Project "OREADEE":
Optimization of Resonances and Eigenvalues Associated with Dissipative Evolution Equations.
Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer: 509859995

• WS 2023/24 Dozent für die Vorlesung "Homogenization-convergence and optimization of eigenvalues" (in English, Universität Bonn)

• SS 2023 Dozent für die Vorlesung "Mathematik II für Physiker" (Universität Bonn)
• WS 2022/23 Dozent für die Vorlesung "Mathematik III für Physiker" (Universität Bonn)
• SS 2022 Dozent für die Vorlesung "Mathematik II für Physiker" (Universität Bonn)
• WS 2021/22 Dozent für das Proseminar zu Analysis I/II (LA Gym) (hybrid), (TU Dortmund)
• SS 2021 Dozent für das Seminar zu Analysis III (LA Gym) (digital), (TU Dortmund)
• WS 2020/21 "Analysis I für LA Gymnasium/BK " (hybrid), Korrekturen, Aufsicht der Klausur, Korrektur der Klausur (TU Dortmund)
• SS 2020 Übungsleiter für "Zufällige Graphen" (TU Dortmund)
• WS 2019/20 Übungsleiter für "Lokalkonvexe Methoden der Analysis" (TU Dortmund)
• WS 2018/19 Dozent für die Vorlesung V5B2 Selected topics in Analysis and PDE
  "Geometric Optimal Control" (in English, Universität Bonn)

• 06/2023 - present, Heisenberg-Programm (Heisenberg-Stelle), Projekt:
  "Optimierung von Resonanzen und Eigenwerten, die mit dissipativen Evolutionsgleichungen verbunden sind".

•  04/2022-05/2023, Wissenschaftlicher Mitarbeiter, Institute for Applied Mathematics, University of Bonn

• 10/2019-03/2022, Wissenschaftlicher Mitarbeiter, Fakultät für Mathematik, TU Dortmund

• 06/2019, 08/2019, Coordinator and Visiting Researcher (scholarship for coordinator of
  a VolkswagenStiftung-funded project), Universität zu Lübeck

• 11/2016-01/2017, 08-12/2017, 08/2018-05/2019, Humboldt Experienced Researcher, University of Bonn

• 01-03/2014, 08-12/2014, 01-04/2015, 06/2015, 08-12/2015, Visiting Researcher, Universität zu Lübeck

• 01/2013-11/2022, Senior Research Fellow, Institute of Applied Mathematics and Mechanics (IAMM) of NAS of Ukraine

• 11/2008-10/2010, PIMS Post-doctoral Fellow, University of Calgary and PIMS (Vancouver), Canada

• 08/2007-07/2008, Post-Doctoral Fellow, University of Calgary, Canada

• 11/2006-04/2007, Post-Doktorand, University of Zurich, Switzerland

• 04/2006-12/2013, Junior Research Fellow, Research Fellow, IAMM of NAS of Ukraine

• 12/2002-04/2006, Assistant, Senior Lecturer, Donetsk National University, Ukraine

Lists of papers in databases:

• mathscinet.ams.org
• arXiv.org
• scholar.google.com

•  M. Eller, I.M. Karabash, M-dissipative boundary conditions and boundary tuples for Maxwell operators, J. Differential Equations 325 (2022), 82–118. doi.org/10.1016/j.jde.2022.04.006

•  M. Eller, I.M. Karabash, Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavities,In: Proceedings of the International Conference ``Days on Diffraction 2021'', St. Petersburg, pp. 29-35, IEEE Xplore, IEEE, 2021. doi.org/10.1109/DD52349.2021.9598789 (see also preprint).

•  S. Albeverio, I.M. Karabash, Asymptotics of random resonances generated by a point process of delta-interactions, In: Albeverio S., Balslev A., Weder R. (eds.) “Schrödinger Operators, Spectral Analysis and Number Theory. In Memory of Erik Balslev”,  pp. 7--26, Springer, 2021. doi.org/10.1007/978-3-030-68490-7_2 (see also preprint).

•  I.M. Karabash, H. Koch, I.V. Verbytskyi, Pareto optimization of resonances and minimum-time control, Journal de Mathématiques Pures et Appliquées 136 (2020), 313-355. doi.org/10.1016/j.matpur.2020.02.005 (see also preprint).

•  S. Albeverio, I.M. Karabash, Generic asymptotics of resonance counting function for Schrödinger point interactions. In: Kurasov P., Laptev A., Naboko S., Simon B. (eds.), ``Analysis as a Tool in Mathematical Physics: in Memory of Boris Pavlov'', Oper. Theory Adv. Appl., Vol. 276, pp. 80-93, Birkhäuser, Cham, 2020. doi.org/10.1007/978-3-030-31531-3_8 (see also preprint).

•  S. Albeverio, I.M. Karabash, On the multilevel internal structure of the asymptotic distribution of resonances, J. Differential Equations 267 (2019), 6171-6197. doi.org/10.1016/j.jde.2019.06.020 (see also preprint).

•  I.M. Karabash, J. Prestin, Recovery of periodicities hidden in heavy-tailed noise, Math. Nachr. 291 (2018), pp. 86-102. doi.org/10.1002/mana.201600361 (see also preprint).

•  I.M. Karabash, O.M. Logachova, I.V. Verbytskyi, Nonlinear bang-bang eigenproblems and optimization of resonances in layered cavities, Integral Equations Operator Theory 88 (2017). doi.org/10.1007/s00020-017-2368-8 (see also preprint).

•  I.M. Karabash, Pareto optimal structures producing resonances of minimal decay under L^1-type constraints, J. Differential Equations 257 (2014). doi.org/10.1016/j.jde.2014.04.002 (see also preprint).

•  I. Karabash, Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures, Asymptotic Analysis 81 (2013). doi.org/10.3233/ASY-2012-1128 (see also preprint).

•  E. Braverman, I. Karabash, Structured stability radii and exponential stability tests for Volterra difference systems, Comput. Math. Appl. 66 (2013).

•  I. Karabash, Optimization of quasi-normal eigenvalues for Krein-Nudelman strings, Integral Equations Operator Theory 75 (2013).

•  E. Braverman, I. Karabash, Bohl-Perron-type stability theorems for linear difference equations with infinite delay. J. Difference Equ. Appl. 18 (2012), no. 5.

•  P. Binding, P.J. Browne, I. Karabash, Sturm-Liouville problems for the p-Laplacian on a half-line. Proc. Edinb. Math. Soc. (2) 53 (2010), no. 2.

•  I. Karabash, A. Kostenko, M. Malamud, The similarity problem for J-nonnegative Sturm-Liouville operators, J. Differential Equations 246 (2009).

•  M. Chugunova, I. Karabash, S.G. Pyatkov, On the nature of ill-posedness of the forward-backward heat equation, Integral Equations Operator Theory 65 (2009).

•  I. Karabash, C. Trunk, Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x, Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 3, 483–503.

•  I. Karabash, A. Kostenko, Indefinite Sturm-Liouville operators with the singular critical point zero, Proc. Roy. Soc. Edinburgh 138A (2008).

•  I. Karabash, M. Malamud, Indefinite Sturm-Liouville operators (sgn x)(-d^2/dx^2 +q) with finite-zone potentials, Oper. Matrices 1 (2007).

•  I. Karabash, S. Khassi, On the similarity between a J-selfadjoint Sturm-Liouville operator with operator potential and a selfadjoint operator, Math. Notes 78 (2005), no.3-4.

•  I. Karabash, J-selfadjoint ordinary differential operators similar to selfadjoint operators, Methods Funct. Anal. Topology 6 (2000), no.2.