• 2023
• 2022
• 2021

2023

• Holzegel, G; Shao, A. 2023. ‘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.
• Marchetti, L; Oriti, D; Pithis, A; Thürigen, J. 2023. ‘Mean-Field Phase Transitions in TGFT Quantum Gravity.’ Physical Review Letters 130: 141501. doi: 10.1103/PhysRevLett.130.141501.
• Eberle, Simon; Jentzen, Arnulf; Riekert, Adrian; Weiss, Georg S. 2023. ‘Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation.’ Electronic Research Archive 31, No. 5: 2519–2554. doi: 10.3934/era.2023128.
• Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar. 2023. ‘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.
• Beck C, Hutzenthaler M, Jentzen A, Kuckuck B. 2023. ‘An overview on deep learning-based approximation methods for partial differential equations.’ Discrete and Continuous Dynamical Systems - Series B 28, No. 6: 3697–3746. doi: 10.3934/dcdsb.2022238.
• Jentzen A, Riekert A. 2023. ‘Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation.’ Journal of Mathematical Analysis and Applications 517, No. 2: 126601. doi: 10.1016/j.jmaa.2022.126601.
• Eberle S, Jentzen A, Riekert A, Weiss GS. 2023. ‘Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation.’ Electronic Research Archive 31, No. 5: 2519–2554. doi: 10.3934/era.2023128.
• Biquard O, Hein HJ. 2023. ‘The renormalized volume of a 4-dimensional Ricci-flat ALE space.’ Journal of Differential Geometry 123: 411–429. doi: 10.4310/jdg/1683307004.
• Krause, Achim; McCandless, Jonas; Nikolaus, Thomas. 2023. Polygonic spectra and TR with coefficients arXiv. doi: 10.48550/arXiv.2302.07686.
• Marchetti, L; Oriti, D; Pithis, A; Thürigen, J. 2023. ‘Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models.’ Journal of High Energy Physics 02: 074. doi: 10.1007/JHEP02(2023)074.
• Jercher, A; Steinhaus, S; Thürigen, J. 2023. Curvature effects in the spectral dimension of spin foams. doi: 10.48550/arXiv.2304.13058.
• Ben Geloun, J; Pithis, A; Thürigen, J. 2023. QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization arXiv. doi: 10.48550/arXiv.2305.06136.
• Graf, O; Holzegel, G. 2023. ‘Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes.’ Classical and Quantum Gravity 40, No. 4. doi: 10.1088/1361-6382/acb0ac.
• Holzegel, G; Kauffman, C. 2023. The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms arXiv. doi: 10.48550/arXiv.2302.06387.
• Nguyen, Kieu Hieu; Viehmann, Eva. 2023. ‘A Harder-Narasimhan stratification of the B_{dR}^+-Grassmannian.’ Compositio Mathematica 159, No. 4: 711–745. doi: 10.1112/S0010437X23007066.
• Schürmann, Jörg; Wulkenhaar, Raimar. 2023. ‘An algebraic approach to a quartic analogue of the Kontsevich model.’ Mathematical Proceedings 174, No. 3: 471–495. doi: 10.1017/S0305004122000366.

2022

• Branahl, Johannes; Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar. 2022. ‘From scalar fields on quantum spaces to blobbed topological recursion.’ Journal of Physics A: Mathematical and Theoretical 55, No. 42: 423001. doi: 10.1088/1751-8121/ac9260.
• Escalier Amandine. 2022. ‘Local-to-Global-rigidity of lattices in SLn(K).’ Annales de l'Institut Fourier 72, No. 5: 1733–1771. doi: 10.5802/aif.3490.
• Brunekreef, J; Lionni, L; Thürigen, J. 2022. ‘One-matrix differential reformulation of two-matrix models.’ Reviews in Mathematical Physics 34, No. 08: 2250026. doi: 10.1142/S0129055X2250026X.
• Branahl, Johannes; Hock, Alexander; Wulkenhaar, Raimar. 2022. ‘Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures.’ Communications in Mathematical Physics 393: 1529–1582. doi: 10.1007/s00220-022-04392-z.
• de Jong, Jins; Hock, Alexander; Wulkenhaar, Raimar. 2022. ‘Nested Catalan tables and a recurrence relation in noncommutative quantum field theory.’ Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions 9, No. 1: 47–72. doi: 10.4171/AIHPD/113.
• Aluffi, P., Mihalcea, L., Schürmann, J., Su C. 2022. ‘Positivity of Segre–MacPherson Classes.’ In Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday, edited by Aluffi P., Anderson D., Hering M., Mustaţă M., Payne S., 1–28. doi: 10.1017/9781108877831.001.
• Maxim, Laurentiu; Schürmann, Jörg. 2022. ‘Constructible Sheaf Complexes in Complex Geometry and Applications.’ In Handbook of Geometry and Topology of Singularities III, edited by Cisneros-Molina, José Luis; Dũng Tráng, Lê; Seade, José, 679–791. Cham, Switzerland: Springer Nature. doi: 10.1007/978-3-030-95760-5.
• Hartl, Urs; Singh, Rajineesh Kumar. 2022. ‘A short review on local shtukas and divisible local Anderson modules.’ In Perfectoid Spaces, edited by D. Banerjee, K. Kedlaya, E. de Shalit, C. Chaudhuri, 51–68. Singapore: Springer International Publishing. doi: 10.1007/978-981-16-7121-0_4.
• Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L. 2022. ‘Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives.’ Discrete and Continuous Dynamical Systems - Series B 27, No. 7: 3707–3724. doi: 10.3934/dcdsb.2021203.
• Beck C, Jentzen A, Kuckuck B. 2022. ‘Full error analysis for the training of deep neural networks.’ Infinite Dimensional Analysis, Quantum Probability and Related Topics 25, No. 2: 2150020. doi: 10.1142/S021902572150020X.
• Jentzen A, Riekert A. 2022. ‘On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks.’ Journal of Machine Learning 1, No. 2: 141–246. doi: 10.4208/jml.220114a.
• Jentzen, Arnulf; Riekert, Adrian. 2022. ‘A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions.’ Journal of Machine Learning Research 23, No. 260: 1–50.
• Jentzen, Arnulf; Riekert, Adrian. 2022. ‘A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions.’ Zeitschrift für Angewandte Mathematik und Physik 73, No. 5: 188. doi: 10.1007/s00033-022-01716-w.
• Cheridito, Patrick; Jentzen, Arnulf; Riekert, Adrian; Rossmannek, Florian. 2022. ‘A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions.’ Journal of Complexity 72: 101646. doi: 10.1016/j.jco.2022.101646.
• Riekert, Adrian. 2022. ‘Convergence rates for empirical measures of Markov chains in dual and Wasserstein distances.’ Statistics and Probability Letters 189: 109605. doi: 10.1016/j.spl.2022-109605.
• Hein HJ, Sun S, Viaclovsky J, Zhang R. 2022. ‘Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface.’ Journal of the American Mathematical Society 2022. doi: 10.1090/jams/978.
• L. Feltes, Guilherme; Weber, Hendrik. 2022. Brownian particle in the curl of 2-d stochastic heat equations arXiv. doi: 10.48550/arXiv.2211.02194.
• Dotto E., Krause A., Nikolaus T., Patchkoria I. 2022. ‘Witt vectors with coefficients and characteristic polynomials over non-commutative rings.’ Compositio Mathematica 158, No. 2: 366–408. doi: 10.1112/S0010437X22007254.
• Antieau, Benjamin; Krause, Achim; Nikolaus, Thomas. 2022. On the K-theory of Z/pn arxiv.org. doi: 10.48550/arXiv.2204.03420.
• Land, Markus; Nikolaus, Thomas; Schlichting, Marco. 2022. L-theory of C∗-algebras arxiv.org. : arXiv. doi: 10.48550/ARXIV.2208.10556.
• E. Arasteh Rad, U. Hartl. 2022. ‘Category of C-Motives over Finite Fields.’ Journal of Number Theory 232: 283–316.
• de Laat T., Zadeh, S. 2022. ‘Weak*-continuity of invariant means on spaces of matrix coefficients.’ Journal of Mathematical Analysis and Applications 506, No. 2. doi: 10.1016/j.jmaa.2021.125669.
• Dafermos, M; Holzegel, G; Rodnianski, I; Taylor, M. 2022. Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes arXiv. doi: 10.48550/arXiv.2212.14093.
• Abadie, Fernando; Gardella, Eusebio; Geffen, Shirly. 2022. ‘Partial C*-dynamics and Rokhlin dimension.’ Ergodic Theory and Dynamical Systems 42, No. 10: 2991–3024. doi: 10.1017/etds.2021.82.
• Zeidler R. 2022. ‘Band width estimates via the Dirac operator.’ Journal of Differential Geometry 122, No. 1: 155–183. doi: 10.4310/jdg/1668186790.
• Benjamin, Beeker; Cordes, Matthew; Gardam, Giles; Gupta, Radhika; Stark, Emily. 2022. ‘Cannon-Thurston maps for CAT(0) groups with isolated flats.’ Mathematische Annalen 384, No. 1-2: 963–987. doi: 10.1007/s00208-021-02245-z.
• Deninger C. 2022. Dynamical systems for arithmetic schemes.

2021

• Pascalie, Romain; Pérez-Sánchez, Carlos Ignacio, Wulkenhaar, Raimar. 2021. ‘Correlation functions of U(N)-tensor models and their Schwinger-Dyson equations.’ Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions 8, No. 3: 377–458. doi: 10.4171/AIHPD/107.
• Branahl, Johannes; Hock, Alexander; Wulkenhaar, Raimar. 2021. ‘Perturbative and geometric analysis of the quartic Kontsevich model.’ Symmetry, Integrability and Geometry: Methods and Applications 17: 085. doi: 10.3842/SIGMA.2021.085.
• Rellensmann J, Schukajlow S, Blomberg J. 2021. „Was ist eine gute Skizze? Strategiewissen beim mathematischen Modellieren im Bereich der Geometrie fördern.“ Mathematik lehren 224: 22–27.
• Kirsten, K. 2021. Beweisprozesse von Studierenden. Ergebnisse einer empirischen Untersuchung zu Prozessverläufen und phasenspezifischen Aktivitäten Dissertation thesis, Universität Münster. Wiesbaden: Springer Spektrum. doi: 10.1007/978-3-658-32242-7.
• de Laat T., Siebenand T. 2021. ‘Exotic group C*-algebras of simple Lie groups with real rank one.’ Annales de l'Institut Fourier 71, No. 5: 2117–2136. doi: 10.5802/aif.3441.
• Jentzen A, Kuckuck B, Neufeld A, von Wurstemberger P. 2021. ‘Strong error analysis for stochastic gradient descent optimization algorithms.’ IMA Journal of Numerical Analysis 41, No. 1: 455–492. doi: 10.1093/imanum/drz055.
• Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L. 2021. ‘On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values.’ Journal of Mathematical Analysis and Applications 502, No. 2: Paper No. 125240. doi: 10.1016/j.jmaa.2021.125240.