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