Dr. Stephan Mescher
Postdoctoral Research Assistant
University of Leipzig
Mathematical Institute
Department: Geometry
Room A 536
Augustusplatz 10
Tel: +49-(0)341-97 32114
E‑Mail: mescher@math.uni-leipzig.de
(Deutsche Version)


Member of the study commisson for mathematics

Teaching

Summer term 2021: Lecture course Mathematics for Physicists 2 (IPSP)

Winter term 2020/2021: Lecture course Mathematics for Physicists 1 (IPSP)

Summer term 2020: Lecture course Topology

Winter term 2019/2020: Exercise classes for Measure and Integration Theory (Prof. Dr. M. Schwarz)

Summer term 2019: Exercise classes for Complex Analysis (Dr. J. Hirsch)

Winter term 2018/2019: Exercise classes for Ordinary Differential Equations (Dr. J. Hirsch)

Summer term 2018: Lecture hall exercises for Analysis II (Prof. Dr. S. Luckhaus)

Winter term 2017/2018: Exercise classes for Analysis I (Prof. Dr. S. Luckhaus)
                              

Research interests

Geometry and topology of manifolds, topological robotics, in particular topological complexity, Morse theory, analysis on free loop spaces.

Publications

Book


Perturbed Gradient Flow Trees and A-infinity-algebra Structures in Morse Cohomology, Atlantis Studies in Dynamical Systems, vol. 6, Springer, 2018.

Papers


Existence results for closed Finsler geodesics via spherical complexities, Calc. Var. Partial Differ. Equ. 59 (2020), No. 5, article number 155, DOI arXiv.

Spherical complexities, with applications to closed geodesics, 2019, to appear in Algebr. Geom. Topol., arXiv.

(with Mark Grant) Topological complexity of symplectic manifolds, Math. Z., vol. 295 (2020), pp. 667-679, DOI, arXiv.

Oriented robot motion planning in Riemannian manifolds, 2018, Topol. Appl., vol. 258 (2019), pp. 1-20, DOI, arXiv.

(with Michael Farber) On the topological complexity of aspherical spaces, J. Topol. Anal. 12 (2020), no. 2, 293–319, DOI, arXiv.

Perturbed gradient flow trees and A-infinity-algebra structures on Morse cochain complexes, 2016, preprint, arXiv.

A primer on A-infinity-algebras and their Hochschild homology, 2016, preprint, arXiv.

                              

Talks

  • Video and slides for my talk at the BIRS Online Workshop "Topological Complexity and Motion Planning", 17-20 September 2020.
  • Slides for my talk in the Minisymposium Nonlinear Analysis, DMV-Jahrestagung 2020.
  • Slides for my talk on "Spherical complexities and closed geodesics", January 2020.
  • Slides for my talk at Geometrietag 2018 on 07.12.2018 at TU Dresden.


Employment

Since October 2017: Postdoctoral Research Assistant at the Chair for Mathematics in the Sciences (Prof. Dr. M. Schwarz), University of Leipzig

October 2016 - September 2017: Postdoctoral Research Assistant (supervisor: Prof. Dr. M. Farber), School of Mathematical Sciences, Queen Mary University of London

October 2012 - September 2016: Research Assistant at the Chair of Analysis (Prof. Dr. A. Abbondandolo), Faculty of Mathematics, Ruhr University Bochum

Education

July 2017: Ph. D. (Dr. rer. nat.) in Mathematics at the Faculty of Mathematics and Computer Science, University of Leipzig
(Advisor: Prof. Dr. M. Schwarz, thesis title: Hochschild homology of Morse cochain complexes and free loop spaces)

April 2008: Diploma (M. Sc.) in Mathematics at Bielefeld University
(Thesis advisor: Dr. K. Frøyshov, title of diploma thesis (in German): Der Spektralfluss von Familien selbstadjungierter elliptischer Operatoren)

June 2003: Abitur (high school graduation) at Gymnasium Antonianum Vechta

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