Prof. (Vertretung) Dr. Christian Rose

Vertretungsprofessor

Kontakt
Raum:
2.09.2.15
Telefon:
+49 331 977-2989

Teaching

SS 24 University of Potsdam

Vorlesung "Mathematik für Physiker_innen II" (bis 30.4.2024). Tragen Sie sich bitte bei Moodle und PULS ein.

WS 23/24 University of Potsdam

Vorlesung "Mathematik für Physiker_innen I". Tragen Sie sich bitte bei Moodle und PULS ein. 

Seminar "Analysis and heat kernels on graphs". Please subscribe to Moodle and PULS

WS 21/22 University of Bremen

Lecture "Funktionentheorie".

Seminar "Einführung in die Analysis auf Graphen".

SS 21 University of Potsdam

Lecture "Topologie". Moodle

Research Interests

According to MathSciNet, my research interests are

  • Differential geometry,
  • Global analysis, analysis on manifolds,
  • Partial differential equations. 

Currently, I am focussing on geometric and global analysis on graphs with unbounded geometry. Besides this, I am also working on properties of spaces with Ricci curvature bounds.

Submitted preprints

  • M. Keller and C. Rose. Gaussian upper bounds for heat kernels on graphs with unbounded geometry. 2022. arXiv
  • J. Jost, F. Münch, and C. Rose. Liouville property and non-negative Ollivier curvature on graphs. 2019. arXiv

Articles in peer-reviewed journals

  • C. Rose and M. Tautenhahn. Unique continuation estimates on manifolds with Ricci curvature bounded below. Journal of Mathematical Physics, 65 (4): Article number 041503, 2024. arXiv
  • M. Keller and C. Rose. Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees. Calculus of Variations and Partial Differential Equations, 63, Article number: 20, 2024. Journal arXiv
  • A. Dicke, C. Rose, A. Seelmann, and M. Tautenhahn. Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials. Journal of Differential Equations, 369: 405-–423, 2023. Journal arXiv
  • X. Ramos Olivé, C. Rose, L. Wang, and G. Wei. Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains. Mathematische Nachrichten, 296 (8):  3559--3578. 2023. Journal arXiv
  • O. Post, X. Ramos Olivé, and C. Rose. Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions. Journal of Geometric Analysis, 33: 70, 2023. Journal arXiv
  • C. Rose and G. Wei. Eigenvalue estimates under Kato-type Ricci curvature conditions.  Analysis & PDE, 15(7): 1703--1724, 2022. Journal arXiv
  • M. Hansmann, C. Rose, and P. Stollmann. Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences. Journal of Geometric Analysis, 32(4): 1--17, 2022. Journal arXiv
  • C. Rose. Almost positive Ricci curvature in Kato sense - an extension of Myers' theorem. Mathematical Research Letters, 28(6): 1841--1849, 2021. Journal arXiv
  • G. Carron and C. Rose. Geometric and spectral estimates based on spectral Ricci curvature assumptions. Journal für die Reine und Angewandte Mathematik. 2021 (772): 121--145, 2021. Journal arXiv
  • F. Münch and C. Rose. Spectrally positive Bakry-Émery Ricci curvature on graphs. Journal de Mathématiques Pures et Appliquées, 143: 334--344, 2020. Journal arXiv
  • S. Liu, F. Münch, N. Peyerimhoff, and C. Rose. Distance bounds for graphs with some negative Bakry-Émery Ricci curvature. Analysis and Geometry on Metric Spaces, 7(1):1--14, 2019. Journal arXiv
  • C. Rose. Li-Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class. Annals of Global Analysis and Geometry, 55(3):443--449,2019. Journal arXiv
  • I. Nakić, C. Rose, and M. Tautenhahn. A quantitative Carleman estimate for second order elliptic operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 149(4): 915--938, 2019. Journal arXiv
  • C. Rose. Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds. Journal of Geometric Analysis, 27:1737--1750, 2017. Journal arXiv
  • C. Rose and P. Stollmann. The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature. Proceedings of the American Mathematical Society, 145(5): 2199--2210, 2017. Journal arXiv

Contributions to books

  • C. Rose and P. Stollmann. Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications. In Analysis and Geometry on Graphs and Manifolds, Volume 461 of London Mathematical Society Lecture Note Series, Cambridge University Press, 2020.
  • D. Borisov, I. Nakić, C. Rose, M. Tautenhahn, and I. Veselić. Multiscale unique continuation properties of eigenfunctions. In Operator semigroups meet complex analysis, harmonic analysis and mathematical physics, volume 250 of Operator Theory Adv. Appl., pages 107--118. Birkhäuser/Springer, Cham., 2015.

Theses

  • Heat kernel estimates based on Ricci curvature integral bounds. PhD thesis, 2017. Advisor: Prof. Dr. Peter Stollmann, Technische Universität Chemnitz.
  • Über die Wärmeleitungshalbgruppe auf Mannigfaltigkeiten. Diploma thesis, 2014. Advisor: Prof. Dr. Peter Stollmann, Technische Universität Chemnitz.

CV

05/2024-todayPostdoc, Technische Universität Hamburg-Harburg
10/2023 - 04/2024 Deputy professor for mathematical physics, University of Potsdam
04/2022 - 09/2023Postdoc, University of Potsdam
10/2021 - 03/2022  Deputy professor for analysis, University of Bremen
12/2020 - 09/2021 Postdoc, University of Potsdam
10/2018 - 09/2020 Postdoc, Max Planck Institute for Mathematics in the Sciences, Leipzig
09/2017 - 09/2018 Postdoc, Chemnitz University of Technology
06/2014 - 08/2017 PhD student, Chemnitz University of Technology
10/2009 - 05/2014 Undergrad Studies in Mathematics, Chemnitz University of Technology