A list of ongoing projects and recent publications can be found below.
You can find more projects and publications on the webpages of the groups.
Current Projects
- COMSCAL – Comparison and rigidity for scalar curvature ( – )
EU-Project Hosted at University the of Münster: EC Horizon Europe - ERC Starting Grant | Project Number: 101116001 - CRC 1442 - A01: Automorphic forms and the p-adic Langlands programme ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, A01 - CRC 1442 - A02: Moduli spaces of p-adic Galois representations ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, A02 - CRC 1442 - A05: Moduli spaces of local shtukas in mixed characteristic ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, A05 - CRC 1442 - D03: Integrability ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, D03 - CRC 1442 - A04: New cohomology theories for arithmetic schemes ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, A04 - CRC 1442 - C02: Homological algebra for stable ∞-categories ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, C02 - CRC 1442 - D01: Amenable dynamics via C*-algebras ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, D01 - CRC 1442 - D05: C*-algebras, groups, and dynamics: beyond amenability ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, D05 - CRC 1442 - B03: Moduli spaces of metrics of positive curvature ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/1, B03 - CRC 1442 - B05: Scalar curvature between Kähler and spin ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/1, B05 - CRC 1442 - C03: K-theory of group algebras ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, C03 - CRC 1442 - B02: Geometric evolution equations ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, B02 - CRC 1442 - B04: Harmonic maps and symmetry ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/1, B04 - CRC 1442 - B01: Curvature and Symmetry ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, B01 - CRC 1442: Geometry: Deformation and Rigidity ( – )
Main DFG-Project Hosted at the University of Münster: DFG - Collaborative Research Centre - CRC 1442 - Z01: Central Task of the Collaborative Research Centre ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, Z01 - CRC 1442 - B06: Einstein 4-manifolds with two commuting Killing vectors ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, B06 - CRC 1442 - D04: Entropy, orbit equivalence, and dynamical tilings ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, D04 - RTG 2553: Symmetries and classifying spaces: analytic, arithmetic and derived (since )
Project Carried out outside the University Münster: DFG - Research Training Group - EXC 2044 - A1: Arithmetic, geometry and representations ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - B1: Smooth, singular and rigid spaces in geometry ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - B2: Topology ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C1: Evolution and asymptotics ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C4: Geometry-based modelling, approximation, and reduction ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 – Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure ( – )
Main DFG-Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - B3: Operator algebras & mathematical physics ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - A2: Groups, model theory and sets ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C3: Interacting particle systems and phase transitions ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - AMAREC – Amenability, Approximation and Reconstruction ( – )
EU-Project Hosted at University the of Münster: EC H2020 - ERC Advanced Grant | Project Number: 834267 - Dynamical systems and irregular gradient flows ( – )
Own Resources Project - SFB TR326 GAUS – Geometry and Arithmetic of Uniformized Structures ( – )
Project Carried out outside the University Münster - Quantization, Singularities and Holomorphic Dynamics ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: LU 1193/2-1 - ViMo – Visualisierungen bei der Bearbeitung von mathematischen Modellierungsaufgaben (since )
Own Resources Project - String Geometry Network (since )
Own Resources Project
- COMSCAL – Comparison and rigidity for scalar curvature ( – )
Latest Publications
- . . ‘Positive Mass Theorems for Spin Initial Data Sets With Arbitrary Ends and Dominant Energy Shields.’ International Mathematics Research Notices 2024, № 9: 7870–7890. doi: 10.1093/imrn/rnad315.
- . . ‘QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization.’ Journal of Mathematical Physics 65: 032302. doi: 10.1063/5.0158724.
- . . ‘On a conjecture of Stolz in the toric case.’ Proceedings of the American Mathematical Society 152, № 8: 3617–3621. doi: 10.1090/proc/16823.
- . . ‘On the homotopy type of the space of metrics of positive scalar curvature.’ Journal of the European Mathematical Society 26, № 9: 3327–3363. doi: 10.4171/JEMS/1333.
- . . ‘Tracially amenable actions and purely infinite crossed products.’ Mathematische Annalen 2024. doi: 10.1007/s00208-024-02833-9.
- . . ‘Motivic Chern classes of Schubert cells, Hecke algebras, and applications to Casselman's problem.’ Annales Scientifiques de l'École Normale Supérieure 57, № 1: 87–141. doi: 10.24033/asens.2571.
- . . ‘Strategische Videos zum Beweisen in der Studieneingangsphase – das Projekt ProVie.’ In Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln, edited by , 127–133. N/A: Selbstverlag / Eigenverlag. doi: 10.17170/kobra-2024081810686-127.
- . . ‘Adaptive Approximation of Persistent Homology.’ Journal of Applied and Computational Topology 8, № 8: 2327–2366. doi: 10.1007/s41468-024-00192-7.
- . . ‘Unitary Lp+-representations of almost automorphism groups.’ Comptes Rendus Mathématique 362: 245–249. doi: 10.5802/crmath.549.
- . . ‘Group C*-algebras of locally compact groups acting on trees.’ International Mathematics Research Notices 2024, № 10: 8520–8539. doi: 10.1093/imrn/rnad259.
- . . ‘Equivariant toric geometry and Euler-Maclaurin formulae—an overview.’ Revue Roumaine des Mathematiques Pures et Appliquees 69, № 2: 105–128. doi: 10.59277/RRMPA.2024.105.128.
- . . ‘From motivic Chern classes of Schubert cells to their Hirzebruch and CSM classes.’ Contemporary Mathematics 804: 1–52. doi: 10.1090/conm/804/16110 .
- . . ‘Tubular neighborhoods of local models.’ Duke Mathematical Journal 173, № 4: 723–743. doi: 10.1215/00127094-2023-0028.
- . . ‘On the normality of Schubert varieties: remaining cases in positive characteristic.’ Annales Scientifiques de l'École Normale Supérieure (4) 57, № 3: 895–959.
- . . ‘Classification of asymptotically conical Calabi-Yau manifolds.’ Duke Mathematical Journal 173, № 5: 947–1015. doi: 10.1215/00127094-2023-0030.
- . . ‘Propagation of regularity for transport equations. A Littlewood-Paley approach.’ Indiana University Mathematics Journal 73, № 2: 445–473.
- . . ‘A note on BKP for the Kontsevich matrix model with arbitrary potential.’ Symmetry, Integrability and Geometry: Methods and Applications 20: 050. doi: 10.3842/SIGMA.2024.050.
- . . ‘Real symmetric Φ^4-matrix model as Calogero-Moser model.’ Letters in Mathematical Physics 114: 25. doi: 10.1007/s11005-024-01772-5.
- . . ‘Cohomogeneity one manifolds with quasipositive curvature.’ Mathematische Annalen 2023. doi: 10.1007/s00208-023-02766-9.
- . . ‘Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes.’ Classical and Quantum Gravity 40, № 4. doi: 10.1088/1361-6382/acb0ac.
- . The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms arXiv. doi: 10.48550/arXiv.2302.06387.
- . . ‘A Harder-Narasimhan stratification of the B_{dR}^+-Grassmannian.’ Compositio Mathematica 159, № 4: 711–745. doi: 10.1112/S0010437X23007066.
- . . ‘On Newton strata in the B_{dR}^+-Grassmannian.’ Duke Mathematical Journal 173, № 1: 177–225. doi: 10.1215/00127094-2024-0005.
- . . ‘Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models.’ Journal of High Energy Physics (JHEP) 02: 074. doi: 10.1007/JHEP02(2023)074.
- . . ‘Curvature effects in the spectral dimension of spin foams.’ Physical Review D (PRD) 108: 066011. doi: 10.1103/PhysRevD.108.066011.
- . . ‘On the derived category of the Iwahori-Hecke algebra.’ Compositio Mathematica 159, № 5: 1042–1110.
- . Primes, knots and periodic orbits arXiv.
- . On the proalgebraic fundamental group of topological spaces and amalgamated products of affine group schemes ArXiv.
- . . ‘Nonnegative scalar curvature on manifolds with at least two ends.’ Journal of Topology 16, № 3: 855–876. doi: 10.1112/topo.12303.
- . . ‘Games on AF-algebras.’ International Mathematics Research Notices 2023. doi: 10.1093/imrn/rnac313.
- . . ‘Complex patch geometry promotes species coexistence through a reverse competition-colonization trade-off.’ Proceedings of the Royal Society B: Biological Sciences 290: 20231554. doi: 10.1098/rspb.2023.1554.
- . . ‘Amenability for actions of étale groupoids on C*-algebras and Fell bundles.’ Transactions of the American Mathematical Society 376, № 7. doi: 10.1090/tran/8909.
- . . ‘K -theory of noncommutative Bernoulli shifts.’ Mathematische Annalen 388, № 3. doi: 10.1007/s00208-023-02587-w.
- . . ‘The weak containment problem for étale groupoids which are strongly amenable at infinity.’ Journal of Operator Theory 89, № 2. doi: 10.7900/jot.2021aug20.2358.
- . . ‘Grassmanniennes affines tordues sur les entiers.’ Forum of Mathematics, Sigma 11, № 12: 1–65. doi: 10.1017/fms.2023.30.
- . Polygonic spectra and TR with coefficients arXiv. doi: 10.48550/arXiv.2302.07686.
- . . ‘The renormalized volume of a 4-dimensional Ricci-flat ALE space.’ Journal of Differential Geometry 123: 411–429. doi: 10.4310/jdg/1683307004.
- . . ‘An overview on deep learning-based approximation methods for partial differential equations.’ Discrete and Continuous Dynamical Systems - Series B 28, № 6: 3697–3746. doi: 10.3934/dcdsb.2022238.
- . . ‘Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation.’ Journal of Mathematical Analysis and Applications 517, № 2: 126601. doi: 10.1016/j.jmaa.2022.126601.
- . . ‘An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition.’ SIAM Journal on Scientific Computing 45, № 4. doi: 10.1137/21M1460016.
- . . ‘Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps.’ Calculus of Variations and Partial Differential Equations 63, № 1: 6. doi: 10.1007/s00526-023-02613-4.
- . . ‘Classifiability of crossed products by nonamenable groups.’ Journal für die reine und angewandte Mathematik 797: 285–312. doi: 10.48550/arXiv.2201.03409.
- . . ‘Shadows of characteristic cycles, Verma modules, and positivity of Chern–Schwartz–MacPherson classes of Schubert cells.’ Duke Mathematical Journal 172, № 17: 3257 –3320. doi: 10.1215/00127094-2022-0101.
- . . ‘Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra.’ Journal of Mathematical Physics 64, № 7: 073505. doi: 10.1063/5.0150975.
- . . ‘One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.’ Calculus of Variations and Partial Differential Equations 62, № 7: 190. doi: 10.1007/s00526-023-02525-3.
- . ‘A pro-algebraic fundamental group for topological spaces.’ Proceedings of the Steklov Institute of Mathematics 320: 62–90. doi: 10.1134/S0081543823010054.
- . . ‘The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes.’ Archive for Rational Mechanics and Analysis 247: 56. doi: 10.1007/s00205-023-01890-9.
- . . ‘Mean-Field Phase Transitions in TGFT Quantum Gravity.’ Physical Review Letters 130: 141501. doi: 10.1103/PhysRevLett.130.141501.
- . ‘Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation.’ Electronic Research Archive 31, № 5: 2519–2554. doi: 10.3934/era.2023128.
- . . ‘A Laplacian to compute intersection numbers on M_{g,n} and correlation functions in NCQFT.’ Communications in Mathematical Physics 399: 481–517. doi: 10.1007/s00220-022-04557-w.