I am a research mathematician working at the intersection of geometry, topology and analysis with a particular focus on problems involving the scalar curvature of a Riemannian manifold. Recently, my main passions have been to establish aspects of a comparison geometry for lower scalar curvature bounds as well as to study closely related geometric problems in the context of general relativity. Moreover, I am interested in topological properties of spaces of Riemannian metrics with positive scalar curvature.

A broad overview of the circle of ideas with which my research is generally concerned can be found in the forthcoming volumes *Perspectives in Scalar Curvature* edited by Misha Gromov and Blaine Lawson.

Currently I am working as a non-permanent lecturer (formal title: *akademischer Rat auf Zeit*) at the Mathematical Institute of the University of Münster, where I am an investigator in the Cluster of Excellence Mathematics Münster. I am also a project leader in a subproject of the DFG priority programme Geometry at Infinity.

During the summer term 2020 I was on leave from Münster in order to serve as a *Vertretungsprofessor* at the Mathematical Institute of the University of Göttingen.

- Scalar and mean curvature comparison via the Dirac operator (with S. Cecchini).
*Geometry & Topology*, to appear. arXiv - Band width estimates via the Dirac operator.
*Journal of Differential Geometry*, 2022. arXiv DOI - On the range of the relative higher index and the higher rho-invariant for positive scalar curvature (with Z. Xie, G. Yu).
*Advances in Mathematics*, 2021. arXiv DOI - Transfer maps in generalized group homology via submanifolds (with M. Nitsche, T. Schick).
*Documenta Mathematica*, 2021. arXiv DOI - Slant products on the Higson-Roe exact sequence (with A. Engel, C. Wulff).
*Annales de l’Institut Fourier*, 2021. arXiv DOI - Width, Largeness and Index Theory.
*SIGMA*, Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday, 2020. arXiv DOI - Positive scalar curvature and low-degree group homology (with N. Bárcenas).
*Annals of K-Theory*, 2018. arXiv DOI - An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds.
*Algebraic & Geometric Topology*, 2017. arXiv DOI - Positive scalar curvature and product formulas for secondary index invariants.
*Journal of Topology*, 2016. arXiv DOI - Coarse median structures and homomorphisms from Kazhdan groups.
*Geometriae Dedicata*, 2016. arXiv DOI

*Nonnegative scalar curvature on manifolds with at least two ends*(with S. Cecchini, D. Räde). arXiv*The positive mass theorem and distance estimates in the spin setting*(with S. Cecchini). arXiv

- Scalar curvature and generalized Callias operators (with S. Cecchini).
*Perspectives in Scalar Curvature*, volume edited by M. Gromov and B. Lawson, World Scientific, 2023. DOI - Scalar and mean curvature comparison via the Dirac operator. Extended abstract in Oberwolfach Rep. 30/2021: Analysis, Geometry and Topology of Positive Scalar Curvature Metrics. DOI
- Secondary large-scale index theory and positive scalar curvature. Extended abstract in Oberwolfach Rep. 36/2017: Analysis, Geometry and Topology of Positive Scalar Curvature Metrics. DOI
- Primary and secondary obstructions to positive scalar curvature via submanifolds. Extended abstract in Oberwolfach Rep. 35/2016: Topologie. DOI
*Secondary large-scale index theory and positive scalar curvature*. Doctoral thesis, University of Göttingen, 2016. DOI*Coarse median structures on groups*, Master’s thesis, University of Vienna, 2013. DOI

- Workshop on Mathematical Relativity, Scalar Curvature and Synthetic Lorentzian Geometry, Fields Institute, Oct 2022. youtube
- Oberwolfach workshop Non-commutative geometry and cyclic homology, Aug 2022.
- Recent Advances on Scalar Curvature Problems, Simons Center for Geometry and Physics, Jun 2022. video
- Differential Geometry in the Large, Karlsruhe, Jun 2022.
- Not Only Scalar Curvature Seminar, Jan 2022. youtube
- The 4th Geometric Analysis Festival, Oct 2021. youtube
- Oberwolfach workshop Analysis, Geometry and Topology of Positive Scalar Curvature Metrics, Jun 2021.
- Topology Seminar Bonn, Jun 2021.
- Forschungsseminar Differentialgeometrie Potsdam, May 2021.
- Oberseminar Differentialgeometrie Münster, Apr 2021.
- Pure Mathematics Colloquium at Southampton, Mar 2021.
- Global Noncommutative Geometry Seminar, Sep 2020. youtube
- Virtual Workshop on Ricci and Scalar Curvature, Aug 2020. youtube

- Seminar: Higher index theory (with G. Frenck). PDF (via sciebo)
- Exercise classes for the lecture “Differential equations” (with B. Santoro). Learnweb

- Seminar on index theory: Local index theory and boundary value problems (with J. Ebert, U. Ludwig). Learnweb
- Exercise classes for the lecture “Fields and Constructions” (with A. Bartels). Learnweb

- Exercise classes for Analysis III (with S. Echterhoff).
- Seminar: Seiberg-Witten theory (with G. Frenck). PDF (via sciebo)

- Exercise classes for Analysis II (with S. Echterhoff). Learnweb

- Exercise classes for Analysis I (with S. Echterhoff). Learnweb
- Seminar: Generalized soap bubbles and scalar curvature (with A. Engel). PDF (via sciebo)

- Lecture course:
*Mathematics for physics students II*. Stud.IP - Oberseminar
*Topology and Geometry*(with S. Cecchini, T. Schick).

- Lecture course:
*Coarse index theory* - (Co-)organized seminars:
*Positive scalar curvature*;*Vector bundles and K-theory*;*Conic sections*;*Topics from analysis*. - Organization of exercises:
*Linear algebra I and II*;*Algebra*(2x);*Foundations of Analysis, Topology and Geometry*;*Group theory*.

- Teaching assistant:
*Introduction to computer infrastructure for mathematicians*(4x).

University of Münster

Mathematisches Institut

Einsteinstr. 62

48149 Münster, Germany

Office: 517

Phone: +49 251 83-33740

Email: rudolf.zeidler@uni-muenster.de