Oberwolfach Publications
http://publications.mfo.de:80
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 01 Nov 2020 01:21:14 GMT2020-11-01T01:21:14ZOberwolfach Publicationshttp://publications.mfo.de/themes/Mirage2/images/apple-touch-icon.png
http://publications.mfo.de:80
Homology and $K$-Theory of Torsion-Free Ample Groupoids and Smale Spaces
http://publications.mfo.de/handle/mfo/3800
Homology and $K$-Theory of Torsion-Free Ample Groupoids and Smale Spaces
Proietti, Valerio; Yamashita, Makoto
Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the $K$-groups of the groupoid C*-algebra when the groupoid has torsion-free stabilizers and satisfies the strong Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam’s homology groups on the second sheet.
Fri, 09 Oct 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/38002020-10-09T00:00:00ZProietti, ValerioYamashita, MakotoGiven an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the $K$-groups of the groupoid C*-algebra when the groupoid has torsion-free stabilizers and satisfies the strong Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam’s homology groups on the second sheet.Unexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$
http://publications.mfo.de/handle/mfo/3799
Unexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$
Pokora, Piotr; Szemberg, Tomasz; Szpond, Justyna
Felix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in $\mathbb{P}^3$. This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the 60 reflection planes in the group $G_{31}$ in the Shephard-Todd list.
In the present note we show that the 60 points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree 6. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of 60 points is a cone with a single singularity of multiplicity 6 and the other has three singular points of multiplicities 4; 2 and 2. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in $\mathbb{P}^3$ with the surprising property that their general projection to $\mathbb{P}^2$ is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of 24 points in $\mathbb{P}^3$ which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property.
Wed, 07 Oct 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37992020-10-07T00:00:00ZPokora, PiotrSzemberg, TomaszSzpond, JustynaFelix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in $\mathbb{P}^3$. This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the 60 reflection planes in the group $G_{31}$ in the Shephard-Todd list.
In the present note we show that the 60 points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree 6. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of 60 points is a cone with a single singularity of multiplicity 6 and the other has three singular points of multiplicities 4; 2 and 2. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in $\mathbb{P}^3$ with the surprising property that their general projection to $\mathbb{P}^2$ is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of 24 points in $\mathbb{P}^3$ which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property.Shape space – a paradigm for character animation in computer graphics
http://publications.mfo.de/handle/mfo/3798
Shape space – a paradigm for character animation in computer graphics
Heeren, Behrend; Rumpf, Martin
Nowadays 3D computer animation is increasingly realistic
as the models used for the characters become
more and more complex. These models are typically
represented by meshes of hundreds of thousands or
even millions of triangles. The mathematical notion
of a shape space allows us to effectively model, manipulate,
and animate such meshes. Once an appropriate
notion of dissimilarity measure between different
triangular meshes is defined, various useful tools
in character modeling and animation turn out to coincide
with basic geometric operations derived from
this definition.
Wed, 07 Oct 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37982020-10-07T00:00:00ZHeeren, BehrendRumpf, MartinNowadays 3D computer animation is increasingly realistic
as the models used for the characters become
more and more complex. These models are typically
represented by meshes of hundreds of thousands or
even millions of triangles. The mathematical notion
of a shape space allows us to effectively model, manipulate,
and animate such meshes. Once an appropriate
notion of dissimilarity measure between different
triangular meshes is defined, various useful tools
in character modeling and animation turn out to coincide
with basic geometric operations derived from
this definition.Higgs bundles without geometry
http://publications.mfo.de/handle/mfo/3793
Higgs bundles without geometry
Rayan, Steven; Schaposnik, Laura P.
Higgs bundles appeared a few decades ago as solutions
to certain equations from physics and have attracted
much attention in geometry as well as other
areas of mathematics and physics. Here, we take a
very informal stroll through some aspects of linear
algebra that anticipate the deeper structure in the
moduli space of Higgs bundles.
Tue, 29 Sep 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37932020-09-29T00:00:00ZRayan, StevenSchaposnik, Laura P.Higgs bundles appeared a few decades ago as solutions
to certain equations from physics and have attracted
much attention in geometry as well as other
areas of mathematics and physics. Here, we take a
very informal stroll through some aspects of linear
algebra that anticipate the deeper structure in the
moduli space of Higgs bundles.Toric Geometry
http://publications.mfo.de/handle/mfo/3791
Toric Geometry
Toric geometry is a subfield of algebraic geometry with rich
interactions with geometric combinatorics, and many other fields of
mathematics. This workshop brought together a broad range of mathematicians interested in toric matters, and their generalizations and applications.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37912019-01-01T00:00:00ZToric geometry is a subfield of algebraic geometry with rich
interactions with geometric combinatorics, and many other fields of
mathematics. This workshop brought together a broad range of mathematicians interested in toric matters, and their generalizations and applications.Large Scale Stochastic Dynamics
http://publications.mfo.de/handle/mfo/3790
Large Scale Stochastic Dynamics
The goal of this workshop was to explore the recent advances in the
mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. There were 55 participants,
including postdocs and graduate students, working in diverse
intertwining areas of probability and statistical mechanics. During
the meeting, 29 talks of 45 minutes were scheduled and an evening
session was organised with 10 more short talks of 10 minutes, mostly by younger participants.
These talks addressed the following topics :
randomness emerging from deterministic dynamics,
hydrodynamic limits, interface growth models and slow convergence to
equilibrium in kinetically
constrained dynamics.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37902019-01-01T00:00:00ZThe goal of this workshop was to explore the recent advances in the
mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. There were 55 participants,
including postdocs and graduate students, working in diverse
intertwining areas of probability and statistical mechanics. During
the meeting, 29 talks of 45 minutes were scheduled and an evening
session was organised with 10 more short talks of 10 minutes, mostly by younger participants.
These talks addressed the following topics :
randomness emerging from deterministic dynamics,
hydrodynamic limits, interface growth models and slow convergence to
equilibrium in kinetically
constrained dynamics.Many-Body Quantum Systems
http://publications.mfo.de/handle/mfo/3789
Many-Body Quantum Systems
The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In
this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37892019-01-01T00:00:00ZThe interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In
this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.Innovative Approaches to the Numerical Approximation of PDEs
http://publications.mfo.de/handle/mfo/3788
Innovative Approaches to the Numerical Approximation of PDEs
This workshop was about the numerical solution of PDEs for which classical
approaches,
such as the finite element method, are not well suited or need further
(theoretical) underpinnings.
A prominent example of PDEs for which classical methods are not well
suited are PDEs posed in high space dimensions.
New results on low rank tensor approximation for those problems were
presented.
Other presentations dealt with regularity of PDEs, the numerical solution
of PDEs on surfaces,
PDEs of fractional order, numerical solvers for PDEs that converge with
exponential rates, and
the application of deep neural networks for solving PDEs.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37882019-01-01T00:00:00ZThis workshop was about the numerical solution of PDEs for which classical
approaches,
such as the finite element method, are not well suited or need further
(theoretical) underpinnings.
A prominent example of PDEs for which classical methods are not well
suited are PDEs posed in high space dimensions.
New results on low rank tensor approximation for those problems were
presented.
Other presentations dealt with regularity of PDEs, the numerical solution
of PDEs on surfaces,
PDEs of fractional order, numerical solvers for PDEs that converge with
exponential rates, and
the application of deep neural networks for solving PDEs.Geometric, Algebraic, and Topological Combinatorics
http://publications.mfo.de/handle/mfo/3787
Geometric, Algebraic, and Topological Combinatorics
The 2019 Oberwolfach meeting "Geometric, Algebraic and Topological Combinatorics"
was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle),
Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered
a wide variety of aspects of Discrete Geometry, Algebraic Combinatorics
with geometric flavor, and Topological Combinatorics. Some of the
highlights of the conference included (1) Karim Adiprasito presented his
very recent proof of the $g$-conjecture for spheres (as a talk and as a "Q\&A"
evening session) (2) Federico Ardila gave an overview on "The geometry of matroids",
including his recent extension with Denham and Huh of previous work of Adiprasito, Huh and Katz.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37872019-01-01T00:00:00ZThe 2019 Oberwolfach meeting "Geometric, Algebraic and Topological Combinatorics"
was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle),
Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered
a wide variety of aspects of Discrete Geometry, Algebraic Combinatorics
with geometric flavor, and Topological Combinatorics. Some of the
highlights of the conference included (1) Karim Adiprasito presented his
very recent proof of the $g$-conjecture for spheres (as a talk and as a "Q\&A"
evening session) (2) Federico Ardila gave an overview on "The geometry of matroids",
including his recent extension with Denham and Huh of previous work of Adiprasito, Huh and Katz.Mathematical Aspects of Hydrodynamics
http://publications.mfo.de/handle/mfo/3786
Mathematical Aspects of Hydrodynamics
The workshop dealt with the partial differential equations that describe fluid motion and related topics.
These topics included both inviscid and viscous fluids in two and three dimensions. Some talks addressed
aspects of fluid dynamics such as the construction of wild weak solutions, compressible shock formation,
inviscid limit and behavior of boundary layers, as well as both polymer/fluid and structure/fluid interaction.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37862019-01-01T00:00:00ZThe workshop dealt with the partial differential equations that describe fluid motion and related topics.
These topics included both inviscid and viscous fluids in two and three dimensions. Some talks addressed
aspects of fluid dynamics such as the construction of wild weak solutions, compressible shock formation,
inviscid limit and behavior of boundary layers, as well as both polymer/fluid and structure/fluid interaction.