Schriften
Monographien
Moduli Spaces of Riemannian Metrics. (with D.J. Wraith) Oberwolfach Seminars Vol. 46, Birkhäuser, Basel 2015.
Endlichkeitssätze und positive Krümmung. Habilitation thesis. MPI MIS Lecture Notes Series 9, Leipzig 2000.
Sofia Kowalewskaja. (with P. Hawig) Scientific biography of the Russian mathematician and author S. W. Kowalewskaja (1850-1891). Birkhäuser, Basel 1993.
Herausgeberschaften
Facets of Contemporary Analysis, Geometry and Non-Euclidean Statistics. HeKKSaGOn Mathematics Group Meetings, Kyoto and Sendai, September 2023. (with Takashi Shioya and Senjo Shimizu) Tohoku Series in Mathematical Sciences. Springer, to appear in 2025.
Differential geometry in the large. Proceedings of the Australian-German workshop on differential geometry in the large, Creswick, Australia, February 4–15, 2019. (with O. Dearricott, Y. Nikolayevsky, T. Leistner, D. Crowley) London Mathematical Society Lecture Note Series 463. Cambridge: Cambridge University Press (2021).
Topics in metric Riemannian geometry. (with F. Fang, X. Rong, Y. Yang) Front. Math. China 11, No. 5, Special Issue. Beijing-Berlin-Heidelberg: Springer/Higher Education Press (2016).
Buchkapitel
Collapsing and Almost Nonnegative Curvature. In: Bär, Lohkamp and Schwarz, Global Differential Geometry, Springer Proceedings in Mathematics 17, 93-106 (2012)
Forschungsartikel
A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity. (with J. Wee, X. Gong, K. Xia) Nature Scientific Reports, https://www.nature.com/articles/s41598-025-93381-y.pdf (2025)
Moduli Spaces of Metrics with Lower or Pinched Curvature Bounds and their Compactifications. Journal of Mathematical Study , Vol. 58, No. 2, pp. 175-187, doi: 10.4208/jms.v58n2.25.04 (2025)
Categorical and geometric methods in statistical, manifold, and machine learning. (with H.-V. Lê, H.-Q. Minh, F. Protin) Facets of Contemporary Analysis, Geometry and Non-Euclidean Statistics. HeKKSaGOn Mathematics Group Meetings, Kyoto and Sendai, September 2023. Tohoku Series in Mathematical Sciences. Springer, to appear in 2025. (https://arxiv.org/abs/2505.03862) (2024)
Moduli Spaces of Nonnegatively Curved Metrics on Closed Manifolds and RCD spaces. Facets of Contemporary Analysis, Geometry and Non-Euclidean Statistics. HeKKSaGOn Mathematics Group Meetings, Kyoto and Sendai, September 2023. (PDF) (2024)
On the topology of moduli spaces of non-negatively curved Riemannian metrics. (with M. Wiemeler) Mathematische Annalen 384, No. 3-4, 1629-1651 (2022)
Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds. (with B. Eltzner, F. Galaz-Garcia, S. F. Huckemann) Proc. Amer. Math. Soc. 149 (2021), 3947-3963, https://doi.org/10.1090/proc/15429 (2021)
Epidemic Dynamics via Wavelet Theory and Machine Learning, with Applications to Covid-19.. (with Frédéric Protin, Hông Vân Lê et al.), Biology 2020 9(12), https://doi.org/10.3390/biology9120477 (2020)
Finiteness and realization theorems for Alexandrov spaces with bounded curvature. (with F. Galaz-Garcia) Bol. Soc. Mat. Mex., III. Ser. 26, No. 2, 749-756 (2020)
Smooth stability and sphere theorems for manifolds and Einstein manifolds with positive scalar curvature. (with M. Wiemeler) Communications in Analysis and Geometry 27, no. 2, 491-509 (2019)
On the Torsion in the Center Conjecture. (with V. Kapovich and A. Petrunin) Electronic Research Announcements in Mathematical Sciences 25, 27-35 (2018)
Nonconnected Moduli Spaces of Nonnegative Sectional Curvature Metrics on Simply Connected Manifolds. (with A. Dessai and S. Klaus) Bull. London Math. Soc. 50, 96–107 (2018)
Spaces and moduli spaces of Riemannian metrics. Front. Math. China 11, no. 5, 1335–1343 (2016)
Fiber-Bragg Gitter basierte Formsensorik in der Ureterorenoskopie - Konstruktion und Test eines Ausführungskonzeptes. (with H. Pauer, D. Teber und H. Woern) In: Tagungsband der 15. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie (CURAC) (2016)
Towards 1-Component Bragg-Grating Based Shape Sensing. (with H. Pauer, M. Rosenberger, M. Girschikofsky, R. Hellmann, H. Woern) In: 19th International Conference on Information Fusion Heidelberg, Germany - July 5-8, 2016 (2016)
Shape Sensing Based on FBG-Technology - Extension of the Application Possibilities Due to Innovative Sensor-Configurations. (with H. Pauer, Chr. Ledermann, J. Raczkowsky, H. Woern) In: Navigation and Actuation of Flexible Instruments in Medical Applications (NAFIMA) Workshop Proceedings - IROS2015 (2015)
Pseudo-Data Generation Software for FBG-Optical Fiber Based Shape Sensing. (with H. Pauer, Chr. Ledermann, H. Woern) In: Proceedings - SENSOR 2015 (AMA Conferences), ISBN 978-3-9813484-8-4 (2015)
Validation of a Pseudo-Data-Generation-Software for FBG-Optical Fiber Based Shape Sensing. (with H. Pauer, Chr. Ledermann, L. Vojkovic, H. Woern) In: Proceedings Innovation Messtechnik 2015, ISBN 978-3-8440-3560-5 (2015)
Non-Linear Compensation of Production Inaccuracies and Material Drift by Adjusting the Sensor Data Fusion Algorithms for Shape Sensing Based on FBG-Optical Fibers. (with H. Pauer, Chr. Ledermann, H. Woern) In: Proceedings of the 2014 IEEE Ninth International Conference on Multisensor Fusion and Information Integration (MFI) (2014)
Consistent Quality Evaluation Method for Shape Sensors based on FBG–Optical Fibers Used in Minimally Invasive Surgery. (with H. Pauer, Chr. Ledermann, H. Woern) In: Proceedings of the 17. ITG / GMA Fachtagung Sensoren und Messsysteme, Editor VDE Verlag Berlin - Offenbach (2014)
Analyse der Anforderungen an Formsensoren zur Verwendung in der minimal-invasiven Chirurgie. (with H. Pauer, H. Kenngott, Chr. Ledermann, H. Woern) In: Tagungsband der 13. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie (CURAC) (2014)
Manifolds with almost nonnegative curvature operator and principal bundles. (with M. Herrmann and D. Sebastian) Annals of Global Analysis and Geometry, DOI10.1007/s10455-013-9372-2 (2013)
Nilpotency, Almost Nonnegative Curvature, and the Gradient Flow on Alexandrov Spaces. (with V. Kapovitch and A. Petrunin) Annals of Mathematics 171, 343–373 (2010)
Nonnegative Curvature and Cobordism Type. (with A. Dessai) Mathematische Zeitschrift, Z 257, no.1, 7–12 (2007)
Nonnegative Pinching, Homotopy Type and Bundles with infinitely many Souls. (with V. Kapovitch and A. Petrunin) Journal of Differential Geometry 71, 365–383 (2005)
Nonnegatively and Positively Curved Invariant Metrics on Circle Bundles. (with K. Shankar and K. Tapp) Proceedings of the A.M.S. 133, 2449-2459 (2005)
Metrics of Positive Ricci Curvature on Quotient Spaces. (with L. Schwachhöfer) Mathematische Annalen 330, 59–91 (2004)
Duality versus Dual Flatness in Quantum Information Geometry. (with N. Ay) Journal of Mathematical Physics 44, 1512–1518 (2003)
Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness. Mathematische Annalen 322, 413–420 (2002)
Smooth Diameter and Eigenvalue Rigidity in Positive Ricci Curvature. Proceedings of the A.M.S. 130, 303–306 (2002)
Dually Flat Manifolds and Global Information Geometry. (with N. Ay) Open Systems and Information Dynamics 9, 195–200 (2002)
Asymptotical Flatness and Cone Structure at Infinity. (with A. Petrunin) Mathematische Annalen 321, 775–788 (2001)
Diffeomorphism Finiteness, Positive Pinching, and Second Homotopy. (with A. Petrunin) Geometric and Functional Analysis (GAFA) 9, 736–774 (1999)
Collapsing versus Positive Pinching. (with A. Petrunin and X. Rong) Geometric and Functional Analysis (GAFA) 9, 699–735 (1999)
Invariant Metrics of Positive Ricci Curvature on Principal Bundles. (with P. Gilkey and J.-H. Park) Mathematische Zeitschrift 227, 455-463 (1998)
Collapsing, Solvmanifolds and Infrahomogeneous Spaces. Differential Geometry and its Applications 7, 251–264 (1997)
On the Structure of Compact Simply Connected Manifolds of Positive Sectional Curvature. Geometriae Dedicata 67, 107–116 (1997)
Hausdorff Convergence and the Fundamental Group. Mathematische Zeitschrift 218, 207–211 (1995)
On the geometry of infrasolvmanifolds. (Zur Geometrie von Infrasolvmannigfaltigkeiten.) (German) Zbl 0885.53040, Bochum: Math. Fak., Univ. Bochum (1993)
Tagungsbeiträge
Sphere Theorems, Space Forms, and Positive Scalar Curvature. (with M. Wiemeler) Oberwolfach Reports 14(3), 2281-2283, European Mathematical Society Publishing House (2017)
Fundamentals of Geometry. Oberwolfach Reports 8(2), 999, European Mathematical Society Publishing House (2011)
Nilpotency and almost nonnegative curvature. Oberwolfach Reports 3(4), 2718-2721, European Mathematical Society Publishing House (2006)
Manifolds of positive Ricci curvature. Recent advances in geometry and topology, 385–390, Cluj University Press, Cluj-Napoca (2004)
Biquotients, curvature and homotopy Type. Oberwolfach Reports 1(4), 2509–2512, European Mathematical Society Publishing House (2004)
Hausdorff convergence and infrasolvmanifolds. Geometry and global analysis (Sendai, 1993), 387–397, Tohoku University Press, Sendai (1993)
Aktuelle Preprints (auf arXiv)
Unified modelling of epidemics by coupled dynamics via Monte-Carlo Markov Chain algorithms (with Frédéric Protin, Hông Vân Lê et al.)
Weitere Preprints
Seifert Fiberings and Collapsing of Infrasolv Spaces (with O. Baues) (2012)
A note on nonnegative curvature and (rational) homotopy type (with A. Dessai) (2011)
Almost Nonnegative Curvature and Cohomogeneity One (with L. Schwachhöfer) (2001)
Lehre, Unterhaltung und Wissenschaftsvermittlung
Albrecht Dürer als Mathematiker (2008)
Differentialgeometrie und Schwarze Löcher (1998)
Raymond Smullyan - Satan, Cantor and infinity, and other mind-boggling puzzles. Transl. from the English by Wilderich Tuschmann. (Satan, Cantor und die Unendlichkeit. Aus dem Englischen übersetzt von Wilderich Tuschmann.) (German) Birkhäuser, Basel (1993), Insel, Frankfurt/Leipzig (1997)
Mitorganisierte Konferenzen & Workshops
Moduli Spaces of Canonical Metrics: Metric Riemannian Geometry and Topology Oberwolfach, 23. - 28. November 2025
Trends in Applied Math and Machine Learning Lishui, 8. - 13. Juni 2025
Applied Geometry for Data Sciences Part II Singapur, 2. - 6. Juni 2025
HeKKSaGOn Mathematics Meeting 2024 Karlsruhe und Göttingen, 25. - 29. November 2024
Applied Geometry for Data Sciences Part I Singapur, 30 September - 12. October 2024
Hekksagon Workshop: Analysis, Geometry and Topology on Metric Spaces Kyoto und Sendai, 25.-29. September 2023
Riemannian Topology Seminar Stuttgart, 15.-16. Mai 2023
Banach Center – Oberwolfach Graduate Seminar Będlewo, 21. - 25. November 2022
Applied Geometry for Data Sciences Chongqing, 25. - 29. Juli 2022
Differential Geometry in the Large Karlsruhe, 7. - 11. Juni 2022 (mit G. Besson)
Conference on Topology and Differential Geometry Sanya, 18. - 22. Januar 2021 (mit A. Gogolyev, Y. Jiang)-->
Spaces of Riemannian Metrics and Positive Scalar Curvature - A-Fri-Ka Karlsruhe, 23. - 24. Januar 2020
DMV Jahrestagung 2019 Karlsruhe, 23. - 26. September 2019
HeKKSaGOn Meeting: Mathematics at the Interface of Science and Technology Universität Heidelberg, 12. - 13. September 2019
Australian-German Workshop on Differential Geometry in the Large Melbourne, 04. - 15. Februar 2019
Riemannian Topology Meeting Universität Freiburg (Schweiz), 08. - 09. November 2018
Workshop on Global Differential Geometry Sanya, 26. Februar - 2. März 2018 (mit F. Fang, T. Farrell, X. Rong, Y. Yang)
HeKKSaGOn Workshop: Stochastics meets Geometry Karlsruhe, 11. - 12. Dezember 2017
Oberwolfach Seminar: Lower Curvature Bounds and Topology Oberwolfach, 19. - 25. November 2017 (mit F. Fang)
Mini-Workshop in Metric Geometry Karlsruhe, 24. Juni 2017
Mini-Workshop on Spaces and Moduli Spaces of Riemannian MetricsOberwolfach, 8. - 14. Januar 2017 (mit F. Th. Farrell)
Geometry, Groups and Topology 2016Karlsruhe, 10. - 14. Oktober 2016 (mit F. Fang, E. Leuzinger, X. Rong, R. Sauer und Y. Yang)
HeKKSaGOn Mini-Workshop 2016: Perspectives and Challenges in Mathematical SciencesKarlsruhe, 1. Oktober 2016
Riemannian Topology Seminar 2015Göttingen, 19. - 20. November 2015 (mit O. Baues und Th. Schick)
Chinese-German workshop on Metric Riemannian GeometrySchanghai, 12. - 16. Oktober 2015 (mit Fuquan Fang, Enrico Leuzinger, Xiaochun Rong, Roman Sauer, Yihu Yang)
Riemannian Topology Seminar 2015Fribourg, 22. - 23. Januar 2015 (mit A. Dessai, F. Galaz-Garcia, M. Herrmann)
Moduli Spaces of Riemannian MetricsOberwolfach, 8. - 14. Juni 2014 (mit David J. Wraith)
Riemannian Topology Seminar 2013: F-Structures in Geometry and TopologyKarlsruhe, 28. - 29. November 2013 (mit A. Dessai)
Geometry, Groups and Topology 2013 Karlsruhe, 7. - 11. Oktober 2013 (mit R. Sauer und G. Weitze-Schmithüsen)
Riemannian Topology Meeting Fribourg, 15. - 16. Juni 2012 (mit A. Dessai, M. Herrmann, L. Kiwi und N. Weisskopf)
Mini-Workshop: Manifolds with Lower Curvature Bounds Oberwolfach, 1. - 7. Januar 2012 (mit A. Dessai und B. Wilking)
Geometry, Groups and Topology 2011 Karlsruhe, 12. - 15. September 2011 (mit A. Dessai und E. Leuzinger)