Vorträge in der Woche 18.07.2022 bis 24.07.2022
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Donnerstag, 21.07.2022: A Classification of Lattice Triangles Contained in a Square
Girtrude Hamm (University of Nottingham)
Understanding lattice polytopes contained in a hypercube is useful for computational problems where we wish to bound the polytopes we consider. I will talk about the simplest non-trivial case: lattice triangles which are a subset of an n x n square. These triangles can be completely classified and counted, up to affine equivalence. I will also present some interesting observations which arise from this classification.
| Uhrzeit: | 14:00 |
| Ort: | Die Veranstaltung findet online statt. Den Zoom-Link erhalten Sie per E-Mail von Frau Martina Neu. |
| Gruppe: | Oberseminar Algebraische Geometrie |
| Einladender: | Batyrev, Hausen, Th. Markwig |
Donnerstag, 21.07.2022: Discretising boundary conditions of fully nonlinear equations
Max Jensen (University of Sussex)
Boundary conditions of fully nonlinear boundary value problems are more diverse compared to the standard PDE theory of semi-linear equations. For example, Dirichlet boundary conditions can be posed in multiple non-equivalent forms: they model different physical/real-world effects and the well-posedness of the BVP may rely on their particular form. Boundary conditions of Neumann- and Robin-type are frequently fully-nonlinear themselves and interact with the PDE operator in intricate ways. In this talk, we review the taxonomy of common boundary conditions, highlight common pitfalls and misconceptions, and discuss recent methodologies to discretise them. Particular emphasis will be paid to Hamilton-Jacobi-Bellman and Isaacs equations and their approximation by finite element methods. This is a joint work with Dr Jaroszkowski (University of Sussex) [1, 2] and Dr Smears (University College London) [3]. [1] Jaroszkowski, Bartosz and Jensen, Max (2022) Finite element methods for isotropic Isaacs equations with viscosity and strong Dirichlet boundary conditions. Applied Mathematics and Optimization, 85. 1-32. https://doi.org/10.1007/s00245-022-09860-5 [2] Jaroszkowski, Bartosz and Jensen, Max (2021) Finite Element Approximation of Hamilton-Jacobi- Bellman equations with nonlinear mixed boundary conditions, https://arxiv.org/abs/2105.09585 [3] Jensen, Max and Smears, Iain (2018) On the notion of boundary conditions in comparison principles for viscosity solutions. Radon Series on Computational and Applied Mathematics. http://dx.doi.org/10.1515/9783110543599-007
| Uhrzeit: | 14:15 - 16:00 |
| Ort: | N8 |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Prohl, Lubich |
Donnerstag, 21.07.2022: Central limit theorem and extremal statistics for non-Hermitian random matrices
Prof. László Erdös (ISTA Klosterneuburg)
We study the spectrum of large random matrices with i.i.d. entries without any symmetry constraint. These matrices are the non-Hermitian counterparts of the celebrated Wigner ensemble. We discuss how standard probabilistic questions, such as law of large numbers, central limit theorem and extremal statistics, emerge in the eigenvalues of such matrices.
| Uhrzeit: | 16:00 |
| Ort: | C3N16 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |
Freitag, 22.07.2022: Universality in Random Matrix Theory beyond Wigner-Dyson-Mehta
Prof. László Erdös (ISTA Klosterneuburg)
Following E. Wigner’s pioneering discovery, the eigenvalues of large random matrices tend to exhibit a universal behaviour; most prominently the gap distribution converges to the celebrated Wigner-Dyson-Mehta statistics. In this talk I give an overview of more recent universality results concerning other physically relevant quantities, in particular I explain the random matrix version of the Eigenstate Thermalisation Hypothesis and the normal fluctuation of the Quantum Unique Ergodicity.
| Uhrzeit: | 16:00 - 18:00 |
| Ort: | N 7 |
| Gruppe: | Kolloquium |
| Einladender: | Stefan Teufel |