HOME
RESEARCH
PUBLICATIONS
TALKS
TEACHING

Welcome to the home page of Artur Stephan.

I am a doctoral student of Prof. Dr. Alexander Mielke at WIAS-Berlin and Berlin Mathematical School working in the area of Applied Analysis.

Contact

Artur Stephan
Humboldt University Berlin
Institute for Mathematics
mail: lastname (at) math.hu-berlin.de

or

Weierstrass Institute
Mohrenstrasse 39
10117 Berlin, Germany
mail: firstname (dot) lastname (at) wias-berlin.de


I am also on ResearchGate.

Scientific interests

  • Operator theory and semigroup theory; split-step approximations with convergence rate estimates. Functional Analysis.
  • Variational methods for evolution equations, ordinary and partial differential equations. Convex analysis and Gamma-convergence.
  • Applications to classical and quantum mechanics; reaction-diffusion systems.
  • Multi-scale problems and mathematical coarse-graining.

Publications

You find preprints of my published papers also on arXiv. If not, please contact me.

  • Convergence rate estimates for approximations of solution operators, with H. Neidhardt and V. A. Zagrebnov, published in Pub. Res. I. Math. Sci., January 2020, Volume 56, Issue 1.
  • On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations, with H. Neidhardt and V. A. Zagrebnov, published in Nanosystems: physics, chemistry, mathematics April 2017, Volume 8, Issue 2, pp 202.
  • Phase response function for oscillators with strong forcing or coupling, with Vl. Klinshov, Vl. Nekorkin and S. Yanchuk, published in Europhysics Letters, August 2017, Volume 118, Number 5.
  • Remarks on the operator-norm convergence of the Trotter product formula, with H. Neidhardt and V. A. Zagrebnov, published in Integral Equations and Operator Theory, April 2018, Volume 90, Number 15.
  • Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey, with H. Neidhardt and V. A. Zagrebnov, published in: Rassias Th. (eds) Current Research in Nonlinear Analysis. Springer Optimization and Its Applications, vol 135. Springer, June 2018.
  • Memory equations as reduced Markov processes, with H. Stephan, published in Discr. Cont. Dyn. Systems, April 2019, Volume 39, Number 4.
  • Trotter Product Fromula and Linear Evolution Equations on Hilbert Spaces, with H. Neidhardt and V. A. Zagrebnov, published in: Rassias Th., Zagrebnov V. A. (eds) Analysis and Operator Theory. Springer Optimization and Its Applications, vol 146. Springer, June 2019.
  • Combinatorial considerations on the invariant measure of a stochastic matrix, Preprint on arXiv, October 2019.
  • On EDP-convergence for gradient systems with different time scales, published in Proc. in Applied Math. and Mechanics, November 2019.
  • Coarse-graining via EDP-convergence for linear fast-slow reaction systems, with A. Mielke, published in M3AS, June 2020, Volue 30, Number 09.
  • Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator, with M. Heida and M. Kantner, Preprint on arXiv, February 2020.
  • EDP-convergence for nonlinear fast-slow reaction systems, Oberwolfach Report 2038, September 2020.
  • EDP-convergence for nonlinear fast-slow reaction systems with detailed balance, with A. Mielke and M. A. Peletier, Preprint on arXiv, Oktober 2020.
  • EDP-convergence for a linear reaction-diffusion system with fast reversible reaction, Preprint on arXiv, December 2020.

Talks and Conferences

  • 24-28/09/2014 -- Autumn School on Laser Dynamics, Bolyai Institute, University of Szeged, Hungary
  • 18/06/2015 -- Young Reseachers Seminar in FU Berlin, Coupled two-mode lasers and how detuning activates modes
  • 20/01/2016 -- Young Reseachers Seminar in TU Berlin, Phase response curve for mode-locked lasers
  • 18/05/2016 -- Oberseminar Nonlinear Partial Differential Equations (Langenbach-Seminar) in WIAS Berlin, On operator-norm estimates for approximations of solutions of evolution quations using the Trotter product formula
  • 14-15/07/2016 -- New Methods in Extension Theory applied to Quantum Mechanics in WIAS Berlin, On operator-norm estimates for approximations of solutions of evolution quations
  • 30/11/2016 -- Research Seminar: Applied Dynamical Systems in TU Berlin, On approximations of solutions of evolution equations using semigroups - Basic setting and problems
  • 14/12/2016 -- Research Seminar: Applied Dynamical Systems in TU Berlin, On approximations of solutions of evolution equations using semigroups - Applications (Part II)
  • 19/06/2017 -- WIAS PhD-Seminar, On approximations of solutions of evolution equations using semigroups
  • 21-23/02/2018 -- 6th BMS Student Conference, Berlin, On the Hamilton-Jacobi equation
  • 17/10/2018 -- Oberseminar Nonlinear Partial Differential Equations (Langenbach-Seminar) in WIAS Berlin, On linear reactions with different time scales
  • 18-22/02/2019 -- Annual Conference of GAMM 2019, Rigorous derivation of the effective equation for linear reactions with different time scales via EDP-convergence
  • 25-28/03/2019 -- COPDESC-Workshop Regensburg, Evolutionary Gamma-convergence for linear reaction-diffusion systems with different time scales
  • 01-05/07/2019 -- Calculus of Variations on Schiermonnikoog 2019, EDP-convergence for linear reaction-diffusion systems with different time scales
  • 10/07/2019 -- Oberseminar Nonlinear Partial Differential Equations (Langenbach-Seminar) in WIAS Berlin, On EDP-convergence for linear reaction-diffusion systems with different time scales
  • 15-19/07/2019 -- ICIAM2019 in Valencia, EDP-convergence for linear reaction-diffusion systems with different time scales
  • 24-29/11/2019 -- Winter School on Gradient Flows and Variational Methods in PDEs, Ulm, Coarse-graining via EDP-convergence for linear reaction-diffusion systems with different time scales
  • 19-22/12/2019 -- Workshop on Operator Theory and Krein Spaces, Vienna, On evolution semigroups and Trotter product operator-norm estimates
  • 20/01/2020 -- Analysis Seminar, Eindhoven, On linear reactions with different time scales
  • 05/02/2020 -- WIAS PhD-Seminar, Reaction-diffusion systems: gradient structures, different time scales, coarse-graining
  • 19-21/02/2020 -- 8th BMS Student Conference, Berlin, On mathematical coarse-graining for linear reaction systems
  • 14-18/09/2020 -- Oberwolfach Workshop on Variational Methods for Evolution, MFO, EDP-convergence for nonlinear fast-slow reaction systems
  • 30/09-02/10/2020 -- Annual Workshop of the GAMM Activity Group "Analysis of partial differential equations, IST Klosterneuburg, online, EDP-convergence for nonlinear fast-slow reaction systems
  • 12-23/10/2020 -- Student Compact Course of the Thematic Einstein Semester on Energy-based Mathematical Methods for Reactive Multiphase Flows, Berlin, online, Coarse-graining for gradient sytems with applications to reaction systems
  • 11/11/2020 -- CRC 1114 PhD seminar, Berlin, online, On gradient flows and gradient systems
  • 25/11/2020 -- CRC 1114 PhD seminar, Berlin, online, On gradient systems with applications to particle systems

Teaching

I have a lectureship for Analysis at HU Berlin.

I have also deputized several lectures on Analysis and Calculus of Variations.

Miscellaneous

  • Master thesis
    Here you find a pdf-file of my master thesis.
  • Media
    I gave a talk at the 6th BMS Student Conference on the Hamilton-Jacobi equation. The talk has been recorded.
  • Membership
    I am a member of the GAMM Activity Group "Analysis of Partial Differential Equations".
  • PhD-student representative
    I was the PhD-student representative in WIAS Berlin from 2018 to 2020.

© Artur Stephan. Last modified: December 2020