Herwig Hauser

Fakultät für Mathematik

Universität Wien

Oskar-Morgenstern-Platz 1

A-1090 Wien Österreich

Tel.: +43 (0)1 4277 50690

herwig hauser univie ac at

Recent Publications

The classical Artin approximation theorems, Preprint 2016, 35 pp.

Triviality of the formal neighborhood of arcs (with C. Chiu), Preprint 2016, 5 pp. PDF

Indefinite increase of residual order (with S. Perlega), Preprint 2016, 6 pp.

On the structure of varieties of power series in one variable (with S. Woblistin), Preprint 2016, 39 pp. PDF

Characterizing the increase of the residual order under blowup in positive characteristic (with S. Perlega), Preprint 2016, 18 pp. PDF

Gabrielov’s counterexample to nested linear Artin approximation (with M.E Alonso, F.J. Castro-Jiménez, C. Koutschan), Preprint 2016, 6 pp. PDF

Encoding algebraic power series (with M.E. Alonso, F.J. Castro-Jiménez), Preprint 2015, 35 pp. PDF

Resolution of Singularities

Blowups and resolution, in: The resolution of singular algebraic varieties, Clay Mathematics Institute Summer School 2012, Obergurgl, Clay Mathematics Institute Proceedings Volume 20 (2014), 1-80. PDF

Alternative invariants for the embedded resolution of purely inseparable surface singularities (with D. Wagner), L'Enseign Math. 60 (2014), 177–224. 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

Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces (with E. Faber), Bull. Amer. Math. Soc. 47 (2010), 373-417. 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

Platonic Stars (with A. Fritz), Math. Intelligencer 32 (2010), 22-36. PDF

Wild Singularities and Kangaroo Points for the Resolution in Positive Characteristic, Manuscript, 2010, 31 pp. PDF

Resolution Principles. In: 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. 51 pp. 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 (with H.Hauser, J.Lipman, F.Oort, A.Quirós), Educational Progress in Math. 181, Birkhäuser (2000). PDF

Resolution of singularities 1860-1999. In: Resolution of Singularities (with H.Hauser, J.Lipman, F.Oort, A.Quirós), Educational Progress in Math. 181, Birkhäuser (2000). PDF

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

Artin approximation (with G. Rond), Preprint 2015, 74 pp. PDF

Multivariate linear recurrences and power series division (with C. Koutschan), Discrete Math. 312 (2012), 3553-3560. PDF

Arcs, Cords and Felts: Six Instances of the Linearization Principle (with C. Bruschek), Amer. J. Math. 132 (2010), 941-986. PDF

Perfect bases for differential equations (with S. Gann). J. Symb. Comp. 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 (1989), 295-307. 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. PDF

Analytic curves in power series rings (with G. Müller). Compos. Math. 76 (1990), 197-201. PDF

Automorphism groups in local analytic geometry, infinite dimensional rank theorem and Lie groups (with G. Müller). Comptes Rendus Acad. Sci. 313, série I (1991), 751-756. PDF

Sur la construction de la déformation semi-universelle d'un germe d'espace analytique. Ann. Éc. Norm. Sup. Paris 18 (1985), 1-56. PDF

An algorithm of construction of the semi-universal deformation of an isolated singularity. Proc. Symp. Pure Appl. Math. Amer. Math. Soc. 40 (1983), 567-573.

Sur la déformation semi-universelle d'une singularitée isolée. Thèse de Troisième 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. PDF

Lie algebras of polynomial vector fields and the Jacobian conjecture (with G. Müller). Monatshefte 126 (1998), 211-213. PDF

On the Lie algebra Θ(X) of vector fields on a singularity (with G. Müller). J. Math. Sci. Univ. Tokyo 1 (1994), 239-250. PDF

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. PDF

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. PDF

Singularities in Complex Analytic Geometry

The cancellation property for direct products of analytic space germs (with G. Müller). Special volume: 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 algébrique et applications (ed.: Aroca et al.), II. Singularités et géométrie 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.


The Resolution of Singular Algebraic Varieties, Obergurgl 2012 (eds. D. Ellwood, H. Hauser, S. Mori, J. Schicho), Clay Mathematics Proceedings vol. 20, Amer. Math. Soc. 2012.

Resolution of Singularities, Obergurgl 1997 (eds. H. Hauser, J. Lipman, F. Oort, A. Quiros), Progress in Mathematics vol. 181, Birkhäuser 2000.

Bilderbuch der Singularitäten, 2010, 80 pp.

Grants & Projects

Chaire Jean-Morlet, Aix-Marseille University und CIRM, Spring 2015: Special semester on Artin Approximation

FWF-Project P-25652 "Resolution of Singularities", 2013-2018

Clay Summer School 2012 "Resolution of Singularities", Obergurgl June 2012

FWF-ANR-Project "Approximation Theorems in algebra and Cauchy-Riemann geometry: When Michael Artin meets Henri Poincaré" 2010-2014; with B. Lamel, N. Mir

FWF-Project P-21461 "Solving Algebraic Equations II" 2009-2013; with J. Schicho

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


Curriculum Vitae

1956 Born in Innsbruck, Austria. Austrian citizen. Married, three children

1974 - 80 Studies at the Universities of Innsbruck and Paris

1980 - PhD 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

1988 - 2007 Associate Professor at the University of Innsbruck

1992 - 94 Visiting Professor at the Universidad Autónoma de Madrid

2007 - present Professor at the University of Vienna, on extended leave from the University of Innsbruck

2015 Chaire Jean Morlet, Aix-Marseille University und CIRM, Spring 2015

Master Theses:

Hana Kovácová, Master 2016, on resolution of curves via higher curvatures, PDF

Valerie Roitner, Master 2015, on lattice walks and generating functions, PDF

Christopher Chiu, Master 2015, on Zariski's Main Theorem, PDF

Markus Müller, Master 2014, on the Rogers-Ramanujan identity, PDF

Alexandra Fritz, Diploma 2010, on platonic stars and invariant theory, PDF

Matthias Schiechtl, Diploma 2008, on zero dimensional algebraic varieties, PDF

Martin Kreidl, Diploma 2007, on methods of commutative algebra in positive characteristic, PDF

Eleonore Faber, Diploma 2007, on tame ideals and blowups, PDF

Dominique Wagner, Diploma 2005, on algebraic power series and division theorems, PDF

Clemens Bruschek, Diploma 2005, on mappings between formal power series spaces,

Andreas Hochenegger, Diploma 2004, on Bernstein's theorem, PDF

PhD. Theses:

Christopher Chiu, on the geometry of arc spaces, ongoing

Stefan Perlega, on resolution of singularities in positive characteristic, ongoing

Eleonore Faber, PhD 2011, on normal crossings in singularity theory PDF

Clemens Bruschek, PhD 2009, on infinite dimensional algebraic geometry and arc spaces PDF

Dominique Wagner, PhD 2009, on resolution of surfaces in positive characteristic PDF

Sebastian Gann, PhD 2005, on polynomial solutions of differential equations PDF

Dominik Zeillinger, PhD 2005, on resolution of singularities and the polyhedral game PDF

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