Marco Rehmeier

I obtained my master's degree in October 2018 at Bielefeld University, where I am now a doctoral student in the Stochastic Analysis Group of Prof. Dr. Michael Röckner.

Research stay at Seoul National University: Originally scheduled Mar-Aug 2020; now planned for May-Jun 2021.

Contact

Office: D5-152
P.O.-Box: #231 (Room V3-128)
E-Mail: mrehmeier(at)math.uni-bielefeld.de

Research Interests

Probability theory and Stochastic Analysis. Currently, I am particularly interested in the following topics
- solution flows for Fokker-Planck-Kolmogorov equations in arbitrary dimension (linear and nonlinear)
- Representation of solutions to (stochastic) Fokker-Planck-Kolmogorov equations via deterministic continuity equations on spaces of measures
- Convex integration approach to fluid dynamical PDEs.
- Uniqueness for generalized Porous Medium Equations, in particular for initial data being a measure.

Publications

1. M. Rehmeier, On Cherny's results in infinite dimensions: A theorem dual to Yamada-Watanabe (to appear in in Stochastics and Partial Differential Equations: Analysis and Computations) $\href{https://arxiv.org/abs/1812.02607}{\text{Link to preprint}}$
2. M. Rehmeier, Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness (to appear in Journal of Evolution Equations) $\href{https://arxiv.org/abs/1904.04756}{\text{Link to preprint}}$

Preprints

M. Rehmeier, Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations (2020). $\href{https://arxiv.org/abs/2012.13530}{\text{arXiv-version}}$

Conferences and Workshops

Co-Organizer of the BGTS Doctoral Day (Bielefeld, Oct 20)

  • 9th International Conference on Stochastic Analysis and Its Applications (Bielefeld, 09/18)
  • Winter School on Stochastic PDEs and Mean Field Games (Bologna, Jan 19)
  • Seventh Bielefeld-SNU Joint Workshop in Mathematics (Bielefeld, Feb 19)
  • 41. Nordwestdeutsches Funktionalanalysis-Kolloquium (Essen, Jun 19)
  • Recent Trends in Stochastic Analysis and SPDEs (Pisa, Jul 2019)
  • 29. Jyväskylä Summer School (topic: Selected Topics in the Theory of BSDEs (Jyväskylä, Aug 19)
  • IRTG Summer School on probability theory and stochastic dynamics (Bielefeld, Aug 19)
  • Annual DMV-Conference 2019 (Karlsruhe, Sep 2019)
  • Touch down of stochastic analysis in Bielefeld (Bielefeld, Sep 19)
  • Eighth Bielefeld-SNU Joint Workshop in Mathematics (Bielefeld, Feb 20)

Talks

  • Contributed talk: On Cherny's results in infinite dimensions: A theorem dual to Yamada-Watanabe (Bielefeld, Mar 19)
  • Contributed talk: Existence of flows for linear FPK-equations and its connection to well-posedness (Essen, Jun 19)
  • Contributed talk: Introduction to quasi-stationary distributions and first general properties (Bielefeld, Aug 19)
  • Contributed talk: On Cherny's results in infinite dimensions: A theorem dual to Yamada-Watanabe (Karlsruhe, Sep 19)
  • Contributed talk: From Interacting Particle Systems to Nonlinear Fokker-Planck Equations (Bielefeld, Oct 20)
  • Several talks in working group seminars, including a series of talks on Convex Integration for fluid dynamical PDEs and its origin in Nash's $C^1$ isometric embedding theorem (Feb 21)

Teaching

  • Tutorials (undergraduate courses), including Analysis (multiple times), Linear Algebra, Measure Theory, Stochastics, Functional Analysis
  • Tutorials (graduate courses), including Probability Theory II

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