Oberwolfach Publications
http://publications.mfo.de:8080
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 21 Oct 2019 07:28:36 GMT2019-10-21T07:28:36ZOberwolfach Publicationshttp://publications.mfo.de/themes/Mirage2/images/apple-touch-icon.png
http://publications.mfo.de:8080
Jahresbericht | Annual Report - 2018
http://publications.mfo.de/handle/mfo/2520
Jahresbericht | Annual Report - 2018
Mathematisches Forschungsinstitut Oberwolfach
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25202019-01-01T00:00:00ZMathematisches Forschungsinstitut OberwolfachConfiguration spaces and braid groups
http://publications.mfo.de/handle/mfo/2519
Configuration spaces and braid groups
Jiménez Rolland, Rita; Xicoténcatl, Miguel A.
In this snapshot we introduce configuration spaces
and explain how a mathematician studies their ‘shape’.
This will lead us to consider paths of configurations
and braid groups, and to explore how algebraic properties
of these groups determine features of the spaces.
Tue, 08 Oct 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25192019-10-08T00:00:00ZJiménez Rolland, RitaXicoténcatl, Miguel A.In this snapshot we introduce configuration spaces
and explain how a mathematician studies their ‘shape’.
This will lead us to consider paths of configurations
and braid groups, and to explore how algebraic properties
of these groups determine features of the spaces.Groups with Spanier-Whitehead Duality
http://publications.mfo.de/handle/mfo/2518
Groups with Spanier-Whitehead Duality
Nishikawa, Shintaro; Proietti, Valerio
We introduce the notion of Spanier-Whitehead $K$-duality for a discrete group $G$, defined as duality in the KK-category between two $C*$-algebras which are naturally attached to the group, namely the reduced group $C*$-algebra and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our
analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups.
Tue, 17 Sep 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25182019-09-17T00:00:00ZNishikawa, ShintaroProietti, ValerioWe introduce the notion of Spanier-Whitehead $K$-duality for a discrete group $G$, defined as duality in the KK-category between two $C*$-algebras which are naturally attached to the group, namely the reduced group $C*$-algebra and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our
analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups.Limits of graph sequences
http://publications.mfo.de/handle/mfo/2516
Limits of graph sequences
Klimošová, Tereza
Graphs are simple mathematical structures used to
model a wide variety of real-life objects. With the
rise of computers, the size of the graphs used for
these models has grown enormously. The need to efficiently
represent and study properties of extremely
large graphs led to the development of the theory of
graph limits.
Wed, 04 Sep 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25162019-09-04T00:00:00ZKlimošová, TerezaGraphs are simple mathematical structures used to
model a wide variety of real-life objects. With the
rise of computers, the size of the graphs used for
these models has grown enormously. The need to efficiently
represent and study properties of extremely
large graphs led to the development of the theory of
graph limits.On Logic, Choices and Games
http://publications.mfo.de/handle/mfo/2515
On Logic, Choices and Games
Oliva, Paulo
Can we always mathematically formalise our taste
and preferences? We discuss how this has been done
historically in the field of game theory, and how recent
ideas from logic and computer science have brought
an interesting twist to this beautiful theory.
Wed, 04 Sep 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25152019-09-04T00:00:00ZOliva, PauloCan we always mathematically formalise our taste
and preferences? We discuss how this has been done
historically in the field of game theory, and how recent
ideas from logic and computer science have brought
an interesting twist to this beautiful theory.Nonlinear Acoustics
http://publications.mfo.de/handle/mfo/2514
Nonlinear Acoustics
Kaltenbacher, Barbara; Brunnhuber, Rainer
Nonlinear acoustics has been a topic of research for
more than 250 years. Driven by a wide range and a
large number of highly relevant industrial and medical
applications, this area has expanded enormously
in the last few decades. Here, we would like to give
a glimpse of the mathematical modeling techniques
that are commonly employed to tackle problems in
this area of research, with a selection of references
for the interested reader to further their knowledge
into this mathematically interesting field.
Wed, 04 Sep 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25142019-09-04T00:00:00ZKaltenbacher, BarbaraBrunnhuber, RainerNonlinear acoustics has been a topic of research for
more than 250 years. Driven by a wide range and a
large number of highly relevant industrial and medical
applications, this area has expanded enormously
in the last few decades. Here, we would like to give
a glimpse of the mathematical modeling techniques
that are commonly employed to tackle problems in
this area of research, with a selection of references
for the interested reader to further their knowledge
into this mathematically interesting field.Group-Graded Rings Satisfying the Strong Rank Condition
http://publications.mfo.de/handle/mfo/2513
Group-Graded Rings Satisfying the Strong Rank Condition
Kropholler, Peter H.; Lorensen, Karl
A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that the base ring $R_1$ is a domain. Using an argument originated by Laurent Bartholdi for studying cellular automata, we prove that $R$ satisfies SRC if and only if
$R_1$ satisfies SRC and $G$ is amenable. The special case of this result for group rings allows us to prove a characterization of amenability involving the group von Neumann algebra that was conjectured by Wolfgang Lück. In addition, we include two applications to the study of group rings and their modules.
Fri, 16 Aug 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25132019-08-16T00:00:00ZKropholler, Peter H.Lorensen, KarlA ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that the base ring $R_1$ is a domain. Using an argument originated by Laurent Bartholdi for studying cellular automata, we prove that $R$ satisfies SRC if and only if
$R_1$ satisfies SRC and $G$ is amenable. The special case of this result for group rings allows us to prove a characterization of amenability involving the group von Neumann algebra that was conjectured by Wolfgang Lück. In addition, we include two applications to the study of group rings and their modules.A Cheeger Type Inequality in Finite Cayley Sum Graphs
http://publications.mfo.de/handle/mfo/2512
A Cheeger Type Inequality in Finite Cayley Sum Graphs
Biswas, Arindam; Saha, Jyoti Prakash
Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $|S| = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is non-bipartite, then the spectrum of its normalised adjacency operator is bounded away from $-1$. We also establish an explicit lower bound for the spectrum of these graphs, namely, the non-trivial eigenvalues of the normalised adjacency operator lies in the interval $\left(-1+\frac{h(G)^{4}}{\eta}, 1-\frac{h(G)^{2}}{2d^{2}}\right]$, where $h(G)$ denotes the (vertex) Cheeger constant of the $d$-regular graph $C_{\Sigma}(G,S)$ and $\eta = 2^{9}d^{8}$. Further, we improve upon a recently obtained bound on the non-trivial spectrum of the normalised adjacency operator of the non-bipartite Cayley graph $C(G,S)$.
Wed, 31 Jul 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25122019-07-31T00:00:00ZBiswas, ArindamSaha, Jyoti PrakashLet $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $|S| = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is non-bipartite, then the spectrum of its normalised adjacency operator is bounded away from $-1$. We also establish an explicit lower bound for the spectrum of these graphs, namely, the non-trivial eigenvalues of the normalised adjacency operator lies in the interval $\left(-1+\frac{h(G)^{4}}{\eta}, 1-\frac{h(G)^{2}}{2d^{2}}\right]$, where $h(G)$ denotes the (vertex) Cheeger constant of the $d$-regular graph $C_{\Sigma}(G,S)$ and $\eta = 2^{9}d^{8}$. Further, we improve upon a recently obtained bound on the non-trivial spectrum of the normalised adjacency operator of the non-bipartite Cayley graph $C(G,S)$.On a Cheeger Type Inequality in Cayley Graphs of Finite Groups
http://publications.mfo.de/handle/mfo/2511
On a Cheeger Type Inequality in Cayley Graphs of Finite Groups
Biswas, Arindam
Let $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C(G,S)$ is an expander graph and is non-bipartite then the spectrum of the adjacency operator $T$ is bounded away from $-1$. In this article we are interested in explicit bounds for the spectrum of these graphs. Specifically, we show that the non-trivial spectrum of the adjacency operator lies in the interval $\left[-1+\frac{h(\mathbb{G})^{4}}{\gamma}, 1-\frac{h(\mathbb{G})^{2}}{2d^{2}}\right]$, where $h(\mathbb{G})$ denotes the (vertex) Cheeger constant of the $d$ regular graph $C(G,S)$ with respect to a symmetric set $S$ of generators and $\gamma = 2^{9}d^{6}(d+1)^{2}$.
Mon, 22 Jul 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25112019-07-22T00:00:00ZBiswas, ArindamLet $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C(G,S)$ is an expander graph and is non-bipartite then the spectrum of the adjacency operator $T$ is bounded away from $-1$. In this article we are interested in explicit bounds for the spectrum of these graphs. Specifically, we show that the non-trivial spectrum of the adjacency operator lies in the interval $\left[-1+\frac{h(\mathbb{G})^{4}}{\gamma}, 1-\frac{h(\mathbb{G})^{2}}{2d^{2}}\right]$, where $h(\mathbb{G})$ denotes the (vertex) Cheeger constant of the $d$ regular graph $C(G,S)$ with respect to a symmetric set $S$ of generators and $\gamma = 2^{9}d^{6}(d+1)^{2}$.Random permutations
http://publications.mfo.de/handle/mfo/2510
Random permutations
Betz, Volker
100 people leave their hats at the door at a party and
pick up a completely random hat when they leave.
How likely is it that at least one of them will get
back their own hat? If the hats carry name tags,
how difficult is it to arrange for all hats to be returned
to their owner? These classical questions of
probability theory can be answered relatively easily.
But if a geometric component is added, answering
the same questions immediately becomes very hard,
and little is known about them. We present some
of the open questions and give an overview of what
current research can say about them.
Fri, 12 Jul 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/25102019-07-12T00:00:00ZBetz, Volker100 people leave their hats at the door at a party and
pick up a completely random hat when they leave.
How likely is it that at least one of them will get
back their own hat? If the hats carry name tags,
how difficult is it to arrange for all hats to be returned
to their owner? These classical questions of
probability theory can be answered relatively easily.
But if a geometric component is added, answering
the same questions immediately becomes very hard,
and little is known about them. We present some
of the open questions and give an overview of what
current research can say about them.