Oberwolfach Publications
http://publications.mfo.de:80
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 20 Jul 2024 02:57:18 GMT2024-07-20T02:57:18ZOberwolfach Publicationshttp://publications.mfo.de/themes/Mirage2/images/apple-touch-icon.png
http://publications.mfo.de:80
Free Boundary Problems in Fluid Dynamics
http://publications.mfo.de/handle/mfo/4155
Free Boundary Problems in Fluid Dynamics
Ai, Albert; Alazard, Thomas; Ifrim, Mihaela; Tataru, Daniel
This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler’s equations in general. A particular set of such problems is given by gaseous stars considered in a vacuum (modeled via the compressible Euler equations) as well as water waves in their full generality (seen as recasts of incompressible irrotational Euler equations). This is a broad research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.
Oberwolfach Seminar 2243a: Free Boundary Problems in Fluid Dynamics
Thu, 20 Jun 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41552024-06-20T00:00:00ZAi, AlbertAlazard, ThomasIfrim, MihaelaTataru, DanielThis book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler’s equations in general. A particular set of such problems is given by gaseous stars considered in a vacuum (modeled via the compressible Euler equations) as well as water waves in their full generality (seen as recasts of incompressible irrotational Euler equations). This is a broad research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.On Overgroups of Distinguished Unipotent Elements in Reductive Groups and Finite Groups of Lie Type
http://publications.mfo.de/handle/mfo/4153
On Overgroups of Distinguished Unipotent Elements in Reductive Groups and Finite Groups of Lie Type
Bate, Michael; Böhm, Sören; Martin, Benjamin; Röhrle, Gerhard
Suppose G is a simple algebraic group defined over an algebraically closed field of good characteristic p. In 2018 Korhonen showed that if H is a connected reductive subgroup of G which contains a distinguished unipotent element u of G of order p, then H is G-irreducible in the sense of Serre. We present a short and uniform proof of this result using so-called good A1 subgroups of G, introduced by Seitz. We also formulate a counterpart of Korhonen’s theorem for overgroups of u which are finite groups of Lie type. Moreover, we generalize both results above by removing the restriction on the order of u under a mild condition on p depending on the rank of G, and we present an analogue of Korhonen’s theorem for Lie algebras.
Tue, 18 Jun 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41532024-06-18T00:00:00ZBate, MichaelBöhm, SörenMartin, BenjaminRöhrle, GerhardSuppose G is a simple algebraic group defined over an algebraically closed field of good characteristic p. In 2018 Korhonen showed that if H is a connected reductive subgroup of G which contains a distinguished unipotent element u of G of order p, then H is G-irreducible in the sense of Serre. We present a short and uniform proof of this result using so-called good A1 subgroups of G, introduced by Seitz. We also formulate a counterpart of Korhonen’s theorem for overgroups of u which are finite groups of Lie type. Moreover, we generalize both results above by removing the restriction on the order of u under a mild condition on p depending on the rank of G, and we present an analogue of Korhonen’s theorem for Lie algebras.Randomness is Natural - an Introduction to Regularisation by Noise
http://publications.mfo.de/handle/mfo/4146
Randomness is Natural - an Introduction to Regularisation by Noise
Djurdjevac, Ana; Elad Altman, Henri; Rosati, Tommaso
Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this "regularisation by noise" phenomenon.
Wed, 22 May 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41462024-05-22T00:00:00ZDjurdjevac, AnaElad Altman, HenriRosati, TommasoDifferential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this "regularisation by noise" phenomenon.On Dykstra’s Algorithm with Bregman Projections
http://publications.mfo.de/handle/mfo/4134
On Dykstra’s Algorithm with Bregman Projections
Pinto, Pedro; Pischke, Nicholas
We provide quantitative results on the asymptotic behavior of Dykstra’s algorithm with Bregman projections, a combination of the well-known Dykstra’s algorithm and the method of cyclic Bregman projections, designed to find best approximations and solve the convex feasibility problem in a non-Hilbertian setting. The result we provide arise through the lens of proof mining, a program in mathematical logic which extracts computational information from non-effective proofs. Concretely, we provide a highly uniform and computable rate of metastability of low complexity and, moreover, we also specify general circumstances in which one can obtain full and effective rates of convergence. As a byproduct of our quantitative analysis, we also for the first time establish the strong convergence of Dykstra’s method with Bregman projections in infinite dimensional (reflexive) Banach spaces.
Tue, 16 Apr 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41342024-04-16T00:00:00ZPinto, PedroPischke, NicholasWe provide quantitative results on the asymptotic behavior of Dykstra’s algorithm with Bregman projections, a combination of the well-known Dykstra’s algorithm and the method of cyclic Bregman projections, designed to find best approximations and solve the convex feasibility problem in a non-Hilbertian setting. The result we provide arise through the lens of proof mining, a program in mathematical logic which extracts computational information from non-effective proofs. Concretely, we provide a highly uniform and computable rate of metastability of low complexity and, moreover, we also specify general circumstances in which one can obtain full and effective rates of convergence. As a byproduct of our quantitative analysis, we also for the first time establish the strong convergence of Dykstra’s method with Bregman projections in infinite dimensional (reflexive) Banach spaces.Waves and Incidences
http://publications.mfo.de/handle/mfo/4133
Waves and Incidences
Yung, Po-Lam
The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem.
Tue, 09 Apr 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41332024-04-09T00:00:00ZYung, Po-LamThe wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem.Ky Fan Theorem for Sphere Bundles
http://publications.mfo.de/handle/mfo/4131
Ky Fan Theorem for Sphere Bundles
Panina, Gaiane; Živaljević, Rade
The classic Ky Fan theorem is a combinatorial equivalent of Borsuk-Ulam theorem. It is a generalization and extension of Tucker’s lemma and, just like its predecessor, it pinpoints important properties of antipodal colorings of vertices of a triangulated sphere Sn. Here we describe generalizations of Ky Fan theorem for the case when the sphere is replaced by the total space of a triangulated sphere bundle.
Fri, 05 Apr 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41312024-04-05T00:00:00ZPanina, GaianeŽivaljević, RadeThe classic Ky Fan theorem is a combinatorial equivalent of Borsuk-Ulam theorem. It is a generalization and extension of Tucker’s lemma and, just like its predecessor, it pinpoints important properties of antipodal colorings of vertices of a triangulated sphere Sn. Here we describe generalizations of Ky Fan theorem for the case when the sphere is replaced by the total space of a triangulated sphere bundle.MFO-RIMS Tandem Workshop 2023: Arithmetic Homotopy and Galois Theory
http://publications.mfo.de/handle/mfo/4128
MFO-RIMS Tandem Workshop 2023: Arithmetic Homotopy and Galois Theory
This report presents a general panorama of recent progress in the arithmetic-geometry theory of Galois and homotopy groups and its ramifications. While still relying on Grothendieck's original pillars, the present program has now evolved beyond the classical group-theoretic legacy to result in an autonomous project that exploits a new geometrization of the original insight and sketches new frontiers between homotopy geometry, homology geometry, and diophantine geometry. This panorama "closes the loop'' by including the last twenty-year progress of the Japanese arithmetic-geometry school via Ihara's program and Nakamura-Tamagawa-Mochizuki's anabelian approach, which brings its expertise in terms of algorithmic, combinatoric, and absolute reconstructions. These methods supplement and interact with those from the classical arithmetic of covers and Hurwitz spaces and the motivic and geometric Galois representations. This workshop has brought together the next generation of arithmetic homotopic Galois geometers, who, with the support of senior experts, are developing new techniques and principles for the exploration of the next research frontiers.
Sun, 01 Jan 2023 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41282023-01-01T00:00:00ZThis report presents a general panorama of recent progress in the arithmetic-geometry theory of Galois and homotopy groups and its ramifications. While still relying on Grothendieck's original pillars, the present program has now evolved beyond the classical group-theoretic legacy to result in an autonomous project that exploits a new geometrization of the original insight and sketches new frontiers between homotopy geometry, homology geometry, and diophantine geometry. This panorama "closes the loop'' by including the last twenty-year progress of the Japanese arithmetic-geometry school via Ihara's program and Nakamura-Tamagawa-Mochizuki's anabelian approach, which brings its expertise in terms of algorithmic, combinatoric, and absolute reconstructions. These methods supplement and interact with those from the classical arithmetic of covers and Hurwitz spaces and the motivic and geometric Galois representations. This workshop has brought together the next generation of arithmetic homotopic Galois geometers, who, with the support of senior experts, are developing new techniques and principles for the exploration of the next research frontiers.Charakterisierungen von inneren Volumina auf konvexen Körpern und konvexen Funktionen
http://publications.mfo.de/handle/mfo/4127
Charakterisierungen von inneren Volumina auf konvexen Körpern und konvexen Funktionen
Mussnig, Fabian
Wenn wir die Größe einer zweidimensionalen Form mittels einer Zahl ausdrücken wollen, dann denken wir gewöhnlich an ihren Flächeninhalt oder ihren Umfang. Aber was macht diese Kennzahlen so besonders? Wir beantworten diese Frage anhand klassischer mathematischer Resultate und werfen einen Blick auf Anwendungen und Verallgemeinerungen dieser Theorie.
Sun, 01 Jan 2023 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41272023-01-01T00:00:00ZMussnig, FabianWenn wir die Größe einer zweidimensionalen Form mittels einer Zahl ausdrücken wollen, dann denken wir gewöhnlich an ihren Flächeninhalt oder ihren Umfang. Aber was macht diese Kennzahlen so besonders? Wir beantworten diese Frage anhand klassischer mathematischer Resultate und werfen einen Blick auf Anwendungen und Verallgemeinerungen dieser Theorie.Braid groups, the Yang–Baxter equation, and subfactors
http://publications.mfo.de/handle/mfo/4126
Braid groups, the Yang–Baxter equation, and subfactors
Lechner, Gandalf
The Yang–Baxter equation is a fascinating equation that appears in many areas of physics and mathematics and is best represented diagramatically. This snapshot connects the mathematics of braiding hair to the Yang–Baxter equation and relates it to current research about systems of infinite dimensional algebras called "subfactors''.
Fri, 01 Jan 2021 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41262021-01-01T00:00:00ZLechner, GandalfThe Yang–Baxter equation is a fascinating equation that appears in many areas of physics and mathematics and is best represented diagramatically. This snapshot connects the mathematics of braiding hair to the Yang–Baxter equation and relates it to current research about systems of infinite dimensional algebras called "subfactors''.Curvatura escalar positiva y aplicaciones
http://publications.mfo.de/handle/mfo/4125
Curvatura escalar positiva y aplicaciones
Rosenberg, Jonathan; Wraith, David
Introducimos la idea de curvatura, incluyendo su desarrollo histórico, y nos enfocamos en la curvatura escalar de una variedad. Uno de los temas principales de investigación actual es entender la curvatura escalar positiva. Discutiremos por qué es interesante y su relación con la teoría general de la relatividad.
Fri, 01 Jan 2021 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41252021-01-01T00:00:00ZRosenberg, JonathanWraith, DavidIntroducimos la idea de curvatura, incluyendo su desarrollo histórico, y nos enfocamos en la curvatura escalar de una variedad. Uno de los temas principales de investigación actual es entender la curvatura escalar positiva. Discutiremos por qué es interesante y su relación con la teoría general de la relatividad.