Illia Karabash, Ph.D., Heisenberg Fellow (Heisenberg-Stelle)

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

Office: 4.043

Telephone: -5602

E-mail: karabash (at) iam (dot) uni-bonn (dot) de


E-Mail-Adresse für die Fragen bzgl. Vorlesungen/Prüfungen: 

ikarabas (at) uni-bonn (dot) de

Address:

Abt. Funktionalanalysis,

Institute for Applied Mathematics,

Universität Bonn, Endenicher Allee 60,

53115 Bonn,

Germany

 

Current and recent teaching

  • SoSe 2024 Dozent für S4B2 - Graduate Seminar on PDE
    "Dissipative boundary value problems for wave equations" (in English, Universität Bonn), Syllabus
    Preliminary meeting: 07 February 2024, 12:00, room 0.011.
    To attend the seminar as an official participant, one need to sign up with the lecturer AND to register technically via BASIS.
    If you cannot come to the preliminary meeting, but are interested in the seminar, please, feel free to contact me by email.

  • WiSe 2023/24 Dozent für die Vorlesung
    "Homogenization-convergence and optimization of eigenvalues" (in English, Universität Bonn)
    eCampus web-page ecampus.uni-bonn.de/goto_ecampus_crs_3169472.html

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

Research interests

  • Analysis, Optimization, Probability
  • Spectral Optimization, Structural Optimization, Stochastic Optimization
  • Wave Equations, Maxwell Equations, Homogenization
  • Resonances, Nonselfadjoint/Nonlinear Eigenvalue Problems
  • Multiparameter Bifurcation/Perturbation Theory, Liquid Film Equations
  • Optimal Control, Hamilton–Jacobi–Bellman Equations
  • Point Processes of Random Eigenvalues
  • Statistical Problem of Hidden Periodicities, Random Fourier Series
  • Parabolic Equations of forward-backward/degenerate types
  • Difference Equations with Delays

Short CV

  • 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:

Main papers:

  • M. Eller, I.M. Karabash, Homogenization and nonselfadjoint spectral optimization for dissipative Maxwell eigenproblems, preprint arXiv:2401.01049 [math.AP], 2024. https://doi.org/10.48550/arXiv.2401.01049

  • 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.

News

Prof. Dr. Lisa Sauermann has been honored with the von Kaven Award 2023 for her outstanding scientific achievements. (16.11.2023)

Prof. Dr. Angkana Rüland has been awarded a New Horizons in Mathematics Prize 2024 for her contributions to applied analysis:
https://www.hcm.uni-bonn.de/hcm-news/angkana-rueland-to-receive-illustrious-new-horizons-prize/
(14.09.2023)

Prof. Dr. Angkana Rüland has been awarded the Calderon Prize that is awarded every two years by the Inverse Problems International Association: https://www.hcm.uni-bonn.de/hcm-news/calderon-prize-for-angkana-rueland/ (06.09.2023)

Prof. Dr. Karl-Theodor Sturm has been elected into the Academia Europaea. (28.06.2022)

Florian Schweiger erhielt den Hausdorff-Gedächtnispreis 2021 der Fachgruppe Mathematik für die beste Dissertation. Er fertigte die Dissertation unter der Betreuung von Prof. Stefan Müller an. Unter anderen wurde Vanessa Ryborz mit einem Preis der Bonner Mathematischen Gesellschaft für ihre von Prof. Sergio Conti betreute Bachelorarbeit ausgezeichnet. (18.01.2022)

Prof. Dr. Sergio Albeverio has been elected into the Academia Europaea and the Accademia Nazionale dei Lincei (more; 02.12.2021).

Contact

Managing Director: Prof. Dr. Juan J. L. Velázquez
Chief Administrator: Dr. B. Doerffel
geschaeftsfuehrung@iam.uni-bonn.de
Imprint | Datenschutzerklärung

Mailing address

Institute for Applied Mathematics
University of Bonn
Endenicher Allee 60
D-53115 Bonn / Germany