebastian Gann, PhD 2005, on polynomial solutions of differential
equations
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Dominique Wagner, PhD 2009, on resolution of singularities in positive
characteristic
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Clemens Bruschek, PhD 2009, on infinite dimensional algebraic geometry and arc spaces
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Eleonore Faber: Singularity theory
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