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 and Preprints

Phylogenetic trees and the moduli of n points on the projective line (with J. Qi and J. Schicho), forthcoming Preprint 2023, 50 pp.

Fuchs' theorem on ordinary linear differential equations in arbitrary characteristic (with F. Fürnsinn), Preprint 2023, 40 pp. PDF

A normal form theorem for Fuchsian differential equations over fields of characteristic zero. Manuscript 2022. PDF

How regular are regular singularities? In: Proceedings of Transient Transcendence in Transylvania, Brasov 2019 (eds. A. Bostan, K. Raschel). Springer 2021 PDF

Arquile varieties - varieties consisting of power series in a single variable (with S. Woblistin). Forum Math. Sigma 9 (2021), 1-39. PDF

Algebraic power series. Lecture Notes 2018, 60 pp.

Algebraic Aspects of Fuchsian Differential Equations. Monograph 2020, 160 pp.

Isosingular loci of algebraic varieties (with C. Chiu). J. Pure Applied Algebra 226 (2022), art. 107131. PDF

On the formal neighborhood of degenerate arcs (with C. Chiu), Manuscript, 9 pp. PDF

Resolving surface singularities in positive characteristic (with S. Perlega), Publications RIMS, 29 pp, to appear.

Resolution of Singularities

Cycles of singularities appearing in the resolution problem in positive characteristic (with S. Perlega), J. Algebraic Geometry 28 (2019), 391-403. PDF

Characterizing the increase of the residual order under blowup in positive characteristic (with S. Perlega), Publications RIMS 55 (2019), 835-857. PDF

Blowups and resolution, in: The resolution of singular algebraic varieties, Clay Mathematics Institute Summer School 2012, Obergurgl. CMI series, Amer. Math. Soc. 2014, pp. 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

Encoding algebraic power series (with M.E. Alonso, F.J. Castro-Jiménez), Found. Comp. Math. 18 (2018), 789-833. PDF

Echelons of power series and Gabrielov’s counterexample to nested linear Artin approximation (with M.E Alonso, F.J. Castro-Jiménez, C. Koutschan), Bull. London Math. Soc. (2018), 635-648. PDF

The classical Artin approximation theorems, Bull. Amer. Math. Soc. 54 (2017), 595-633. PDF

Corrigendum to "The classical Artin approximation theorems", Bull. Amer. Math. Soc. 55 (2018), 289-293. PDF

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

FWF-Project P-34765 "Algebraic Aspects of Fuchsian Differential Equations", 2021-2025

FWF-Project P-31338 "Artin Approximation, Arc Spaces, and Resolution of Singularities", 2018-2021

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

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

2007 - 2021 Professor at the University of Vienna

2021 - present Mathematician & Researcher

PhD Theses:

Florian Fürnsinn, on ordinary linear differential equations in positive characteristic, ongoing

Sergey Yurkevich, PhD 2023, on integer sequences, algebraic series and differential operators, PDF

Hana Melánová, PhD 2020, on the curvature of singular algebraic surfaces PDF

Christopher Chiu, PhD 2020, on the geometry of arc spaces PDF

Stefan Perlega, PhD 2018, on resolution of singularities in positive characteristic PDF

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

Master Theses:

Nicholas Merkl Master 2022, on ordinary linear differential equations with irregular singularities, PDF

Florian Fürnsinn Master 2022, on normal forms of ordinary linear differential equations, PDF

Johannes Droschl Master 2020, on blowups in monomial ideals and stacks, PDF

Sergey Yurkevich, Master 2020, on algebraic power series in zero characteristic, PDF

David Stinner, Master 2020, on Hilbert functions and polynomials

Hana Melánová, 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

Online Lectures: Fuchsian Differential Equations, Vienna, Fall 2022

Trailer watch

Lecture 1 watch

Description Lecture 1

Lecture 2 watch

Description Lecture 2

Lecture 3 watch

Description Lecture 3

Lecture 4 watch

Description Lecture 4

Lecture 5 watch

Description Lecture 5

Lecture 6 watch

Description Lecture 6

Lecture 7 watch

Description Lecture 7

Lecture 8 watch

Description Lecture 8

Lecture 9 watch

Description Lecture 9

Lecture 10 watch

Description Lecture 10

Lecture 11 watch

Description Lecture 11

Lecture 12 watch

Description Lecture 12

last modified 10/16/2016 21:26:4310/16/2016 21:26:00
eXTReMe Tracker