January 2022 - Present, Senior Lecturer, University of the Free State, Bloemfontein, South Africa

October 2019 - December 2021, Postdoctoral Fellow, North-West University, Potchefstroom, South Africa

October 2016 - September 2019, PhD Student (Functional Analysis), Bergische Universität Wuppertal, Wuppertal, Germany

October 2015 - August 2016, PhD Student (cancelled), Vrije Universiteit Brussel, Brussels, Belgium

September 2010 - August 2015, BSc and MSc in Mathematics, Radboud Universiteit Nijmegen, Nijmegen, The Netherlands

External funding:

The following grants have been awared to me:

• DFG - Walter-Benjamin Program (2021): "Perturbation Methods for Abstract Cauchy Problems associated to Evolution Equations" (Project Number: 468736785)
• NRF Schholarship: Innovation and Freestanding Postdoctoral Fellowships (2022): "Well-Posedness and perturbations of (non)autonomous evolution equations" (Grant number: 138497)
• DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) - Research Grant (2023):"Evolution equations on graph limits" (Reference number: 2022-54-OPA-Evolution)
• NRF Knowledge, Interchange & Collaboration (KIC) - Second Call (2023): Visiting Foreign Researcher: Dr. Christian Seifert (Hamburg, Germany), 2023, (Grant number: KIC22080247403)
• NRF Competitive Support for Unrated Researchers (2023 - 2025): "(Non)autonomous abstract Cauchy problems and beyond - Solutions and perturbation methods for evolution equations" (Grant number: SRUG220317136)
• DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) - Research Grant (2024):"Bi-Continuous Semigroups: Applications and Beyond" (Reference number: 2024-031-OPA-Bi-Continuous Semigroups)
• NRF Knowledge, Interchange & Collaboration (KIC) - Second Call (2024): Visiting Foreign Researcher: Dr. Christian Seifert (Hamburg, Germany), 2023, (Grant number: KIC230816143482)

Peer-reviewed publications

1. C. Budde, On bi-continuous cosine families, accepted to Quaest. Math. (2024).

2. C. Budde and C. Seifert, Perturbations of non-autonomous second-order abstract Cauchy problems, accepted to Anal. Math. (2024)..

3. C. Budde and M. Kramar Fijavž, Well-posedness of non-autonomous transport equation on metric graphs, 2022, accepted to Semigroup Forum (2024).

4. C. Budde, A Banach bundle approach to dynamical processes on changing networks, accepted to Poincare J. Anal. Appl. (2024).

5. C. Budde and J. Kreulich, On Splittings and Integration of Almost Periodic Functions With and Without Geometry, accepted to Semigroup Forum (2024).

6. C. Budde, How to approach stability of bi-continuous semigroups?, Math. Pannonica (N.S.),29:2, 282–290 (2023), URL https://doi.org/10.1556/314.2023.00029
7. C. Budde, On Trotter-Kato type inductive limits in the category of C0-semigroups, Adv. Dyn. Syst. Appl., 18:2, 125–136 (2023), URL https://dx.doi.org/10.37622/ADSA/18.2.2023.125-136
8. R. Benjamin and C. Budde, A note on the order Lozanovsky spectrum for positive operators, Complex Anal. Oper. Theory, 17:61 (2023), URL https://doi.org/10.1007/s11785-023-01374-4
9. C. Budde, A. Dobrick, J. Glück and M. Kunze, A monotone convergence theorem for strong Feller semigroups, Ann. Mat. Pura Appl. 202:1573-1589 (2023), URL https://doi.org/10.1007/s10231-022-01293-9 
10. C. Budde and J. Kreulich, Application of abstract semigroup theory to the asymptotic behavior of C0-semigroups, Complex Anal. Oper. Theory., 16:105 (2022), URL https://doi.org/10.1007/s11785-022-01285-w
11. C. Budde, L. Labuschagne and C. Steyn, Almost everywhere convergence for noncommutative spaces, Banach J. Math. Anal., 16:56 (2022), URL https://doi.org/10.1007/s43037-022-00209-2
12. C. Budde and S.-A. Wegner, A Lumer-Phillips type generation theorem for bi-continuous semigroups, Z. Anal. Anwend., 41(1-2):65-80, URL https://doi.org/10.4171/ZAA/1695 (2022)
13. C. Budde, Semigroups for flows on limits of graphs, Univ. Iagel. Acta Math., 7–21, URL https://doi.org/10.4467/20843828AM.21.001.14982.
14. C. Budde, Positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces, Acta Sci. Math. (Szeged), 87 (2021), 571–594, URL https://doi.org/10.14232/actasm-021-914-5.
15. C. Budde, Perturbations of uniformly mean ergodic semigroups, J. Semigroup Theory Appl. (2021), Article ID 1, URL http://dx.doi.org/10.28919/jsta/5509.
16. C. Budde and M. Kramar Fijavž, Bi-Continuous semigroups for flows on infinite networks, Netw. Heterog. Media, 16 (2021), 553–567, URL https://doi.org/10.3934/nhm.2021017.
17. C. Budde and R. Heymann, Extrapolation of operator-valued multiplication operators, Quaest. Math., 45 (2022), 347–356, URL https://doi.org/10.2989/16073606.2020.1859639.
18. C. Budde, Positive Miyadera-Voigt perturbations of bi-continuous semigroups, Positivity, 25 (2021), 1107–1129, URL https://doi.org/10.1007/s11117-020-00806-1.
19. C. Budde and B. Farkas, A Desch-Schappacher perturbation theorem for bi-continuous semigroups, Math. Nachr., 293 (2020), 1053–1073, URL https://doi.org/10.1002/mana.201800534.
20. C. Budde and B. Farkas, Intermediate and extrapolated spaces for bi-continuous operator semigroups, J. Evol. Equ., 19 (2019), 321–359, URL https://doi.org/10.1007/s00028-018-0477-8.
21. C. Budde and K. Landsman, A bounded transform approach to self-adjoint operators: functional calculus and affiliated von Neumann algebras, Ann. Funct. Anal., 7 (2016), 411–420, URL https://doi.org/10.1215/20088752-3605384.

Proceeding Articles

1. C. Budde and C. Seifert, Non-autonomous Desch-Schappacher perturbations, In: Choi, Y., Daws, M., Blower, G. (eds) Operators, Semigroups, Algebras and Function Theory. IWOTA 2021. Operator Theory: Advances and Applications, Vol 292. Birkhauser, Cham., 71–90 (2023), URL https://doi.org/10.1007/978-3-031-38020-4_4.

Theses

1. C. Budde, General Extrapolation Spaces and Perturbations of Bi-Continuous Semigroups, PhD thesis, Bergische Universität Wuppertal, 2019, Supervisor: Prof.Dr. Bálint Farkas, Second reader: Prof.Dr. Abdelaziz Rhandi.
2. C. Budde, Operator Algebras and Unbounded Self-Adjoint Operators, Master’s thesis, Radboud Universiteit Nijmegen, 2015, Supervisor: Prof.Dr. Klaas Landsman, Second reader: Dr. Jens Kaad.
3. C. Budde, Representation of Groups and Their Applications, Bachelor thesis, Radboud Universiteit Nijmegen, 2013, Original Dutch title: Representaties van groepen en hun Toepassingen, Supervisor: Prof.Dr. Gert Heckman, Second reader: Dr.Michael Müger.

Preprints

1. J. Allison, C. Budde, J. du Pisanie and J. Visagie, A critical review of existing and new population stability testing procedures in credit risk scoring, Submitted, arXiv:2303.01227. 
2. C. Budde and C. Seifert, Perturbations of non-autonomous second-order abstract Cauchy problems, Submitted, arXiv:2302.11270.
3. C. Budde and M. Kramar Fijavž, Well-posedness of non-autonomous transport equation on metric graphs, Submitted, arXiv:2206.02540

Current Teaching 

In 2024, I will lecture the following modules:

1st Semester: MATM3714 - Complex Analysis

2nd Semester: MATM2624 - Linear Algebra

2nd Semester: MATF6824 - Measure and Integration Theory

Past Teaching

At the University of the Free State, I presented the following modules: 

1st Semester (2022/2023): MATM3714 - Complex Analysis

2nd Semester (2022/2023): MATM2624 - Linear Algebra & MATE6824 - Functional Analysis

During my time as postdoc at the North-West University (Potchefstroom) I taught the following modules: 

1st Semester (2020): MTHS 614 - Measure and Integration

2nd Semester (2021): STTK887 - Advanced Probability Theory

Teaching Assistance

As student as well as during my PhD I had the opportunity to assist the following modules: 

Analysis III (Bergische Universität Wuppertal)

Analysis II (Bergische Universität Wuppertal)

Analysis I (Bergische Universität Wuppertal)

Ordinary Differential Equations (Bergische Universität Wuppertal)

Calculus (Vrije Universiteit Brussel)

Introductory Mathematical Physics (Radboud Universiteit Nijmegen)

Theses Projects

If you are interested in writing a honours or Master thesis in the area of (functional) analysis, please do not hesitate to contact me directly by e-mail then I can send you a list of possible projects.