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Your search keyword '"Institut für Mathematik ( FU Berlin )"' showing total 5 results
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5 results on '"Institut für Mathematik ( FU Berlin )"'

1. Investigations of structures in the parameter space of three-dimensional Turing-like patterns

Author

Martin Skrodzki, Ulrich Reitebuch, Eric Zimmermann, Computer Graphics and Visualization, Delft University of Technology (TU Delft), Institut für Mathematik (FU Berlin), and Freie Universität Berlin

Subjects
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Abstract

International audience; In this paper, we are interested in classifying the different arising (topological) structures of three-dimensional Turing-like patterns. By providing examples for the different structures, we confirm a conjecture regarding these structures within the setup of three-dimensional Turing-like pattern. Furthermore, we investigate how these structures are distributed in the parameter space of the discrete model. We found twofold versions of so-called "zero-" and "one-dimensional" structures as well as "two-dimensional" structures and use our experimental findings to formulate several conjectures for three-dimensional Turing-like patterns and higher-dimensional cases.

Published
2021

2. Non-Ulrich representation type

Author

Giangiacomo Sanna, Daniele Faenzi, Francesco Malaspina, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Dipartimento di Scienze Matematiche, Politecnico di Torino = Polytechnic of Turin (Polito), Institut für Mathematik (FU Berlin), Freie Universität Berlin, GNASA-INdAMMIUR grant Dipartimenti di EccellenzaE11G18000350001ISITE-BFC project Motivic Invariants of Algebraic Varieties ANR-IS-IDEX-OOOB and EIPHIANR-17-EURE-0002, ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017), ANR-20-IDES-0006,IDISITEBFC,Intégration & Développement de l'Initiative pour le SITE Bourgogne Franche-Comté(2020), Fédération Bourgogne Franche-Comté Mathématiques (BFC-Math ), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Politecnico di Torino [Torino] (Polito), and ANR: 'Investissements d’Avenir' program, project ISITE-BFC,ANR-lS-IDEX-OOOB

Subjects
Cohen–Macaulay modules, Pure mathematics, Subvariety, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik, Scroll, arithmetically Cohen-Macaulay sheaves, Type (model theory), Commutative Algebra (math.AC), Mathematics - Algebraic Geometry, Mathematics::Algebraic Geometry, Quartic function, FOS: Mathematics, [MATH]Mathematics [math], Representation (mathematics), wild representation type, Algebraic Geometry (math.AG), Mathematics, Algebra and Number Theory, wild representation typ, Mathematics::Commutative Algebra, Plane (geometry), Cohen-Macaulay modules, Mathematics - Commutative Algebra, arithmetically Cohen–Macaulay sheaves, Cohen-Macaulay sheaves and modules, Ulrich sheaves, Product (mathematics), Cohen–Macaulay modules, arithmetically Cohen–Macaulay sheaves, Ulrich sheaves, moduli of vectorbundles, wild representation typ, moduli of vectorbundles, Line (geometry), Geometry and Topology, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], representation type of algebras, moduli of vector bundles
Abstract

International audience; We show a remarkable property of the CM-wild variety P-1 x P-2 , namely that the only ACM sheaves moving in positive-dimensional families are Ulrich bundles. A complete classification of the non-Ulrich range is given.We prove that this feature is unique in the sense that any other ACM reduced closed subscheme X subset of P-N of dimension n >= 1 belongs to the well-known list of CM-finite or CM-tame varieties, or else it remains CM-wild upon removing Ulrich sheaves.

Published
2021
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3. Strichartz inequalities with white noise potential on compact surfaces

Author

Mouzard, Antoine, Zachhuber, Immanuel, Université de Rennes (UNIV-RENNES), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Institut für Mathematik (FU Berlin), Freie Universität Berlin, AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Université de Rennes (UR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest

Subjects
Schrödinger operator, Paracontrolled calculus, Probability (math.PR), FOS: Physical sciences, Strichartz inequalities, Mathematical Physics (math-ph), White noise, Mathematics - Spectral Theory, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Analysis of PDEs, Anderson Hamiltonian, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Spectral Theory (math.SP), Mathematical Physics, Mathematics - Probability, Analysis of PDEs (math.AP), [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
Abstract

We prove Strichatz inequalities for the Schr{\"o}dinger equation and the wave equation with multiplicative noise on a two-dimensional manifold. This relies on the Anderson Hamiltonian H described using high order paracontrolled calculus. As an application, it gives a low regularity solution theory for the associated nonlinear equations.

Published
2021

4. Dyck path triangulations and extendability (extended abstract)

Author

Cesar Ceballos, Camilo Sarmiento, Arnau Padrol, Department of Mathematics and Statistics [Toronto], York University [Toronto], Institut für Mathematik (FU Berlin), Freie Universität Berlin, Institut fuer Algebra und Geometrie, Magdeburg, Otto-von-Guericke University [Magdeburg] (OVGU), James Haglund, and Jiang Zeng

Subjects
Triangulation (topology), Path (topology), Discrete mathematics, Mathematics::Combinatorics, General Computer Science, Mathematics::Analysis of PDEs, triangulations, products of simplices, Computer Science::Computational Geometry, Cartesian product, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Dyck paths, Matroid, Theoretical Computer Science, Combinatorics, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], symbols.namesake, Oriented matroid, Condensed Matter::Superconductivity, symbols, Discrete Mathematics and Combinatorics, tropical oriented matroids, Mathematics
Abstract

We introduce the Dyck path triangulation of the cartesian product of two simplices $\Delta_{n-1}\times\Delta_{n-1}$. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations of $\Delta_{r\ n-1}\times\Delta_{n-1}$ using rational Dyck paths. Our study of the Dyck path triangulation is motivated by extendability problems of partial triangulations of products of two simplices. We show that whenever$m\geq k>n$, any triangulations of $\Delta_{m-1}^{(k-1)}\times\Delta_{n-1}$ extends to a unique triangulation of $\Delta_{m-1}\times\Delta_{n-1}$. Moreover, with an explicit construction, we prove that the bound $k>n$ is optimal. We also exhibit interpretations of our results in the language of tropical oriented matroids, which are analogous to classical results in oriented matroid theory., Nous introduisons la triangulation par chemins de Dyck du produit cartésien de deux simplexes $\Delta_{n-1}\times\Delta_{n-1}$. Les simplexes maximaux de cette triangulation sont donnés par des chemins de Dyck, et cette construction se généralise de façon naturelle pour produire des triangulations $\Delta_{r\ n-1}\times\Delta_{n-1}$ qui utilisent des chemins de Dyck rationnels. Notre étude de la triangulation par chemins de Dyck est motivée par des problèmes de prolongement de triangulations partielles de produits de deux simplexes. On montre que $m\geq k>n$ alors toute triangulation de $\Delta_{m-1}^{(k-1)}\times\Delta_{n-1}$ se prolonge en une unique triangulation de $\Delta_{m-1}\times\Delta_{n-1}$. De plus, avec une construction explicite, nous montrons que la borne $k>n$ est optimale. Nous présentons aussi des interprétations de nos résultats dans le langage des matroïdes orientés tropicaux, qui sont analogues aux résultats classiques de la théorie des matroïdes orientés.

Published
2015

5. From metastable to coherent sets- Time-discretization schemes.

Author

Fackeldey K, Koltai P, Névir P, Rust H, Schild A, and Weber M

Abstract

Given a time-dependent stochastic process with trajectories x(t) in a space Ω, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable setsM are defined in space M⊂Ω, and coherent setsM(t)⊂Ω are defined in space and time. Hence, if we extend the space Ω by the time-variable t, coherent sets are metastable sets in Ω×[0,∞) of an appropriate space-time process. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

Published
2019
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