Projects

Current Cluster Publications

Current Cluster Publications of ehem. Sen.-Prof. Dr. Jean Bellissard

$\bullet $ Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld. An efficient Monte Carlo scheme for Zakai equations. Communications in Nonlinear Science and Numerical Simulation, 126:107438, November 2023. doi:10.1016/j.cnsns.2023.107438.

$\bullet $ M Ali Asadi-Vasfi, Hannes Thiel, and Eduard Vilalta. Ranks of soft operators in nowhere scattered c*-algebras. arXiv e-prints, October 2023. arXiv:2310.00663.

$\bullet $ Qi Yao. Geodesic equations on asymptotically locally Euclidean hler manifolds. arXiv e-prints, July 2023. arXiv:2307.01991.

$\bullet $ Jan Nienhaus, Peter Petersen, and Matthias Wink. Betti numbers and the curvature operator of the second kind. Journal of the London Mathematical Society, July 2023. doi:10.1112/jlms.12790.

$\bullet $ Jan Nienhaus and Matthias Wink. New expanding Ricci solitons starting in dimension four. arXiv e-prints, July 2023. arXiv:2307.16683.

$\bullet $ Jan Nienhaus, Peter Petersen, Matthias Wink, and William Wylie. Holonomy restrictions from the curvature operator of the second kind. Differential Geometry and its Applications, 88:102010, June 2023. doi:10.1016/j.difgeo.2023.102010.

$\bullet $ Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, and Benno Kuckuck. An overview on deep learning-based approximation methods for partial differential equations. Discrete and Continuous Dynamical Systems - B, 28(6):3697–3746, June 2023. doi:10.3934/dcdsb.2022238.

$\bullet $ Jan Nienhaus and Matthias Wink. Einstein metrics on the ten-sphere. arXiv e-prints, April 2023. arXiv:2303.04832.

$\bullet $ Christian Beck, Arnulf Jentzen, Konrad Kleinberg, and Thomas Kruse. Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems. arXiv e-prints, March 2023. arXiv:2303.03390.

$\bullet $ Ramon Antoine, Francesc Perera, Leonel Robert, and Hannes Thiel. Traces on ultrapowers of $\mathsf C^*$-algebras. arXiv e-prints, March 2023. arXiv:2303.01929.

$\bullet $ Jan Nienhaus. An improved four-periodicity theorem and a conjecture of Hopf with symmetry. arXiv e-prints, November 2022. doi:2211.13151.

$\bullet $ Jan Nienhaus, Peter Petersen, Matthias Wink, and William Wylie. Holonomy restrictions from the curvature operator of the second kind. arXiv e-prints, August 2022. arXiv:2208.13820.

$\bullet $ Christian Beck, Arnulf Jentzen, and Benno Kuckuck. Full error analysis for the training of deep neural networks. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 25(2):2150020, June 2022. doi:10.1142/S021902572150020X.

$\bullet $ Jan Nienhaus, Peter Petersen, and Matthias Wink. Betti numbers and the curvature operator of the second kind. arXiv e-prints, June 2022. arXiv:2206.14218.

$\bullet $ Qi Yao. Mass and expansion of asymptotically conical Kähler metrics. arXiv e-prints, June 2022. arXiv:2206.06505.

$\bullet $ Ramon Antoine, Francesc Perera, Leonel Robert, and Hannes Thiel. $c^*$-algebras of stable rank one and their Cuntz semigroups. Duke Mathematical Journal, 171(1):33–99, January 2022. doi:10.1215/00127094-2021-0009.

$\bullet $ Hannes Thiel and Eduard Vilalta. Covering dimension of Cuntz semigroups. Advances in Mathematics, 394:108016, January 2022. doi:10.1016/j.aim.2021.108016.

$\bullet $ Hannes Thiel and Eduard Vilalta. Nowhere scattered $C^*$-algebras. arXiv e-prints, December 2021. arXiv:2112.09877.

$\bullet $ Romain Pascalie, Carlos I. Pérez-Sánchez, and Raimar Wulkenhaar. Correlation functions of U($N$)-tensor models and their Schwinger–Dyson equations. Ann. Inst. Henri Poincaré D, 8(3):377–458, September 2021. doi:10.4171/aihpd/107.

$\bullet $ Christian Beck, Lukas Gonon, Martin Hutzenthaler, and Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete Contin. Dyn. Syst. Ser. B, 26(9):4927–4962, September 2021. doi:10.3934/dcdsb.2020320.

$\bullet $ Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld. Deep splitting method for parabolic PDEs. SIAM J. Sci. Comput., 43(5):A3135–A3154, September 2021. doi:10.1137/19M1297919.

$\bullet $ Christian Beck, Martin Hutzenthaler, and Arnulf Jentzen. On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations. Stoch. Dyn., 21(8):2150048, July 2021. doi:10.1142/S0219493721500489.

$\bullet $ Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, and Arnulf Jentzen. Solving the Kolmogorov PDE by means of deep learning. J. Sci. Comput., 88(3):Paper No. 73, 28 pp., July 2021. doi:10.1007/s10915-021-01590-0.

$\bullet $ Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, and Emilia Magnani. Full history recursive multilevel picard approximations for ordinary differential equations with expectations. arXiv e-prints, March 2021. arXiv:2103.02350.

$\bullet $ Hannes Thiel. The generator rank of $C^\ast $-algebras. Journal of Functional Analysis, 280(4):108874, 34, February 2021. doi:10.1016/j.jfa.2020.108874.

$\bullet $ Matteo. Laudonio, Romain Pascalie, and Adrian Tanasa. Combinatorial aspects of the Sachdev-Ye-Kitaev model. Rom. J. Pure Appl. Math., 66(2):485–522, January 2021.

$\bullet $ Qi Yao. Invariant scalar-flat kähler metrics on line bundles over generalized flag varieties. arXiv e-prints, December 2020. arXiv:2012.04496.

$\bullet $ Christian Beck, Fabian Hornung, Martin Hutzenthaler, Arnulf Jentzen, and Thomas Kruse. Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. Journal of Numerical Mathematics, 28(4):197–222, December 2020. doi:10.1515/jnma-2019-0074.

$\bullet $ Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld. Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems. arXiv e-prints, December 2020. arXiv:2012.01194.

$\bullet $ Hannes Thiel. Diffuse traces and Haar unitaries. arXiv e-prints, September 2020. arXiv:2009.06940.

$\bullet $ Christian Beck, Arnulf Jentzen, and Thomas Kruse. Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations. arXiv e-prints, September 2020. arXiv:2009.13989.

$\bullet $ Hannes Thiel. Generators in $\mathcal Z$-stable $C*$-algebras of real rank zero. arXiv e-prints, June 2020. arXiv:2006.08404.

$\bullet $ Hannes Thiel. The generator rank of subhomogeneous $C*$-algebras. arXiv e-prints, June 2020. arXiv:2006.03624.

$\bullet $ Christian Beck, Lukas Gonon, and Arnulf Jentzen. Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations. arXiv e-prints, March 2020. arXiv:2003.00596v1.

$\bullet $ Romain Pascalie. A solvable tensor field theory. Letters in Mathematical Physics, pages 125, December 2019. doi:10.1007/s11005-019-01245-0.

$\bullet $ Ramon Antoine, Francesc Perera, and Hannes Thiel. Abstract bivariant Cuntz semigroups II. Forum Mathematicum, September 2019. doi:10.1515/forum-2018-0285.

$\bullet $ Yemon Choi, Eusebio Gardella, and Hannes Thiel. Rigidity results for $L^p$-operator algebras and applications. arXiv e-prints, September 2019. arXiv:arXiv:1909.03612.

$\bullet $ Ramon Antoine, Francesc Perera, Leonel Robert, and Hannes Thiel. Edwards' condition for quasitraces on $C^*$-algebras. arXiv e-prints, September 2019. arXiv:1909.12787.

$\bullet $ Christian Beck, Weinan E, and Arnulf Jentzen. Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. J. Nonlinear Sci., 29:1563–1619, August 2019. doi:10.1007/s00332-018-9525-3.

$\bullet $ Hannes Thiel. Ranks of operators in simple $C^*$-algebras with stable rank one. Communications in Mathematical Physics, July 2019. doi:10.1007/s00220-019-03491-8.

$\bullet $ Romain Pascalie, Carlos I. Pérez-Sánchez, Adrian Tanasa, and Raimar Wulkenhaar. On the large N limit of Schwinger-Dyson equations of a rank-3 tensor field theory. Journal of Mathematical Physics, 60(7):073502, July 2019. doi:10.1063/1.5080306.

$\bullet $ Thomas Krajewski, Matteo Laudonio, Romain Pascalie, and Adrian Tanasa. Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model. Physical Review D, 99(12):126014, June 2019. doi:10.1103/physrevd.99.126014.

$\bullet $ Eusebio Gardella and Hannes Thiel. Extending representations of Banach algebras to their biduals. Mathematische Zeitschrift, May 2019. doi:10.1007/s00209-019-02315-8.

$\bullet $ Ramon Antoine, Francesc Perera, and Hannes Thiel. Cuntz semigroups of ultraproduct $C^*$-algebras. arXiv e-prints, May 2019. arXiv:1905.03208.

$\bullet $ Hannes Thiel. Inductive limits of semiprojective $C^*$-algebras. Advances in Mathematics, 347:597–618, April 2019. doi:10.1016/j.aim.2019.02.030.

$\bullet $ Eusebio Gardella and Hannes Thiel. Representations of $p$-convolution algebras on $L^q$-spaces. Transactions of the American Mathematical Society, 371(3):2207–2236, February 2019. doi:10.1090/tran/7489.

$\bullet $ Eusebio Gardella and Hannes Thiel. Isomorphisms of algebras of convolution operators. arXiv e-prints, September 2018. arXiv:1809.01585.

$\bullet $ Ramon Antoine, Francesc Perera, and Hannes Thiel. Abstract bivariant Cuntz semigroups. International Mathematics Research Notices, July 2018. doi:10.1093/imrn/rny143.

$\bullet $ Hannes Thiel. Semiprojectivity and semiinjectivity in different categories. arXiv e-prints, February 2018. arXiv:arXiv:1802.05037.