Workgroup Numerics

Dr. rer. nat. Markus Weimar

Philipps-University Marburg
Faculty of Mathematics and Computer Science
Workgroup Numerics and Optimization
Hans-Meerwein-Straße
Lahnberge
35032 Marburg, Germany

Office: Level D6 - 14 (06D14)
Consultation Hour: by appointment
Phone: +49 (0) 6421 / 28-27058
Fax: +49 (0) 6421 / 28-26945
E-mail: weimar (at) mathematik.uni-marburg.de

University of Siegen
Department of Mathematics
Workgroup Numerics
Emmy-Noether-Campus (ENC)
Walter-Flex-Straße 3
57068 Siegen

Office: ENC-B 302 (Level 3)
Consultation Hours: Lecture Period: Fri 12:30-1:30 pm, ENC-B 302,
and by appointment
Phone: +49 (0) 271 / 740-3609

News Research & publications Conferences & workshops Academic CV Teaching Miscellaneous

News:

  • Organizer of the minisession High dimensional numerical integration at MCQMC 2016 in Stanford
  • Attention: changed consultation hours in Siegen!
  • Paper Almost diagonal matrices and Besov-type spaces based on wavelet expansions published within J. Fourier Anal. Appl.
  • Paper Rank-1 lattice rules for multivariate integration in spaces of permutation-invariant functions: Error bounds and tractability (with D. Nuyens and G. Suryanarayana) published within Adv. Comput. Math.
  • Lecture Stochastics and Reading Course (Seminar) Theoretical Numerics announced for summer term 2016 in Siegen
  • Paper Besov regularity of solutions to the p-Poisson equation (with S. Dahlke, L. Diening, C. Hartmann and B. Scharf) published within Nonlinear Anal.
  • Again Interim professor for numerics at the Department of Mathematics, University of Siegen, during summer term 2016
  • Paper Besov regularity for operator equations on patchwise smooth manifolds (with S. Dahlke) published within J. Found. Comput. Math.


Area of research:


Complete list of publications [ pdf, bib ]

Preprints:

  1. Construction of quasi-Monte Carlo rules for multivariate integration in spaces of permutation-invariant functions (with D. Nuyens and G. Suryanarayana)
    Under revision
    Preprint: Bericht Mathematik Nr. 2015-01 des Fachbereichs Mathematik und Informatik, Universität Marburg
    [ pdf (29/07/2015), arXiv (29/07/2015), bib ]

Articles (peer reviewed):

  1. Rank-1 lattice rules for multivariate integration in spaces of permutation-invariant functions: Error bounds and tractability (with D. Nuyens and G. Suryanarayana)
    Adv. Comput. Math. 42(1) (2016), 55-84, doi:10.1007/s10444-015-9411-6
    [ pdf (13/05/2014), arXiv (14/05/2014), bib ]

  2. Besov regularity of solutions to the p-Poisson equation (with S. Dahlke, L. Diening, C. Hartmann, and B. Scharf)
    Nonlinear Anal. 130 (2016), 298-329, doi:10.1016/j.na.2015.10.015
    [ pdf (15/08/2014), arXiv (19/08/2014), bib ]

  3. Almost diagonal matrices and Besov-type spaces based on wavelet expansions
    J. Fourier Anal. Appl. 22(2) (2016), 251-284, doi:10.1007/s00041-015-9423-0
    [ pdf (11.06.2015), arXiv (20.08.2014), bib ]

  4. Notes on (s,t)-weak tractability: A refined classification of problems with (sub)exponential information complexity (with P. Siedlecki)
    J. Approx. Theory 200 (2015), 227–258, doi:10.1016/j.jat.2015.07.007
    [ pdf (13/11/2014), arXiv (13/11/2014), bib ]

  5. Besov regularity for operator equations on patchwise smooth manifolds (with S. Dahlke)
    J. Found. Comput. Math. 15(6) (2015), 1533-1569, doi:10.1007/s10208-015-9273-9
    [ pdf (01/09/2014), arXiv (01/09/2014), bib ]

  6. Breaking the curse of dimensionality
    Dissertationes Math. 505 (2015), 112 pp., doi:10.4064/dm505-0-1
    [ see No.2 in Theses, bib ]

  7. On lower bounds for integration of multivariate permutation-invariant functions
    J. Complexity 30(1) (2014), 87-97, doi:10.1016/j.jco.2013.10.003
    [ pdf (18/09/2013), arXiv (15/10/2013), bib ]

  8. Probabilistic star discrepancy bounds for double infinite random matrices (with C. Aistleitner)
    J. Dick, F.Y. Kuo, G.W. Peters, and I.H. Sloan (Eds.) - Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer, Berlin, 2013, pp 271-287. doi:10.1007/978-3-642-41095-6_10
    [ pdf (18/04/2012), bib ]

  9. The complexity of linear tensor product problems in (anti)symmetric Hilbert spaces
    J. Approx. Theory 164(10) (2012), 1345-1368, doi:10.1016/j.jat.2012.05.016
    [ pdf (short, 18/05/2012), arXiv (extended, 31/10/2011), bib ]

  10. Tractability results for weighted Banach spaces of smooth functions
    J. Complexity 28(1) (2012), 59-75, doi:10.1016/j.jco.2011.03.004
    [ pdf (11/03/2011), bib ]

Reports and posters:

  1. Wavelet und Frame Techniken für BEM in der Akustik (mit W. Kreuzer und T. Hrycak)
    To appear in: Fortschritte der Akustik, DAGA 2016, 42. Jahrestagung für Akustik, Aachen. Deutsche Gesellschaft für Akustik e.V., 2016.
    [ web, bib ]

  2. (s,t)-weak tractability
    A. Hinrichs, J.F. Traub, H. Woźniakowski, and L. Yaroslavtseva (Eds.) - Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 15391). Dagstuhl Reports 5(9), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2016, p 74. doi:10.4230/DagRep.5.9.57
    [ web, bib ]

  3. Besov regularity of solutions to the p-Poisson equation (with S. Dahlke, L. Diening, C. Hartmann, and B. Scharf)
    Poster (2014)
    [ pdf, bib ]

  4. On lower bounds for integration of multivariate permutation-invariant functions
    M. Gnewuch, F.Y. Kuo, H. Niederreiter, and Woźniakowski, H. (Eds.) - Uniform Distribution Theory and Applications. Oberwolfach Reports 10(4), EMS Publishing House, Zürich, 2013, pp 2904-2905. doi:10.4171/OWR/2013/49
    [ web, bib ]

  5. Probabilistic star discrepancy bounds for double infinite random matrices
    A. Keller, F.Y. Kuo, A. Neuenkirch, and J.F. Traub (Eds.) - Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 12391). Dagstuhl Reports 2(9), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2013, p 223. doi:10.4230/DagRep.2.9.200
    [ web, bib ]

Theses:

  1. Several Approaches to Break the Curse of Dimensionality
    Ph.D. thesis, Friedrich-Schiller-University Jena, 20/02/2013, urn:nbn:de:gbv:27-20130822-105914-9
    supervised by Prof. Dr. Erich Novak
    [ pdf (15/05/2013), arXiv (17/05/2013), bib ]

  2. Das Haar'sche System in Funktionenräumen vom Typ Asp,q(IR)
    Diploma thesis, Friedrich-Schiller-University Jena, 08/09/2009
    supervised by Prof. Dr. Hans-Jürgen Schmeißer and Prof. Dr. Dr. h.c. Hans Triebel
    [ pdf (abstract, german), bib ]


Conferences and workshops:



Academic curriculum vitae:

Research stays:

Talks (selected):

  • TBA, Bedlewo (Poland), August/September 2016
  • Approximation properties of wavelet trees, Basel (Switzerland), March 2016
  • Adaptive algorithms - theory and practice, Banff (Canada), September/October 2015
  • (s,t)-weak tractability, Dagstuhl, September 2015 [ pdf ]
  • Approximation of embeddings between spaces of Besov type (semi-plenary), Siegmundsburg, July 2015
  • (s,t)-weak tractability, Bedlewo (Poland), April/May 2015
  • On optimal wavelet approximations in spaces of Besov type, Hasenwinkel, March 2015
  • On optimal wavelet approximations in spaces of Besov type (semi-plenary), Kaiserslautern, February 2015 [ pdf ]
  • Regularity of boundary integral equations in Besov-type spaces based on wavelet expansions, Montevideo (Uruguay), December 2014 [ pdf ]
  • A refined classification of problems with (sub)exponential information complexity, Montevideo (Uruguay), December 2014 [ pdf ]
  • Besov-type function spaces on patchwise smooth manifolds and regularity analysis of operator equations in these scales (semi-plenary), Traunkirchen (Austria), August 2014 [ pdf ]
  • Integration of permutation-invariant functions, Leuven (Belgium), April 2014 [ pdf ]
  • Besov regularity for operator equations on patchwise smooth manifolds, Hasenwinkel, March 2014 [ pdf ]
  • Besov regularity for operator equations on patchwise smooth manifolds, Bestwig, January/February 2014
  • On lower bounds for integration of multivariate permutation-invariant functions, Oberwolfach, October 2013 [ pdf ]
  • Integration of permutation-invariant functions, Annecy (France), July 2013
  • Several Approaches to Break the Curse of Dimensionality (thesis defense), Jena, 13/05/2013 [ pdf (german) ]
  • Probabilistic star discrepancy bounds for double infinite random matrices, Dagstuhl, September 2012
  • Probabilistic star discrepancy bounds for double infinite random matrices, Smolenice (Slovakia), June 2012 [ pdf ]
  • Linear tensor product problems in (anti-) symmetric Hilbert spaces, Sydney (Australia), February 2012
  • Tractability of L-approximation on weighted Banach spaces of smooth functions, Bonn, June 2011 [ pdf ]
  • Remarks on Lp-approximation of infinitely differentiable multivariate functions, Jena, December 2010
  • On error bounds for L-approximation of smooth functions, Oppurg, October 2010 [ pdf ]
  • Komplexität hochdimensionaler Probleme - Eine Einführung, Siegmundsburg, July 2010 [ pdf (german) ]
  • Upper error bounds for L-approximation by means of embeddings, Jena, May 2010
  • Haar bases in function spaces from the type Asp,q(IR), Jena, December 2009 [ pdf ]

Scholarships, Grants, Awards:

  • Travel grant: Research Group of Computational Mathematics, University of Basel, 2016
  • Travel grant: Ruhr-Universität Bochum, 2015
  • Travel grant: Banff International Research Station, Canada, 2015
  • Travel grant: Polish Academy of Sciences for attending the Information-based Complexity conference, 2015
  • Travel grant: Research Group of Computational Mathematics, University of Basel, 2015
  • Travel grant: Adolf Haeuser Stiftung for attending the Foundations of Computational Mathematics (FoCM) Conference, 2014
  • Short-term scholarship: ICERM Semester Program on High-dimensional Approximation, 2014
  • Travel grant/Award: Oberwolfach Leibniz Graduate Student, 2013
  • Short-term scholarship: Department of Computer Science, KU Leuven, 2013
  • Travel grant: Philipps-University Marburg, 2013
  • Short-term scholarship: Department of Computer Science, KU Leuven, 2012
  • Scholarship: German National Academic Foundation ('Studienstiftung des deutschen Volkes'), 2007-2009

Referee work:



Teaching:



Miscellaneous:



last update: 08/04/2016