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

Publikationen

Projekte

Curriculum Vitae

Vorträge

Visualisierungen

Skripten






Recent Papers

Resolution Principles. Proceedings of Clay Research Conference 2009, to appear. PDF
Wild Singularities and Kangaroo Points for the Resolution in Positive Characteristic, Preprint, 2009, 18 pp. PDF
Two new Invariants for the Resolution of Surfaces in Positive Characteristic (with D. Wagner), Preprint, 2009, 35 pp. PDF
Arcs, Cords and Felts: Six Instances of the Linearization Principle (with C. Bruschek). to appear in American Journal of Mathematics, 2010, 38 pp. PDF
Platonic Stars (with A. Fritz), Math. Intelligencer, to appear. PDF
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
Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces (with E. Faber), Bull. Amer. Math. Soc. 2010, to appear. PDF
Plain Varieties (with G. Bodnar, J. Schicho, O. Villamayor), Bull. London Math. Soc. 40 (2008), 965-971. PDF
Linear Recurrences and Power Series Division (with C. Koutschan). Preprint, 2008. PDF


Resolution of Singularities

Desingularization of ideals and varieties, Proceedings Winter School on Resolution of Singularities, Marseille 2005 (ed. Anne Pichon), 37 pp PDF
Seven short stories on blowups and resolution. Proceedings Gökova Conference on Geometry and Topology 2005 (ed. Selman Akbulut), International Press 2006, pp 1-48 PDF
Explizite Auflösung von ebenen Kurvensingularitäten in beliebiger Charakteristik (with G. Regensburger). L'Enseign. Math. 50 (2004), 305-353. PDF
Three power series techniques. Proc. London Math. Soc. 88 (2004), 1-24. PS PDF
Why the characteristic zero proof of resolution of singularities fails in positive characteristic. Manuscript 2003. 51pp PDF
The Hironaka Theorem on resolution of singularities (Or: A proof that we always wanted to understand). Bull. Amer. Math. Soc. 40 (2003), 323-403. PS PDF
Strong resolution of singularities in characteristic zero (with S. Encinas). Commentarii Math. Helvetici 77(2002), 421-445. PS PDF
Excellent surfaces and their taut resolution. In: Resolution of Singularities, Progress in Math. 181, Birkhäuser (2000).
Resolution of singularities 1860-1999. In: Resolution of Singularities, Progress in Math. 181, Birkhäuser (2000).
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
Blowup-Algebra. Contribution to the Encyclopaedia of Mathematics. Kluwer (1997).


Division Theorems

Perfect bases for differential equations (with Sebastian Gann). Journal of Symbolic Computation 40 (2005), 979-997 PDF
Continuous division for differential operators (with L. Narváez). Ann. Inst. Fourier 51 (2001), 769-778.PDF
Comparing modules of differential operators by their evaluation on polynomials. Compos. Math. 69, 295-307 (1989). PDF


Vector Fields in Algebraic Geometry

The reduced Bautin index of planar vector fields (with J.-J. Risler, B. Teissier). Duke J. Math. 100 (2000), 425-446. PS PDF
Dérivations et idéaux réels invariants (with J.-J. Risler). Publ. RIMS, Kyoto Univ. 35 (1999), 585 - 598.
Lie algebras of polynomial vector fields and the Jacobian conjecture (with G. Müller). Monatshefte 126 (1998), 211-213.
On the Lie algebra Θ(X) of vector fields on a singularity (with G. Müller). J. Math. Sci. Univ. Tokyo 1 (1994), 239-250. PS DVI
Affine varieties and Lie algebras of vector fields (with G. Müller). Manuscr. Math. 80 (1993), 309-337. PDF
Analytic varieties versus integral varieties of Lie algebras of vector fields (with G. Müller). Bull. Amer. Math. Soc. 26 (1992), 276-279. PS
Frobenius type theorems and the Gröbner correspondence (with G. Müller). In: Congrès Singularités, Lille 1991 (ed. J.-P. Brasselet), IRMA, Université de Lille.
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.


Infinite Dimensional Geometry and Applications to Singularity Theory

A rank theorem for analytic maps between power series spaces (with G. Müller). Publ. Math. I.H.E.S. 80 (1994), 95-115. PS PDF
Semi-universal unfoldings and orbits of the contact group (with. G. Müller). Abh. Math. Sem. Hamburg 66 (1996), 1-9. PS DVI
Analytic curves in power series rings (with G. Müller). Compos. Math. 76 (1990), 197-201.PDF
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.
Sur la construction de la déformation semi-universelle dún germe déspace analytique. Ann. Éc. Norm. Sup. Paris 18, 1-56 (1985).PDF
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).
Sur la déformation semi-universelle d'une singularitée isolée. Thése de Troisiéme Cycle, Université Paris-Sud, Orsay, 1980.


Singularities in Complex Analytic Geometry

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
The trivial locus of an analytic map germ (with G. Müller). Ann. Inst. Fourier 39, 831-844 (1989).PDF
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).
Algebraic singularities have maximal reductive automorphism groups (with G. Müller). Nagoya Math. J. 113, 181-186 (1989).
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.
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.
Characterizing singularities of varieties and of mappings (with T. Gaffney). Invent. math. 79, 427-447 (1985). PDF
On the singular subspace of an analytic variety. Adv. Studies Pure Math. 8, 125-134 (1986).
Simplification et factorisation unique des germes d'espaces analytiques complexes (with G. Müller). Comptes Rendus Acad. Sci. 309, série I, 617-619 (1989).


Miscellaneous

Book Review on "Resolution of Curve and Surface Singularities. Algebras and Applications" by K. Kiyek, J. L. Vicente, Bull. Amer. Math. Soc. 2006
Report on the problem session (with D. Randell). In: Singularities Iowa 1986 (ed. D. Randell), Contemporary Mathematics vol 90.
Alemanual para matemáticos. Deutschbuch für spanische Mathematiker zur Lektüre deutscher Mathematik-Texte. Universidad Autónoma de Madrid 1994.


Skripten

Algebra 1. Vorlesungsskriptum WS2004/2005, Universität Innsbruck. Vorlesung PDF
Kombinatorik. Vorlesungsskriptum und Proseminar 2003, Universität Innsbruck. PDF Proseminar PDF
Funktionalanalysis. Vorlesungsskriptum 2002, Universität Innsbruck. PDF
Ideals, blowups and resolution. Vorlesungsskriptum 2001, Universität Innsbruck.
Der Satz von Frobenius in der Kontrolltheorie. Vorlesungsskriptum 1997, Universität Innsbruck.


Projekte

FWF-Projekt P-15551 "Explicit Resolution and Related Methods in Algebraic Geometry and Number Theory" 2002-2006
FWF-Projekt P-18992 "Solving Algebraic Equations" 2006-2009
FWF-Projekt P-21461 "Solving Algebraic Equations II" 2009-2012
FWF-ANR-project "Approximation Theorems in algebra and Cauchy-Riemann geometry: When Michael Artin meets Henri Poincaré" (with B. Lamel, N. Mir)


Vorträge

Lecture on Resolution, Clay Institute 2009

Visualisierungen



Bildergalerie

Animationen von Flächen

Kalender der Singularitäten

Platonischer Stern

Ausstellung "IMAGINARY"
Enzensberger Stern - Medienpreis der DMV für Hans Magnus Enzensberger, Berlin, 12/2006


Artikel: Algebraisches Origami - Die Schönheit der Mathematik, Frankfurter Allgemeine Zeitung online,12/2006: faz.net
Artikel: Formeln zum Abfeiern, Wissenschaftsteil der Frankfurter Allgemeine Zeitung am Sonntag,12/2006
Artikel: Enzensberger Stern, iPoint Universität Innsbruck,12/2006: iPoint
Artikel: Jetzt wird abgerechnet, Süddeutsche Zeitung Magazin 02/2006 Süddeutsche Zeitung
Artikel: La Recherche 02/2006: La Recherche - L'Actualité des Sciences
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


Curriculum Vitae

1956 Born and grown up in Innsbruck, Austria. Married, three children
1974 - 80 Studies at the Universities of Innsbruck and Paris
PhD 1980 in Paris with Teissier and Douady on the semi-universal deformation of singularities
1980 - 88 Assistent professor at the University of Innsbruck
1982 - 84 Visiting Brandeis and Northeastern University
1988 Habilitation in singularity theory
1988 - 2007 Associate Professer at the University of Innsbruck
1992 - 94 Visiting Universidad Autónoma de Madrid
2002 - 06 FWF-project "Explicit Resolution and Related Methods in Algebraic Geometry and Number Theory" (with J. Schicho)
2006 Movie "ZEROSET - I spy with my little eye" at the ICM at Madrid
2006 - 09 FWF-project "Solving Algebraic Equations" (with J. Schicho)
2007 - Professor at the University of Vienna
2008 Exposition series "IMAGINARY" with Mathem. Forschungsinstitut Oberwolfach
2009 - 12 FWF-project "Solving Algebraic Equations II" (with J. Schicho)
2010 - 13 FWF-ANR-project "Approximation Theorems in algebra and Cauchy-Riemann geometry: When Michael Artin meets Henri Poincare" (with B. Lamel, N. Mir)


PhD students:
Dominik Zeillinger, PhD 2005, on resolution of singularities
Sebastian Gann, PhD 2005, on polynomial solutions of differential equations
Dominique Wagner, PhD 2009, on resolution of singularities in positive characteristic
Clemens Bruschek, PhD 2009, on infinite dimensional algebraic geometry and arc spaces
Eleonore Faber: Singularity theory




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