Prof. Dr. Tobias Kaiser

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Assistance:

PD Dr. Lydia Außenhofer

Room 119 IM, Tel.: +49(0)851/509-3059

lydia.aussenhoferuni-passau.de

Sabrina Lehner

Room 245 IM, Tel.: +49(0)851/509-3204

sabrina.lehneruni-passau.de

Our research is fincancially supported by the Deutsche Forschungsgemeinschaft (DFG project KA 3297/1-1: O-minimal structures and their applications to dynamical systems, complex analysis and potential theory).

• Geometrische Eigenschaften von Gevreyfunktionen.
  Diploma thesis, University of Regensburg, 1999.
  
  
• Dirichletregularität in polynomial beschränkten o-minimalen Strukturen auf R.
  Doctoral thesis, Regensburger Mathematische Schriften 31, 2001.
  
  
• An o-minimal version of the Riemann Mapping Theorem and the Dirichlet Problem.
  Habilitation thesis, University of Regensburg, 2006.
  
  

[1] Capacity in subanalytic geometry.
    Illinois Journal of Mathematics 49 (2005), no. 3, 719-736.

[2] On the convergence of integrals in o-minimal structures on archimedean
    real closed fields.
    Annales Polonici Mathernatici 87 (2005), 175-192.

[3] Definability results for the Poisson equation.
    Advances in Geometry 6 (2006), 627-644.

[4] Dirichlet regularity in arbitrary o-minimal structures on the field R up to
    dimension 4.
    Mathematische Nachrichten 279 (2006), no. 15, 1669-1683.

[5] Capacity density of subanalytic sets in higher dimension.
    Potential Analysis 20 (2007), no. 4, 397 - 407.

[6] Real closed graded fields.
    Order 24 (2007), no.2, 107 -120.

[7] Dirichlet regularity of subanalytic domains.
    Transactions of the American Mathematical Society 360 (2008), 6573-6594.

[8] The Riemann Mapping Theorem for semianalytic domains and o-minimality.
    Proceedings of the London Mathematical Society (3) 98, no. 2 (2009), 427-444.

[9] The Dirichlet problem in the plane with semianalytic raw data, quasianalyticity
    and o-minimal struetures.
    Duke Mathematical Journal 147, no. 2 (2009), 285-314.

[10] Transition maps at non-resonant hyperbolie singularities are o-minimal
     (with Jean Philippe Rolin und Patrick Speissegger).
     Journal für die reine and angewandte Mathematik, 636 (2009), 1-45.

[11] Asymptotic Behaviour of the Mapping Function at an Analytic Cusp 
       with small Perturbation of Angles.
      Computational Methods and Function Theory 10, no. 1 (2010), 35-47

[12] Harmonic measure and subanalytically tame measures.
      Journal of Logic and Analysis 2: 7 (2010), 1-29.

[13] Conformal mapping of o-minimal corners.
       Analysis 32 (2012), 1001-1013.

[14] First order tameness of measures.
      Annals of Pure and Applied Logic 163 (2012), 1903-1927

[15] Integration of semialgebraic functions and integrated Nash functions.
       To appear at Mathematische Zeitschrift, 18 p.

• Multivariate Puiseux series induced by a Weierstraß system and twisted group rings.
  Submitted to Communications in Algebra.

• Homogeneous rings and their real spectra (with Niels Schwartz).

• Quasianalytic classes with monomials definable in the real eponential field with restricted analytic functions (with Patrick Speissegger).
  
  
• R-analytic functions.
  

• Manis valuations and Prüfer extensions II (with Manfred Knebusch).
  Submitted to Lecture Notes in Mathematics.

• Geometric properties of Gevrey functions.
  Workshop on metric properties of subanalytic sets, Münster, September 1999.
  
  
• Dirichlet problem on semianalytic domains.
  Spectre et espaces singulieres, Le Bourget-du-Lac, May 2000.
  
  
• Dirichlet regularity in polynomially bounded o-minimal structures on R.
  RAAG 01, Rennes, June 2001.
  
  
• Dirichlet regularity in polynomially bounded o-minimal structures on R.
  Metric geometry and singular spaces, Münster, September 2001.
  
  
• Capacity density of subanalytic sets.
  Reelle algebraische und analytische Geometrie, Mathematisches Forschungsinstitut Oberwolfach, March 2002.
  
  
• Energy and capacity in o-minimal structures.
  Fourth Annual Colloquiumsfest, University of Saskatchewan, Saskatoon,  March 2003.
  
  
• On convergence of integrals in o-minimal structures.
  Annual Network Conference RTN RAAG, Salamanca,  June 2004.
  
  
• An o-minimal version of the Riemann Mapping Theorem.
  Annual Network Conference RTN RAAG, Passau, September 2005.
  
  
• An o-minimal version of the Riemann Mapping Theorem.
  Workshop Topology of Real Algebraic Varieties; semi-algebraic, subanalytic and o-minimal Geometries, Institut Henri Poincaré, Paris, December 2005.
  
  
• An o-minimal version of the Riemann Mapping Theorem.
  Canadian Mathematical Society Summer 2006 Meeting, Calgary,  July 2006.
  
  
• Hilbert 16, Riemann Mapping Theorem and the Dirichlet Problem.
  MODNET Mid-Term Conference, Antalya, November 2006.
  
  
• Hilbert 16, Riemann Mapping Theorem, Dirichlet problem and o-minimality.
  O-minimality: model theory and geometry. MODNET Conference, Haifa,  September 2008.
  
  
• On the resolution of singularities for power series with perturbation by logarithmic terms.
  Workshop on Finiteness Problems in Dynamical Systems. Fields Institute, Toronto, June 2009.

• Spherical blow up.
  O-minimal Structures and Real Analytic Geometry Retrosphective Workshop. Fields Institute, Toronto, August 2011.

• Integration of semialgebraic functions and antiderivatives of Nash functions.
  Emerging developments in Real Algebraic Geometry. Otto-von-Guericke University Magdeburg, February 2012.

• Integration of semialgebraic functions and antiderivatives of Nash functions.
  Model Theory in Wroclaw 2012, Wroclaw, June 2012.

• Classical boundary value problems in real geometry.
  Oberseminar Analysis, University of Würzburg, February 2001.
  
  
• Dirichlet regularity in polynomially bounded o-minimal structures on R.
  Logic Seminar, University of Wisconsin, Madison,  October 2002.
  
  
• Dirichlet regularity in polynomially bounded o-minimal structures on R.
  Research Seminar in logic, Wesleyan University, December 2002.
  
  
• Definability results for the Poisson equation.
  Geometry and model theory seminar, Fields Institute, Toronto, September 2004.
  
  
• Definability results for the Poisson equation.
  Séminaire Equations Différentielles et Théorie du Contrôle, Université de Bourgogne, Dijon, February 2005.
  
  
• An o-minimal version of the Riemann Mapping Theorem and the Dirichlet Problem.
  Model theory seminar, McMaster, Hamilton, October 2005.
  
  
• Hilbert 16, Riemann Mapping Theorem, Dirichlet Problem and o-minimality.
  Logic seminar, University of Oxford, June 2006.
  
  
• Der Riemannsche Abbildungssatz, das Dirichletproblem und o-minimale Strukturen.
  Kolloquium, University of Regensburg, November 2006.
  
  
• Complex analysis and o-minimal structures.
  Geometry and model theory seminar, Ecole Normale Supérieure, Paris, October
  2007.
  
  
• Generation of o-minimal structures by quasianalytic classe.
  Model theory seminar, University of Lyon, March 2008.
  
  
• O-minimale structures. Wie durch Logik Analysis und Geometrie verbunden werden. University of Passau, April 2008.
  
  
• Hilbert 16, Riemann Mapping Theorem, Dirichlet problem and o-minimality.
  Logic and Model theory seminar, University of Illinois at Urbana-Champaign, September 2008.
  
  
• O-minimality of the transition map at non-resonant hyperbolic singularities.
  Thematic Program on O-minimal Structures and Real Analytic Geometry, Fields Institute, Toronto, January 2009.
  
  
• The first order content of the Riemann mapping theorem.
  University of Illinois at Urbana-Champaign, January 2009.
  
  
• Zahme Geometrie und Analysis.
  Oberseminar Geometrische Analysis, University of Frankfurt (Main), January 2010.
  
  
• Der Riemannsche Abbildungssatz und zahme Geometrie.
  Oberseminar Funktionentheorie, University of Würzburg, February 2010.
  
  
• Tame measures.
  Geometry and Model Theory Seminar, Fields Insitute, Toronto, September 2010.
  
  
• Tame measures.
  Logic Seminar, University of Illinois at Urbana-Champaign, September 2010.
  
  
• Tame measures.
  Logic Seminar, University of Oxford, January 2011.
  
  
• Zahme Maße.
  Oberseminar Reelle Geometrie und Algebra, University of Konstanz, May 2011.

• Integration and tameness.
  Colloquium, Istanbul Bilgi University, March 2012.

• Ein algebraisch-geometrischer Riemannscher Abbildungssatz.
  University of Erfurt, July 2012.

• Ein geometrischer Riemannscher Abbildungssatz.
  University of Würzburg, July 2012.
  
  
• A very first step towards an algebraic understanding of the ring of analytic functions that are globally subanalytic.
  Logic seminar, University of Illinois at Urbana-Champaign, November 2012.
  
  
• Integration of semialgebraic functions and antiderivatives of Nash functions.
  Logic seminar, McMaster, Hamilton, November 2012.
  
  
• R-analytic functions.
  Model theory seminar, University of Lyon, March 2013.

Summer Semester 2009:

• Analysis I
• Principles of Mathematics II

Winter Semester 2009/2010:

• Principles of Mathematics I
• Principles of Geometry

Summer Semester 2010:

• Vector Analysis
• Principles of Mathematics II

Winter Semester 2010/2011:

• Linear Algebra I
• Principles of Mathematics I

Summer Semester 2011:

• Linear Algebra II
• Principles of Mathematics II

Winter Semester 2011/2012:

• Introduction to Probability Theory

Summer Semester 2012:

• Vector Analysis
• Principles of Mathematics II

Summer Semester 2013:

• Algebra and Number Theory I
• Prinicples of Mathematics II

no news in this list.