Professor Peter Alexander Markowich

Career

  • 1979-80: Research Assistant, IIASA (International Institute for Applied Systems Analysis); Laxenburg, Austria
  • 1980-81: Research Assistant, Mathematics Research Center, University of Wisconsin-Madison, USA
  • 1981-82: Assistant Professor, Mathematics Department and Computer Science Department, University of Texas at Austin, USA
  • 1982-1989: Assistant Professor, Institute for Applied and Numerical Mathematics, TU-Vienna
  • 1989: Visiting Professor, Centre des Mathematiques Appliquées, Ecole Polytechnique, Paris
  • 1989-1990: Professor (C3), Department of Mathematics, TU Berlin
  • 1990-91: Full Professor, Department of Mathematics, Purdue University, West Lafayette, USA
  • 1991-98: Professor (C4), Department of Mathematics, TU Berlin
  • 1998-99: O.- Univ. Professor of Analysis, Institute of Analysis and Numerical Mathematics, Johannes Kepler Universität Linz, Austria
  • 1999-: O.- Univ. Professor of Applied Analysis, Department of Mathematics, University of Vienna
  • 2007- : Professor of Applied Mathematics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge and  Professor of Applied Analysis, Faculty of Mathematics, University of Vienna

Awards and Honours

  • 2000: Wittgenstein Award of the Austrian Science Fund
  • 2003: Plenary Lecture: ICIAM 2003 (5th International Congress on Industrial and Applied Mathematics, Sydney, Australia)
  • 2004: Seminario Matematico e Fisico di Milano
  • 2005: Corresponding Member of the Austrian Academy of Sciences
  • 2005: Japan Society for the Promotion of Science, Invitation Fellowship at Kyoto University
  • 2007: Royal Society Wolfson Research Merit Award
  • 2008: Inaugural KAUST Investigator Award
  • 2009: elected Professorial Fellow of Clare Hall
  • 2009: Ramanujan Memorial Lecture at the Saha Institute Kolkata
  • 2009: Humboldt Research Award
  • 2010: Invited Lecture at the ICM 2010 (International Congress of Mathematicians 2010, Hyderabad, India)
  • 2010: Wolfgang Wasow Memorial Lecture, University of Wisconsin Madison
  • 2011: Matheon Lectures, Berlin
  • 2011: Excellence Chair of the Fondation Sciences Mathématiques de Paris

Research

Applied Partial Differential Equations: Analysis, Numerics and Modeling.

  • nonlinear Schrödinger equations
    • high frequency asymtotics: WKB methods and Wigner functions,
    • Gross-Pitaevskii equation,
    • electron dynamics in crystals and nanostructures,
    • nonlinear wave propagation,
    • dispersion estimates,
    • spectral-time splitting discretisations.
  • classical and quantum kinetic equations
    • entropy dissipation techniques and convex Sobolev inequalities,
    • simulations of Bose-Einstein condensates,
    • quantum scattering in semiconductors: Boltzmann equation,
    • collective behaviour of swimming mirco-organismns and chemotaxis,
    • kinetics and mean field models for human crowding behaviour, Pareto economics and opinion formation in human societies,
    • mean-field limits.
  • reaction-diffusion/convection systems
    • drift and diffusion of charge carries in semiconductors,
    • large-time asymptotics
    • finte element discretisations.

Selected Recent Publications

  • P.A.Markowich, T.Paul, C.Sparber, Bohmian measures and their classical limit, J. Funct. Anal. 259, pp 1542 - 1576, 2010
  • P.A.Markowich, Numerical Analysis of Schrödinger Equations in the Highly Oscillatory Regime, Proc. ICM, Hyderadab, 2010
  • M. Di Francesco, K. Fellner, P.A.Markowich, The entropy dissipation method for spatially inhomogeneous reactiondiffusion-type systems, Proceedings of the Royal Society A: Mathematical, Physical and  Engineering Sciences, Volume 464, Number 2100 / December 08, 2008
  • P.A. Markowich, Applied Partial Differential Equations: A Visual Approach, Springer- Verlag, Wien-New York, 2006
  • J. Dolbeault, P.A. Markowich, D. Ölz and C. Schmeiser, Nonlinear Diffusions as Limit of Kinetic Equations with Relaxation Collision Kernels, Archive Rational Mechanics and Anal., 2007
  • C. Klein, C. Sparber and P.A. Markowich, Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation, J. Nonlinear Science, Vol. 17, Issue 5, pp 429-470, 2007
  • Z. Huang, S. Jin, P.A. Markowich and C. Sparber, A Bloch Decomposition based Numerical method for Quantum Dynamics in Periodic Potentials, SIAM J. Sci. Comp., Vol. 29, pp 515-538, 2007
  • S. Wang, Z. Xin & P.A. Markowich, Quasineutral Limit of the Drift Diffusion Models for Semiconductors: The Case of General Sign-changing Doping Profile, SIAM. J. Math. Anal., Volume 37, Issue 6, pp 1854-1889, 2005
  • A. Arnold, J. A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel, C. Lederman, P. A. Markowich, G. Toscani & C. Villani, Entropies and Equilibria of Many- Particle Systems: An Essay on Recent Research, Monatshefte für Mathematik, vol. 142, No 1-2, pp 35-43, 2004
  • W. Bao, D. Jaksch and P. A. Markowich, Three Dimensional Simulation of Jet Formation in Collapsing Condensates, J. Physics B: At.Mol.Opt.Phys., Vol. 37, No.2, pp. 329-343, 2004
  • F. A. C. C. Chalub, P. A. Markowich, B. Perthame and C. Schmeiser, Kinetic Models for Chemotaxis and their Drift-Diffusion Limits, Monatshefte für Mathematik, Vol. 142, No.1/ 2, pp 123-141, 2004