Herwig Hauser


Fakultät für Mathematik
Universität Wien
Oskar-Morgenstern-Platz 1
A-1090 Wien
Österreich

Tel.:(+43)-1-4277-50690
Fax: (+43)-1-4277-9506
Herwig.Hauser@univie.ac.at

Publications

Curriculum Vitae

Visualizations

Dodecahedral Star

Positions

Grants & Projects

Master & PhD. Theses

Lecture Notes






Recent Papers

Artin Approximation (with G. Rond), Manuscript 2013, 67 pp. PDF
Blowups and resolution, Proc. of the Clay Summer School 2012, to appear, 60 pp. PDF
Multivariate linear recurrences and power series division (with C. Koutschan), Discrete Math. 312 (2012), 3553-3560. PDF
Encoding algebraic power series (with M.E. Alonso, F.J. Castro-Jiménez), Manuscript 2014, 35 pp. PDF
A game for the resolution of singularities (with J. Schicho), Proc. London Math. Soc. 105 (2012), 1149-1182. PDF
Forty Questions on Singularities (with J. Schicho), Asian J. Math. 15 (2011), 417-436 PDF
Wild Singularities and Kangaroo Points for the Resolution in Positive Characteristic, Manuscript, 2010, 31 pp. PDF
Arcs, Cords and Felts: Six Instances of the Linearization Principle (with C. Bruschek); Amer. J. Math., 132 (2010), 941-986. PDF
Platonic Stars (with A. Fritz), Math. Intelligencer, 32 (2010), 22-36. PDF
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
Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces (with E. Faber), Bull. Amer. Math. Soc. 47 (2010), 373-417. PDF


Resolution of Singularities

Two alternative Invariants for the Embedded Resolution of Surface Singularities in Positive Characteristic (with D. Wagner), L'Enseignement Math., to appear, 35 pp. PDF
Resolution Principles. Proceedings of Clay Research Conference 2009 PDF
Plain Varieties (with G. Bodnár, J. Schicho, O. Villamayor), Bull. London Math. Soc. 40 (2008), 965-971. PDF
Desingularization of ideals and varieties, In: Singularity Theory, Marseille 2005 (ed. Anne Pichon), pp. 33-69. World Sci. Publ. 2007 PDF
Seven short stories on blowups and resolution. Proceedings Gökova Conference on Geometry and Topology 2005 (ed. Selman Akbulut), International Press 2006, 1-48 PDF
Explizite Auflösung von ebenen Kurvensingularitäten in beliebiger Charakteristik (with G. Regensburger). L'Enseign. Math. 50 (2004), 305-353. 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. PDF
Strong resolution of singularities in characteristic zero (with S. Encinas). Commentarii Math. Helvetici 77 (2002), 421-445. 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).


Commutative Algebra and Infinite Dimensional Geometry

Perfect bases for differential equations (with Sebastian Gann). Journal of Symbolic Computation 40 (2005), 979-997. PDF
Three power series techniques. Proc. London Math. Soc. 88 (2004), 1-24. 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
A rank theorem for analytic maps between power series spaces (with G. Müller). Publ. Math. I.H.E.S. 80 (1994), 95-115. PDF
Semi-universal unfoldings and orbits of the contact group (with. G. Müller). Abh. Math. Sem. Hamburg 66 (1996), 1-9. PS
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.


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. 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
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.


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 (1990), 209-223. PDF
The trivial locus of an analytic map germ (with G. Müller). Ann. Inst. Fourier 39 (1989), 831-844. 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 (1989), 181-186.
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, (1985) 427-447. PDF
On the singular subspace of an analytic variety. Adv. Studies Pure Math. 8 (1986), 125-134.
Simplification et factorisation unique des germes d'espaces analytiques complexes (with G. Müller). Comptes Rendus Acad. Sci. 309, série I (1989), 617-619.




Lecture Notes

Algebra & Geometrie, 2013, Universität Wien.
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.


Grants & Projects

FWF-Project P-15551 "Explicit Resolution and Related Methods in Algebraic Geometry and Number Theory" 2002-2006; with J. Schicho
FWF-Project P-18992 "Solving Algebraic Equations" 2006-2009; with J. Schicho
FWF-Project P-21461 "Solving Algebraic Equations II" 2009-2013; with J. Schicho
FWF-ANR-Project "Approximation Theorems in algebra and Cauchy-Riemann geometry: When Michael Artin meets Henri Poincaré" 2010-2014; with B. Lamel, N. Mir
Clay Summer School 2012 "Resolution of Singularities", Obergurgl June 2012
FWF-Project P-25652 "Resolution of Singularities", 2013-2016



Visualizations

Docahedral Star

Gallery of Singularities

Sculptures

Platonic stars

Expositions



Curriculum Vitae

1956 Born in Innsbruck, Austria. Austrian citizen. 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 Professor at the University of Innsbruck
1992 - 94 Visiting Professor at the Universidad Autónoma de Madrid
2006 Presentation of the movie "ZEROSET - I spy with my little eye" at the ICM at Madrid
2007 - Professor at the University of Vienna, on extended leave from the University of Innsbruck
2008 Exposition series "IMAGINARY" organized by Mathem. Forschungsinstitut Oberwolfach
2011 Organization of the special program "Algebraic versus Analytic Geometry" at the Erwin-Schrödinger-Institute, Vienna
2012 Organization of the Clay Summer School on Resolution of Singularities, Obergurgl, Austria


Master & PhD. Theses

Diploma/Master Theses:

Christopher Chiu, ongoing, on Noether normalization and Zariski's Main Theorem
Markus Müller, ongoing, on the Rogers-Ramanujan identity
Alexandra Fritz, Diploma 2010, on platonic stars and invariant theory, thesis
Matthias Schiechtl, Diploma 2008, on zero dimensional algebraic varieties, thesis
Martin Kreidl, Diploma 2007, on methods of commutative algebra in positive characteristic, thesis
Eleonore Faber, Diploma 2007, on tame ideals and blowups, thesis
Dominique Wagner, Diploma 2005, on algebraic power series and division theorems, thesis
Clemens Bruschek, Diploma 2005, on mappings between formal power series spaces, thesis
Andreas Hochenegger, Diploma 2004, on Bernstein's theorem, thesis


PhD. Theses:

Stefan Perlega, ongoing, on resolution of singularities
Eleonore Faber, PhD 2011, on normal crossings in singularity theory
Clemens Bruschek, PhD 2009, on infinite dimensional algebraic geometry and arc spaces
Dominique Wagner, PhD 2009, on resolution of singularities in positive characteristic
Sebastian Gann, PhD 2005, on polynomial solutions of differential equations
Dominik Zeillinger, PhD 2005, on resolution of singularities




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