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: Thu 10:30-11:30 am, ENC-B 302,
and by appointment
Phone: +49 (0) 271 / 740-3609

News Research & publications Conferences & workshops Academic CV Teaching Miscellaneous

News:

  • Starting in October 2016 I'll be Lecturer at the Department of Mathematics, University of Siegen
  • Lecture Analysis I announced for winter term 2016 in Siegen
  • Attention: changed consultation hours in Siegen!
  • Report Wavelet und Frame Techniken für BEM in der Akustik (with W. Kreuzer und T. Hrycak) published within: Fortschritte der Akustik, DAGA 2016
  • Organizer of the Special Session High dimensional numerical integration at MCQMC 2016 in Stanford
  • 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


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)
    Fortschritte der Akustik, DAGA 2016, 42. Jahrestagung für Akustik. Deutsche Gesellschaft für Akustik e.V., Aachen, 2016, pp 855-858.
    [ 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, Barcelona (Spain), July 2017
  • Improved regularity estimates for solutions to quasi-linear operator equations on Lipschitz domains, 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

Further Professional Activities:



Teaching:

Moreover, since WS 2013/'14 I have (co-)supervised and/or reviewed 3 master's theses, 1 state examination thesis, as well as 13 Bachelor's theses on different topics in Analysis, Numerics and Stochastics.



Miscellaneous:



last update: 28/07/2016