Abstracts for many of the research publications can be found here.

• Winding and focussing for geodesics passing a thin cuspidal neck (with Jørgen Lye), Preprint 2025, https://arxiv.org/abs/2510.20355
  
• Analysis on fibred cusp spaces (with Álvaro Sánchez Hernández and Boris Vertman), Preprint 2025, https://arxiv.org/abs/2507.15467
  
• Phase transitions and minimal interfaces on manifolds with conical singularities (with S. Held, H. Uecker and B. Vertman), Nonlinearity, vol 38 no 2 (2025). DOI: 10.1088/1361-6544/ada47c, arXiv.
  
• Geodesics orbiting a singularity (with J. Lye), Journal of Geometry, vol 115 no 1 (2024). DOI: 10.1007/s00022-023-00701-6, arXiv.
  
• The Calderón Projector for Fibred Cusp Operators (with K. Fritzsch and E. Schrohe), Journal of Functional Analysis, vol 285 no 10 (2023). DOI: 10.1016/j.jfa.2023.110127, arXiv.
  
• Spectral geometry on manifolds with fibred boundary metrics I: Low energy resolvent (with M. Talebi and B. Vertman), Journal de l'École polytechnique - Mathématiques 9 (2022), 959-1019. DOI: 10.5802/jep.198, arXiv.
  
• Scales, blow-up and quasimode constructions, in: Geometric and Computational Spectral Theory, A. Girouard et al, eds, Contemp. Math. 700, AMS, 207-266 (2017). DOI: 10.1090/conm/700/14188, arXiv.
  
• Soliton transport in tubular networks: Transmission at vertices in the shrinking limit (with H. Uecker, Z. Sobirov, D. Babajanov, Doniyor and D. Matrasulov), Phys. Rev. E 91 (2015), Doi 10.1103/PhysRevE.91.023209. DOI: 10.1103/PhysRevE.91.023209, arXiv.
  
• The exponential map at a cuspidal singularity (with V. Grandjean), Journal für die reine und angewandte Mathematik (Crelles Journal) (2015), 1-35. DOI: 10.1515/crelle-2015-0020, arXiv.
  
• A new simple proof of the Aztec diamond theorem (with M. Fendler), Graphs and Combinatorics (2015), 1-7. DOI: 10.1007/s00373-015-1663-x, arXiv.
  
• A Parametrix Construction for the Laplacian on Q-rank 1 Locally Symmetric Spaces (with E. Hunsicker), Proceedings of the Workshop on Fourier Analysis and Pseudo-Differential Operators, Aalto, Finland. Trends in Mathematics, Birkhäuser, Basel 2014. DOI: 10.1007/978-3-319-02550-6_8, arXiv.
  
• The plasmonic eigenvalue problem, Rev. Math. Phys. 26, 1450005 (2014) (26 pp.). DOI: 10.1142/S0129055X14500056, arXiv.
  
• Hearing the shape of a triangle (with S. Maronna), Notices of the American Mathematical Society 60 (12/2013), 1440-1447. DOI: 10.1090/NOTI1063, arXiv.
  
• Monotone unitary families, Proc. Amer. Math. Soc. 141 (2013), 997-1005. DOI: 10.1090/S0002-9939-2012-11552-7, arXiv.
  
• A natural differential operator on conic spaces, Discrete Contin. Dyn. Syst. (8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden 2010), 2011, p. 568-577. DOI: 10.3934/PROC.2011.2011.568, paper.
  
• Perturbation theory for plasmonic eigenvalues (with S.-A. Biehs, M. Holthaus, O. Huth, F. Rüting, and H. Uecker), Phys. Rev. B 80 (2009), 245405 (8pp). DOI: 10.1103/PhysRevB.80.245405, paper.
  
• Surface plasmon resonances of an arbitrarily shaped nanoparticle: High frequency asymptotics via pseudo-differential operators (with F. Rüting), J. Phys. A: Math. Theor. 42 135204 (6pp) DOI: 10.1088/1751-8113/42/13/135204, arXiv.
  
• Pseudodifferential operator calculus for generalised Q-rank 1 locally symmetric spaces, I (with E. Hunsicker), Journal of Functional Analysis 257 (2009), pp. 3748-3801. DOI: 10.1016/j.jfa.2009.09.016, arXiv.
  
• Asymptotics of eigenfunctions on plane domains (with D. Jerison), Pacific J. of Mathematics 240 (2009), 109-133. DOI: 10.2140/pjm.2009.240.109, arXiv.
  
• Thin tubes in mathematical physics, global analysis and spectral geometry, in: Analysis on Graphs and its Applications. Proceedings of Symposia in Pure Mathematics, P. Exner, J. Keating, P. Kuchment, T. Sunada, and A. Teplyaev (eds.), AMS, 2008, 565-594. DOI: 10.1090/pspum/077/2459891, arXiv.
  
• Spectra of graph neighbourhoods and scattering, Proceedings of the London Mathematical Society 97 (2008), 718-752. DOI: 10.1112/plms/pdn020, arXiv.
  
• Geodesics on singular surfaces, Oberwolfach Reports No. 41/2007. Paper, full volume.
  
• The first eigenvalue of the Laplacian, isoperimetric constants, and the Max Flow Min Cut Theorem, Archiv der Mathematik 87 (2006), 75-85. DOI: 10.1007/s00013-005-1623-4, paper.
  
• Cheeger's inequality revisited, Oberwolfach Reports No. 39/2005. Paper, full volume.
  
• Local geometry of singular real analytic surfaces, Trans. Amer. Math. Soc.355 (2003), 1559-1577. DOI: 10.1090/S0002-9947-02-03168-9, arXiv.
  
• On the L^2-Stokes theorem and Hodge theory for singular algebraic varieties (with M. Lesch), Math. Nachr. 246-247 (2002), 68-82. DOI: 10.1002/1522-2616(200212)246:1<68::AID-MANA68>3.0.CO;2-Y, paper.
  
• Quasiisometry of singular metrics, Houston J. Math 28 (2002), 741-752. DOI: 10.1090/S0002-9947-02-03168-9 paper.
  
• Uniform bounds for eigenfunctions of the Laplacian on compact manifolds with boundary, Comm. PDE 27 (2002), 1283-1299. DOI: 10.1081/PDE-120005839, paper.
  
• Singular asymptotics lemma and Push-forward theorem (with M. Gruber), in J.B.Gil et al. (eds.), Approaches to Singular Analysis, 117-130, Operator Theory: Advances and Applications, 125th Advances in Partial Differential Equations, Birkhäuser, Basel, 2001. DOI: 10.1007/978-3-0348-8253-8_4, paper.
  
• Basics of the b-calculus, in J.B.Gil et al. (eds.), Approaches to Singular Analysis, 30-84, Operator Theory: Advances and Applications, 125th Advances in Partial Differential Equations, Birkhäuser, Basel, 2001. DOI: 10.1007/978-3-0348-8253-8_2, paper.
  
• The free boundary problem in the optimization of composite membranes (with S. Chanillo and K. Kurata), in: Differential Geometric Methods in the Control of Partial Differential Equations, R. Gulliver et al. (eds), Cont. Math. 268 (2000), 61-81. Paper.
  
• Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes (with S. Chanillo and K. Kurata - on the theory, and M. Imai and I. Ohnishi - on the numerics), Comm. Math. Physics 214 (2000), 315-337. DOI: 10.1007/PL00005534, arXiv.
  
• The size of the first eigenfunction of a convex planar domain (with D. Jerison), Journal of the AMS 11 (1998), 41-72. DOI: 10.1090/S0894-0347-98-00254-9paper.
  
• Asymptotics of the first nodal line of a convex domain (with D. Jerison), Inventiones Math. 125 (1996), 197-219. DOI: 10.1007/s002220050073paper.
  
• Asymptotics of the first nodal line (with D. Jerison), in "Journees Equations aux derivees partielles'' St-Jean-de-Monts 1995. Paper.
  
• Counting complements in the partition lattice, and hypertrees, J.Comb.Th.A 57 (1991), 144-150. DOI: 10.1016/0097-3165(91)90012-6, paper.
  
• Some results on the complexity of families of sets, Disc.Math. 88 (1991), 179-192. DOI: 10.1016/0012-365X(91)90008-P, paper.
  
• Hook-free colourings and a problem of Hanson (with M. Aigner), Combinatorica 8(2) (1988), 143-148. DOI: 10.1007/BF02122795, paper.
  
• On the representing number of intersecting families (with M. Aigner and P. Erdös), Arch.Math. 49 (1987), 114-118. DOI: 10.1007/BF01200473, paper.

• Mathematical Problem Solving and Proving in Oldenburg (with A. Beyer and S. Schlüters), in: Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen. Concepts, practical examples and research results, Reinhard Hochmuth, Rolf Biehler, Michael Liebendörfer and Niclas Schaper (eds.), 2021.
  
• Discovery-based learning using the example of the theorem on implicit functions, Der Mathematikunterricht 3 (2019), 45-53.
  
• Mathematik lehren an der Hochschule: Perspektiven aus Mathematik und Didaktik (with R. Hochmuth), in: Beiträge zum Mathematikunterricht (2018), 25-32, WTM-Verlag Münster.
  
• Beginners' lectures (with M. Hoffmann and W. Koepf and J. Kramer), Der Mathematikunterricht 5 (2018), 48-54.
  
• Mathematical problem solving and proof: Discovering learning in the introductory phase of studies, contribution to the workshop 'Learning mathematics at school and at university: similarities, differences and consequences' from 22 to 26 April 2013 at the Hausdorff Research Institute for Mathematics (HIM) at the University of Bonn, 15 pages.
  
• Mathematical problem solving and proof: A new concept in the introductory phase of study, in: 'Lehren und Lernen von Mathematik in der Studieneingangsphase. Herausforderungen und Lösungsansätze', Hoppenbrock, A. and Biehle, R. and Hochmuth, R. and Rück, H.-G. (eds.), pp. 661-676, Springer 2016.

• Probleme der singulären Analysis, Habilitationsschrift, May 2001.
• L^p bounds for eigenfunctions and spectral projections of the Laplacian near concave boundaries, (pdf file) Dissertation, UCLA, 1992.

• Microlocal Methods in Mathematical Physics and Global Analysis (with S.Teufel and A.Vasy), Trends in Mathematics / Research Perspectives, Birkhäuser Verlag, Basel, 2012.
  
  
• Approaches to Singular Analysis (with J.Gil and M.Lesch), Operator Theory: Advances and Applications, 125th Advances in Partial Differential Equations, Birkhäuser Verlag, Basel, 2001.

• Mathematical problem solving and proof: Eine Entdeckungsreise in die Mathematik,
  Bachelorkurs Mathematik, Springer Spektrum, 2013.
• Analysis I - Eine Einführung in die Mathematik des Kontinuums,
  Bachelorkurs Mathematik, Springer Spektrum, 2015.
• Mathematical problem solving and proof: Eine Entdeckungsreise in die Mathematik,
  Springer Studium Mathematik - Bachelor, Springer Spektrum, 2nd edition, 2017.
  Supplementary material: notes for teachers
• Exploring Mathematics - Problem-Solving and Proof,
  Springer Undergraduate Mathematics Series, Springer, 2018.
  

• Where do the Bernoulli numbers actually come from? Teacher's Corner, DMV Mitteilungen 4-2001, 56.
• Basic ideas of Galois theory: A short introduction for interested people with (almost) no previous knowledge. Mathematical Education -- Mathematical Achievement. Commemorative publication for Michael Neubrand on his 60th birthday. A. Peter-Koop, A. Bikner-Ahsbahs (Eds.). Publisher Franzbecker, 2007.
• On eigenvalues, integrals and Pi^2/6: The idea of the trace formula, Math. Sem.ber. 54 (2007), 199-217.

• The Oldenburg Maths Camp (with M. Hawighorst), Mitteilungen der Deutschen Mathematiker-Vereinigung 26 (2018), 132-133.
• The geometry of overtones. Insights (Research Magazine of the University of Oldenburg) No. 48 (2008), 22-25.
• Why are soap bubbles round? Nordwest-Zeitung, 12 July 2006.