English Intern
Wissenschaftliches Rechnen

Wissenschaftlicher Mitarbeiter

Dr. Markus Weimar

Dozent
Lehrstuhl für Mathematik IX
Emil-Fischer-Straße 30
97074 Würzburg
Gebäude: 30 (Mathematik West)
Raum: 00.010
Telefon: +49 931 31-84633
Fax: +49 931 31-838430
Portrait Markus Weimar

Forschungsinteressen

Area of Research

  • Regularity Theory for Operator Equations (Besov Regularity)
    • (Nonlinear) Partial Differential Equations
    • Boundary Integral Equations
    • Theory of Function Spaces
  • (Theoretical) Numerical Analysis
    • Adaptive (Wavelet and FE) Methods
    • (Nonlinear) Approximation Theory

Further interests:

  • Applied Harmonic Analysis
  • High-dimensional Problems
  • Tensor Product Structures
  • Information-Based Complexity (IBC)
  • Multivariate Integration (Lattice Rules)
  • Discrepancy Theory

Nachrichten

  • I'm invited to give a talk in the mathematical colloquium at the University of Osnabrück
  • New Preprint Rate-optimal sparse approximation of compact break-of-scale embeddings (with G. Byrenheid and J. Hübner) available on arXiv
  • Lecture Hochdimensionale Numerik und Diskrepanz (Moodle course → 150260-SoSe22) announced for summer term 2022
  • GAMM announced to publish a short report on my work in their GAMM-Rundbrief 2022 Issue 1
  • Glenn Byrenheid (Friedrich Schiller University Jena) visited our group from January 20 - 22, 2022.
  • I was elected to join the Early Career Researchers (ECR) Board at RUB
  • I joined the recently founded GAMM Junior Research Group at RUB as a senior member
  • Paper On the lack of interior regularity of the p-Poisson problem with p>2 published in Math. Nachr.
  • From April 2020 until March 2022 I act as interim professor (W2) for Numerical Analysis at RUB
  • Positive (intermediate) evaluation of the junior professorship
 

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Academic Curriculum Vitae

  • 04/2020 - 03/2022: Interim Professor (W2) for Numerical Analysis at Ruhr University Bochum (RUB)
  • 01/2020: Positive (intermediate) evaluation of the junior professorship
  • Since 03/2017: Assistant Professor (“Juniorprofessor”) for Numerics at RUB,
    Faculty of Mathematics
  • 10/2016 - 02/2017: Senior Lecturer (“Akademischer Oberrat auf Zeit”) at University of Siegen,
    Department of Mathematics, Applied Analysis and Numerics Section
  • 04/2015 - 09/2016: Interim Professor (“Lehrstuhlvertretung”, W3) for Numerics at University of Siegen,
    Department of Mathematics, Workgroup Numerics
  • 05/2013 - 09/2016: Postdoctoral Researcher (“Wiss. Mitarbeiter”) at Philipps-University Marburg,
    Faculty of Mathematics and Computer Science, Workgroup Numerics and Optimization (Prof. Dr. Stephan Dahlke)
    D-A-CH project Adaptive Wavelet and Frame Techniques for Acoustic BEM
  • 04/2010 - 04/2013: Research Associate (“Wiss. Mitarbeiter”, 50%) at Friedrich-Schiller-University (FSU) Jena,
    Faculty of Mathematics and Computer Science, Mathematical Institute,
    Chair for Theoretical Numerical Analysis (Prof. Dr. Erich Novak)
  • 12/2009 - 05/2013: Ph.D. Student (Dr. rer. nat.) at FSU Jena
    Focus on Information-Based Complexity and Theoretical Numerical Analysis
    Thesis: Several Approaches to Break the Curse of Dimensionality (final grade: summa cum laude)
    supervised by Prof. Dr. Erich Novak
  • WS 2009/'10: Graduate Teaching Assistant at FSU Jena,
    Faculty of Mathematics and Computer Science, Mathematical Institute
  • WS 2004/'05 - SS 2009: Study of Mathematics (Dipl.-Math.) at FSU Jena
    Focus on Analysis and Applied Computer Sciences
    Thesis: Das Haar'sche System in Funktionenräumen vom Typ Asp,q(IR) (final grade: 1.1)
    supervised by Prof. Dr. Hans-Jürgen Schmeißer
    Partially supported by German National Academic Foundation (“Studienstiftung”)
  • 03/2005 - 09/2005: Alternative Civilian Service (“Zivildienst”) at LebenshilfewerkWeimar/Apolda e.V.
  • 07/2004 - 09/2004: Basic Military Service (“Grundwehrdienst”) in Hammelburg
  • 05/2004: Abitur at Staatl. Gymnasium 'Bergschule' Apolda (final grade: 1.5)
  • Born on 28/02/1986 in Weimar
   

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Preprints:

  1. Rate-optimal sparse approximation of compact break-of-scale embeddings (with G. Byrenheid and J. Hübner)
    35p. (2022)
    [ arXiv ]

Articles and Book chapters (peer reviewed):

  1. Higher order regularity shifts for the p-Poisson problem (with A.Kh. Balci and L. Diening)
    In: F.J. Vermolen and C. Vuik (eds.) - Numerical Mathematics and Advanced Applications ENUMATH 2019, Springer, Cham, 2021, pp 1147–1155
    [ pdf, doi ]
  2. On the lack of interior regularity of the p-Poisson problem with p>2
    Math. Nachr. 294(6) (2021), 1186-1205
    [ arXiv, ruhr.paD 2020-01, doi ]
  3. On the limit regularity in Sobolev and Besov scales related to approximation theory (with P.A. Cioica-Licht)
    J. Fourier Anal. Appl. 26(1) (2020), Art. 10, 1-24
    [ arXiv, ruhr.paD 2019-01, doi ]
  4. Higher Order Calderón-Zygmund Estimates for the p-Laplace Equation (with A.Kh. Balci and L. Diening)
    J. Differential Equations 268 (2020), 590-635
    [ arXiv, ruhr.paD 2019-02, doi ]
  5. Besov regularity of solutions to the p-Poisson equation in the vicinity of a vertex of a polygonal domain (with C. Hartmann)
    Results Math. 73(1) (2018), Art. 41, 1-28
    [ pdf, doi ]
  6. Adaptive wavelet BEM for boundary integral equations: Theory and numerical experiments (with S. Dahlke, H. Harbrecht, and M. Utzinger)
    Numer. Funct. Anal. Optim. 39(2) (2018), 208-232
    [ arXiv, doi ]
  7. Construction of quasi-Monte Carlo rules for multivariate integration in spaces of permutation-invariant functions (with D. Nuyens and G. Suryanarayana)
    Constr. Approx. 45(2) (2017), 311-344
    [ arXiv, doi ]
  8. 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
    [ arXiv, doi ]
  9. 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
    [ arXiv, doi ]
  10. Almost diagonal matrices and Besov-type spaces based on wavelet expansions
    J. Fourier Anal. Appl. 22(2) (2016), 251-284
    [ arXiv, doi ]
  11. 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
    [ arXiv, doi ]
  12. Besov regularity for operator equations on patchwise smooth manifolds (with S. Dahlke)
    J. Found. Comput. Math. 15(6) (2015), 1533-1569
    [ arXiv, doi ]
  13. Breaking the curse of dimensionality
    Dissertationes Math. 505 (2015), 112 pp.
    [ see No.2 in Theses, doi ]
  14. On lower bounds for integration of multivariate permutation-invariant functions
    J. Complexity 30(1) (2014), 87-97
    [ arXiv, doi ]
  15. 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
    [ pdf, doi ]
  16. The complexity of linear tensor product problems in (anti)symmetric Hilbert spaces
    J. Approx. Theory 164(10) (2012), 1345-1368
    [ arXiv (extended version), doi ]
  17. Tractability results for weighted Banach spaces of smooth functions
    J. Complexity 28(1) (2012), 59-75
    [ pdf, doi ]

Reports and posters:

  1. Wavelet und Frame Techniken für BEM in der Akustik (with 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 ]
  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
    [ web, doi ]
  3. Besov regularity of solutions to the p-Poisson equation (with S. Dahlke, L. Diening, C. Hartmann, and B. Scharf)
    Poster (2014)
    [ pdf ]
  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
    [ web, doi ]
  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
    [ web, doi ]

Theses:

  1. Several Approaches to Break the Curse of Dimensionality
    Ph.D. thesis, Friedrich-Schiller-University Jena, 20/02/2013
    supervised by Prof. Dr. Erich Novak
    [ arXiv, urn ]
  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) ]

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Upcoming:

Previous:

Permanent:

  • Supervision of Bachelor's and Master's Theses...
  • Individual Reading Courses for Master Students...
    ... on various topics in theoretical numerics and applied analysis → Arrange an appointment!

Current:

  • WS 2022/23:

Previous:

  • WS 2021/'22: Vorlesung - Deep Learning (Moodle course → 150332-WiSe21/22, Service Lecture - Master Class IT Security, eng!, 4+2h, with Prof. Dr. Fischer)
  • WS 2021/'22: Vorlesung - Interpolationstheorie (Moodle course → 150291-WiSe21/22, Lecture - Interpolation Theory, 4+2h)
  • WS 2021/'22: Seminar (Reading Course) - Modern Mathematics of Deep Learning (Moodle course → 150564-WiSe21/22, 2h, with Prof. Dr. Fischer)
  • WS 2021/'22: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Henning)
  • SS 2021: Vorlesung - Numerik II: Partielle Differentialgleichungen (Moodle course → 150268-SoSe21, Lecture - Numerics of PDEs, 4+2h)
  • SS 2021: Vorlesung - Numerical Methods and Stochastics (Moodle course → 126510-SoSe21, Service Lecture - Master Class Computational Engineering, Numerics part, eng!)
  • SS 2021: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Henning)
  • WS 2020/'21: Vorlesung - Numerik I: Gewöhnliche Differentialgleichungen (Moodle course → 150266-WiSe20/21, Lecture - Numerics of ODEs, 4+2h)
  • WS 2020/'21: Vorlesung - Adaptive Finite Element Methods (Moodle course → 127507-WiSe20/21, Service Lecture - Master Class Computational Engineering, eng!)
  • WS 2020/'21: Seminar zur Numerik: Iterative Methoden (Moodle course → 150516-WiSe20/21, Seminar Numerics, 2h)
  • WS 2020/'21: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Henning, Prof. Dr. Verfürth)
  • SS 2020: Vorlesung - Einführung in die Numerik (Moodle course → 150212-SoSe20, Lecture - Numerics, 4+2h)
    Starting point of the (german!) four-course-cycle on numerical analysis at RUB (see → overview for details)
  • SS 2020: Vorlesung - Numerik II: Partielle Differentialgleichungen (Moodle course → 150268-SoSe20, Lecture - Numerics of PDEs, 4+2h)
  • SS 2020: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • WS 2019/'20: Vorlesung - Numerik I: Gewöhnliche Differentialgleichungen (Moodle course → 150266-WiSe19/20 , Lecture - Numerics of ODEs, 4+2h)
  • WS 2019/'20: Seminar zur Numerik: Monte Carlo-Methoden (Moodle course → 150544-WiSe19/20, Seminar Numerics, 2h)
  • WS 2019/'20: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • SS 2019: Vorlesung - Numerical Methods and Stochastics (Moodle course → 126510-SoSe19, Service Lecture - Master Class Computational Engineering, Numerics part, eng!)
  • SS 2019: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • WS 2018/'19: Vorlesung - Klassische Approximationstheorie (Moodle course → 150279-WiSe18/19, Lecture - Classical Approximation Theory, 3+1h)
  • WS 2018/'19: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • SS 2018: Vorlesung - Numerik II: Partielle Differentialgleichungen (Moodle course → 150268-SoSe18, Lecture - Numerics of PDEs, 4+2h)
  • SS 2018: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • WS 2017/'18: Vorlesung - Numerik I: Gewöhnliche Differentialgleichungen (Moodle course → 150266-WiSe17/18, Lecture - Numerics of ODEs, 4+2h)
  • WS 2017/'18: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • SS 2017: Vorlesung - Einführung in die Numerik (Moodle course → 150212-SoSe17, Lecture - Numerics, 4+2h)
    Starting point of the (german!) four-course-cycle on numerical analysis at RUB (see → overview for details)
  • SS 2017: Oberseminar Numerik (Research Seminar Numerical Analysis, 2h, with Prof. Dr. Verfürth)
  • WS 2016/'17: Vorlesung - Analysis I (Lecture - Calculus, 4+2+2h, University of Siegen)
  • SS 2016: Vorlesung - Elemente der Stochastik (Lecture - Stochastics, 2+2h, University of Siegen)
  • SS 2016: Seminar (Reading Course) - Theoretische Numerik (Seminar Theoretical Numerics, 2h, University of Siegen)
  • SS 2016: Oberseminar Numerik (Research Seminar Numerics, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke, Prof. Dr. Pfander)
  • WS 2015/'16: Vorlesung - Numerik III: Numerik partieller Differentialgleichungen (Lecture - Numerics III: Numerics for PDEs, 4+2h, University of Siegen)
  • WS 2015/'16: Vorlesung - Quasi-Monte Carlo Methoden & Diskrepanz (Lecture - Quasi-Monte Carlo & Discrepancy, 4+0h, University of Siegen)
  • WS 2015/'16: Oberseminar Numerik (Research Seminar Numerics, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke)
  • SS 2015: Vorlesung - Approximationstheorie (Lecture - Approximation Theory, 3+1h, University of Siegen)
  • SS 2015: Vorlesung - Elemente der Stochastik (Lecture - Stochastics, 2+2h, University of Siegen)
  • SS 2015: Oberseminar Numerik (Research Seminar Numerics, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke, Prof. Dr. Schmitt)
  • SS 2015: Seminar zur Numerik (Seminar Numerics, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke, Prof. Dr. Schmitt)
  • WS 2014/'15: Oberseminar Numerik (Research Seminar Numerics, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke, Prof. Dr. Schmitt)
  • WS 2014/'15: Seminar (Reading Course) - Inverse Probleme (Seminar - Inverse Problems, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke, Prof. Dr. Holzmann, Prof. Dr. Schmitt)
  • SS 2014: Vorlesung - Reelle Interpolationstheorie (Lecture - Real Interpolation Theory, 2+0h, Philipps-University Marburg)
  • WS 2013/'14: Seminar zur Numerik (Seminar Numerics, 2h, Philipps-University Marburg, with Prof. Dr. Dahlke, Prof. Dr. Schmitt)
  • WS 2012/'13: Übung - Analysis III (Exercises - Analysis 3, Physics / Math / WiMa B.Sc, Friedrich-Schiller-University Jena, Prof. Dr. Schmeißer)
  • SS 2012: Oberseminar Theoretische Numerik (Research Seminar Theoretical Numerics, 2h, Friedrich-Schiller-University Jena, with Prof. Dr. Novak)
  • WS 2011/'12: 2 Übungen - Einführung in die Numerische Mathematik und das Wissenschaftliche Rechnen (Exercises - Numerics 1, Math B.Sc, Friedrich-Schiller-University Jena, Prof. Dr. Novak)
  • SS 2011: Übung - Analysis II (Exercises - Analysis 2, Physics B.Sc, Friedrich-Schiller-University Jena, PD Dr. Hinrichs)
  • WS 2010/'11: Übung - Analysis I (Exercises - Analysis 1, Physics B.Sc, Friedrich-Schiller-University Jena, PD Dr. Hinrichs)
  • SS 2010: Übung - Analysis II (Exercises - Analysis 2, Math B.Sc / WiMa B.Sc, Friedrich-Schiller-University, Prof. Dr. Carl)
  • WS 2009/'10: 2 Übungen - Analysis III (Exercises - Analysis 3, Lehramt Gymnasium, Friedrich-Schiller-University, Dr. Haberland)

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Miscellaneous:

My current Erdős number is 4, via one of the following paths:

  1. Christoph Aistleitner → István Berkes → Endre Csáki → Paul Erdős
  2. Stephan Dahlke → Ronald A. DeVore → Henry A. Kiersteadl → Paul Erdős
  3. Stephan Dahlke → Holger Rauhut → Allan M. Pinkus → Paul Erdős
  4. Dirk Nuyens → Jonathan Michael Borwein → Neil J. Calkin → Paul Erdős

My accounts in scientific networks:

Journals:

Data bases / useful links:

Some external colleagues:

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