AG Numerik

Dr.  Marc Hovemann

Philipps-Universität
Fachbereich Mathematik und Informatik
AG Numerik und Optimierung

Hans-Meerwein-Straße
Lahnberge
35032 Marburg

Raum: Ebene D6 - 18 (06D18)
Telefon: +49 (0) 6421/28-25459
E-Mail: hovemann@mathematik (.uni-marburg.de)

Important note: This website will not be updated after 1.9.2024 anymore. Please visit my new website.

    Research Interests:

    • quarklet characterizations for function spaces
    • adaptive quarklet tree approximation
    • quarklets as multiwavelets
    • function spaces (especially Besov-type and Triebel-Lizorkin-type spaces)
    • equivalent quasi-norms for function spaces
    • characterizations for function spaces in terms of higher-order differences
    • Hedberg-Netrusov approach to function spaces
    • interpolation and composition operators

    PhD Thesis:

    • M. Hovemann: Smoothness Morrey Spaces and Differences: Characterizations and Applications
      (Supervisor: Prof. W. Sickel, 2021) [PDF]

    Publications and Preprints:

    • M. Hovemann, M. Weimar: Oscillations and differences in Besov-Morrey and Besov-type spaces.
      arXiv:2405.20662 [PDF]
    • M. Hovemann: Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products.
      arXiv:2403.14388 [PDF]
    • M. Hovemann, M. Weimar: Oscillations and differences in Triebel-Lizorkin-Morrey spaces.
      Rev. Mat. Complut. [PDF]
    • S. Dahlke, M. Hovemann, T. Raasch, D. Vogel: Adaptive Quarklet Tree Approximation.
      arXiv:2301.04111 [PDF]
    • M. Hovemann, A. Kopsch, T. Raasch, D. Vogel: B-Spline Quarklets and Biorthogonal Multiwavelets.
      Int. J. Wavelets Multiresolut. Inf. Process. , published online. [PDF]
    • M. Hovemann, S. Dahlke: Quarklet Characterizations for Triebel-Lizorkin spaces.
      J. Approx. Theory 295, 105968, 2023. [PDF]
    • M. Hovemann: Triebel-Lizorkin-Morrey Spaces and Differences.
      Math. Nachr. 295, 725-761, 2022. [PDF]
    • M. Hovemann: Besov-Morrey spaces and differences.
      Math. Rep. (Bucur.), 23(73), No. 1-2, 175-192, 2021. [PDF]
    • M. Hovemann: Besov-Morrey spaces and differences (extended version).
      arXiv:2010.10856 [PDF]
    • M. Hovemann: Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces.
      Nonlinear Anal., 204, 112239, 2021. [PDF]
    • M. Hovemann, W. Sickel: Besov-type spaces and differences.
      Eurasian Math. J.13(1), 25-56, 2020. [PDF]
    • C. Zhuo, M. Hovemann, W. Sickel: Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains.
      Anal. Geom. Metr. Spaces, 8, 268-304, 2020. [PDF]

    Awards and Funding :

    • DFG Project "Adaptive Quarklet Methods for the numerical Solution of Elliptic Partial Differential Equations with exponential Convergence"
      ( since 1.9.2023 )
    • Promotionspreis des Dekans 2022
      ( 13.1.2023 , FSU Jena)
    • Auszeichnung für herausragende Leistungen als Übungsleiter für das Fach Analysis 2
      ( 20.11.2020 , FSU Jena , verliehen von der Physikalisch-Astronomischen Fakultät )
    • Landesgraduiertenstipendium der FSU Jena
      ( 1.3.2018 - 28.2.2021 , zur Erstellung der Promotion )
    • Examenspreis des Dekans 2018
      ( 2.11.2018 , FSU Jena , wegen der Masterarbeit "Strichartz-Charakterisierungen von F^s_{p,q}" )

    Talks (in Seminars or Conferences):

    • Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products
      ( 31.5.2024 , function spaces seminar Jena )
    • Multivariate Quarklets in the Context of Bessel-Potential Spaces on Unit Cubes
      ( 9.2.2024 , Rhein-Ruhr-Workshop , Bestwig )
    • Poster: "Adaptive near-best Quarklet Tree Approximation"
      ( 26.9.2023 , Two-day workshop on Approximation Theory , Giessen )
    • Triebel-Lizorkin-Morrey Spaces and Oscillations
      ( 28.8.2023 , Siegmundsburg seminar )
    • Triebel-Lizorkin-Morrey Spaces and Oscillations
      ( 2.6.2023 , function spaces seminar Jena )
    • Adaptive near-best Quarklet Tree Approximation
      ( 10.2.2023 , Rhein-Ruhr-Workshop , Bestwig )
    • Quarklet Characterizations for Triebel-Lizorkin Spaces
      ( 6.10.2022 , International Conference on Function Spaces and Applications , Apolda )
    • Adaptive near-best Quarklet Tree Approximation
      ( 1.8.2022 , Siegmundsburg seminar )
    • B-Spline Quarklets and their Connections to the Theory of biorthogonal Multiwavelets
      ( 15.7.2022 , function spaces seminar Jena )
    • Quarklets and their Connections to the Theory of biorthogonal Multiwavelets
      ( 6.7.2022 , Oberseminar zur Numerik und Optimierung Marburg )
    • Poster: "Quarklet Characterizations for Triebel-Lizorkin spaces"
      ( 23.6.2022 , Conference "Applied Harmonic Analysis and Friends", Strobl, Austria )
    • Triebel-Lizorkin-Morrey Spaces and Differences: Characterizations and Applications
      ( 3.3.2022 , Ruhr-Universität Bochum, Research Seminar Numerical Analysis )
    • Quarklet Characterizations for Triebel-Lizorkin Spaces
      ( 2.2.2022 , Oberseminar zur Numerik und Optimierung Marburg )
    • Quarklet Characterizations for Triebel-Lizorkin Spaces
      ( 31.8.2021 , Siegmundsburg seminar )
    • Quarklet Characterizations for Triebel-Lizorkin and Triebel-Lizorkin-Morrey Spaces
      ( 2.7.2021 , function spaces seminar Jena )
    • Quarklet Characterizations for Triebel-Lizorkin Spaces
      ( 16.6.2021 , Oberseminar zur Numerik und Optimierung Marburg )
    • Triebel-Lizorkin-Morrey spaces and differences: characterizations and applications
      ( 16.12.2020 , Oberseminar zur Numerik und Optimierung Marburg )
    • Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces
      ( 10.7.2020 , function spaces seminar Jena )
    • Besov-Morrey spaces and truncations - an introduction
      ( 12.2.2020 , function spaces seminar Jena )
    • Besov-Morrey spaces and differences
      ( 27.1.2020 , PhD seminar Jena )
    • Besov-Morrey spaces and differences
      ( 26.8.2019 , Siegmundsburg seminar )
    • Triebel-Lizorkin-Morrey spaces and differences
      ( 14.6.2019 , FSDONA, Turku, Finnland )
    • Triebel-Lizorkin-Morrey spaces and differences: necessary conditions
      ( 18.1.2019 , function spaces seminar Jena )
    • Triebel-Lizorkin-Morrey spaces and differences: sufficient conditions
      ( 11.1.2019 , function spaces seminar Jena )
    • Triebel-Lizorkin-Morrey spaces and differences
      ( 23.11.2018 , The Prague seminar on function spaces )
    • Strichartz-Charakterisierungen von F^{s}_{p,q}
      ( 24.7.2018 , Siegmundsburg seminar )
    • Characterizations of Triebel-Lizorkin spaces by differences
      ( 14.5.2018 , PhD seminar Jena )

    Short CV:

    • since 9/2023 : Principal Investigator at the Philipps-Universität Marburg
      (Workgroup Numerics, DFG project "Adaptive Quarklet Methods for the numerical Solution of Elliptic Partial Differential Equations with exponential Convergence")
    • 6/2021 - 5/2023 : Postdoc at the Philipps-Universität Marburg
      (Workgroup Numerics, DFG project "adaptive high-order quarklet frame methods for elliptic operator equations")
    • 3/2018 - 5/2021 : Dr. rer. nat. in Mathematics at the Friedrich-Schiller-University Jena
      ( summa cum laude )
    • 2015 - 2017 : M. Sc. in Mathematics at the Friedrich-Schiller-University Jena
      (final mark : 1,0 ) (Examenspreis of the dean of the department of mathematics and computer science)
    • 2012 - 2015 : B. Sc. in Mathematics at the Friedrich-Schiller-University Jena
    • 2002 - 2010 : Abitur at the Friedrich-Schiller-Gymnasium Eisenberg
      (final mark : 1,0)
    • 22.06.1991 : born in Speyer (Germany)

    Teaching (past semesters, Jena and Marburg)

    • Lecture Nonlinear Optimization
      (M.Sc. Mathematik , summer term 2023)
    • Exercise Analysis 2
      (B.Sc. Mathematik , summer term 2020)
    • Exercise Analysis 1
      (B.Sc. Mathematik , winter term 2019/2020)
    • Exercise Numerische Mathematik
      (B.Sc. Informatik , summer term 2019)
    • Exercise Mathematik 1
      (B.Sc. Werkstoffwissenschaften , winter term 2018/2019)
    • Exercise Analysis 2
      (Lehramt Gymnasium , summer term 2018)
    • Exercise Mathematik 1
      (B.Sc. Werkstoffwissenschaften , winter term 2017/2018)
    • Exercise Analysis 1
      (Lehramt Gymnasium , winter term 2017/2018)
    • Tutorial Numerische Mathematik
      (B.Sc. Informatik , summer term 2017)

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