Oberwolfach Publications
http://publications.mfo.de:80
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 23 May 2020 19:37:34 GMT2020-05-23T19:37:34ZOberwolfach Publicationshttp://publications.mfo.de/themes/Mirage2/images/apple-touch-icon.png
http://publications.mfo.de:80
Space-Time Euler Discretization Schemes for the Stochastic 2D Navier-Stokes Equations
http://publications.mfo.de/handle/mfo/3744
Space-Time Euler Discretization Schemes for the Stochastic 2D Navier-Stokes Equations
Bessaih, Hakima; Millet, Annie
We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in $L^2(\Omega)$, and describe the rate of convergence for an $H^1$-valued initial condition. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme, we can prove strong convergence of this space-time approximation. The speed of the $L^2(\Omega)$-convergence depends on the diffusion coefficient and on the viscosity parameter. In case of Scott-Vogelius mixed elements and for an additive noise, the convergence is polynomial.
Wed, 06 May 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37442020-05-06T00:00:00ZBessaih, HakimaMillet, AnnieWe prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in $L^2(\Omega)$, and describe the rate of convergence for an $H^1$-valued initial condition. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme, we can prove strong convergence of this space-time approximation. The speed of the $L^2(\Omega)$-convergence depends on the diffusion coefficient and on the viscosity parameter. In case of Scott-Vogelius mixed elements and for an additive noise, the convergence is polynomial.l-Torsion Bounds for the Class Group of Number Fields with an l -Group as Galois Group
http://publications.mfo.de/handle/mfo/3742
l-Torsion Bounds for the Class Group of Number Fields with an l -Group as Galois Group
Klüners, Jürgen; Wang, Jiuya
We describe the relations among the $\ell$-torsion conjecture for $\ell$-extensions, the discriminant multiplicity conjecture for nilpotent extensions and a conjecture of Malle giving an upper bound for the number of nilpotent extensions. We then prove all of these conjectures in these cases.
Mon, 04 May 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37422020-05-04T00:00:00ZKlüners, JürgenWang, JiuyaWe describe the relations among the $\ell$-torsion conjecture for $\ell$-extensions, the discriminant multiplicity conjecture for nilpotent extensions and a conjecture of Malle giving an upper bound for the number of nilpotent extensions. We then prove all of these conjectures in these cases.Determinacy versus indeterminacy
http://publications.mfo.de/handle/mfo/3739
Determinacy versus indeterminacy
Berg, Christian
Can a continuous function on an interval be uniquely
determined if we know all the integrals of the function
against the natural powers of the variable? Following
Weierstrass and Stieltjes, we show that the answer is
yes if the interval is finite, and no if the interval is
infinite.
Wed, 22 Apr 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37392020-04-22T00:00:00ZBerg, ChristianCan a continuous function on an interval be uniquely
determined if we know all the integrals of the function
against the natural powers of the variable? Following
Weierstrass and Stieltjes, we show that the answer is
yes if the interval is finite, and no if the interval is
infinite.Vertex-to-Self Trajectories on the Platonic Solids
http://publications.mfo.de/handle/mfo/3737
Vertex-to-Self Trajectories on the Platonic Solids
Athreya, Jayadev S.; Aulicino, David
We consider the problem of walking in a straight line
on the surface of a Platonic solid. While the tetrahedron,
octahedron, cube, and icosahedron all exhibit
the same behavior, we find a remarkable difference
with the dodecahedron.
Wed, 15 Apr 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37372020-04-15T00:00:00ZAthreya, Jayadev S.Aulicino, DavidWe consider the problem of walking in a straight line
on the surface of a Platonic solid. While the tetrahedron,
octahedron, cube, and icosahedron all exhibit
the same behavior, we find a remarkable difference
with the dodecahedron.Random matrix theory: Dyson Brownian motion
http://publications.mfo.de/handle/mfo/3736
Random matrix theory: Dyson Brownian motion
Finocchio, Gianluca
The theory of random matrices was introduced by
John Wishart (1898–1956) in 1928. The theory was
then developed within the field of nuclear physics
from 1955 by Eugene Paul Wigner (1902–1995) and
later by Freeman John Dyson, who were both concerned
with the statistical description of heavy atoms
and their electromagnetic properties. In this snapshot,
we show how mathematical properties can have
unexpected links to physical phenomenena. In particular,
we show that the eigenvalues of some particular
random matrices can mimic the electrostatic repulsion
of the particles in a gas.
Wed, 15 Apr 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37362020-04-15T00:00:00ZFinocchio, GianlucaThe theory of random matrices was introduced by
John Wishart (1898–1956) in 1928. The theory was
then developed within the field of nuclear physics
from 1955 by Eugene Paul Wigner (1902–1995) and
later by Freeman John Dyson, who were both concerned
with the statistical description of heavy atoms
and their electromagnetic properties. In this snapshot,
we show how mathematical properties can have
unexpected links to physical phenomenena. In particular,
we show that the eigenvalues of some particular
random matrices can mimic the electrostatic repulsion
of the particles in a gas.From Betti numbers to ℓ²-Betti numbers
http://publications.mfo.de/handle/mfo/3735
From Betti numbers to ℓ²-Betti numbers
Kammeyer, Holger; Sauer, Roman
We provide a leisurely introduction to ℓ²-Betti numbers,
which are topological invariants, by relating
them to their much older cousins, Betti numbers. In
the end we present an open research problem about
ℓ²-Betti numbers.
Wed, 15 Apr 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37352020-04-15T00:00:00ZKammeyer, HolgerSauer, RomanWe provide a leisurely introduction to ℓ²-Betti numbers,
which are topological invariants, by relating
them to their much older cousins, Betti numbers. In
the end we present an open research problem about
ℓ²-Betti numbers.Representations of Finite Groups
http://publications.mfo.de/handle/mfo/3730
Representations of Finite Groups
The workshop Representations of Finite Groups was organised by Joseph Chuang (London), Meinolf Geck (Stuttgart), Radha Kessar (London) and Gabriel Navarro (Valencia). It covered a wide variety of aspects of representation theory of finite groups and its relations to other areas of mathematics.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37302019-01-01T00:00:00ZThe workshop Representations of Finite Groups was organised by Joseph Chuang (London), Meinolf Geck (Stuttgart), Radha Kessar (London) and Gabriel Navarro (Valencia). It covered a wide variety of aspects of representation theory of finite groups and its relations to other areas of mathematics.Contemporary Coding Theory
http://publications.mfo.de/handle/mfo/3729
Contemporary Coding Theory
Coding Theory naturally lies at the intersection of a large number
of disciplines in pure and applied mathematics. A multitude of
methods and means has been designed to construct, analyze, and
decode the resulting codes for communication. This has suggested to
bring together researchers in a variety of disciplines within
Mathematics, Computer Science, and Electrical Engineering, in order
to cross-fertilize generation of new ideas and force global
advancement of the field. Areas to be covered are Network Coding,
Subspace Designs, General Algebraic Coding Theory, Distributed
Storage and Private Information Retrieval (PIR), as well as
Code-Based Cryptography.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37292019-01-01T00:00:00ZCoding Theory naturally lies at the intersection of a large number
of disciplines in pure and applied mathematics. A multitude of
methods and means has been designed to construct, analyze, and
decode the resulting codes for communication. This has suggested to
bring together researchers in a variety of disciplines within
Mathematics, Computer Science, and Electrical Engineering, in order
to cross-fertilize generation of new ideas and force global
advancement of the field. Areas to be covered are Network Coding,
Subspace Designs, General Algebraic Coding Theory, Distributed
Storage and Private Information Retrieval (PIR), as well as
Code-Based Cryptography.Uncertainty Quantification
http://publications.mfo.de/handle/mfo/3728
Uncertainty Quantification
Uncertainty quantification (UQ) is concerned with including and characterising uncertainties in mathematical models.
Major steps comprise proper description of system uncertainties, analysis and efficient quantification of uncertainties in predictions and design problems, and statistical inference on uncertain parameters starting from available measurements.
Research in UQ addresses fundamental mathematical and statistical challenges, but has also wide applicability in areas such as engineering, environmental, physical and biological applications.
This workshop focussed on mathematical challenges at the interface of applied mathematics, probability and statistics, numerical analysis, scientific computing and application domains.
The workshop served to bring together experts from those disciplines in order to enhance their interaction, to exchange ideas and to develop new, powerful methods for UQ.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37282019-01-01T00:00:00ZUncertainty quantification (UQ) is concerned with including and characterising uncertainties in mathematical models.
Major steps comprise proper description of system uncertainties, analysis and efficient quantification of uncertainties in predictions and design problems, and statistical inference on uncertain parameters starting from available measurements.
Research in UQ addresses fundamental mathematical and statistical challenges, but has also wide applicability in areas such as engineering, environmental, physical and biological applications.
This workshop focussed on mathematical challenges at the interface of applied mathematics, probability and statistics, numerical analysis, scientific computing and application domains.
The workshop served to bring together experts from those disciplines in order to enhance their interaction, to exchange ideas and to develop new, powerful methods for UQ.Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories
http://publications.mfo.de/handle/mfo/3727
Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories
The mini-workshop featured some open questions
about the cohomology of Hopf algebras
and tensor categories.
Questions included whether the cohomology ring
of a finite dimensional Hopf algebra or a finite tensor category is
finitely generated, questions about corresponding
geometric methods in representation theory, and
questions about noetherian Hopf algebras.
The workshop brought together mathematicians currently
working on these and other open problems.
Tue, 01 Jan 2019 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37272019-01-01T00:00:00ZThe mini-workshop featured some open questions
about the cohomology of Hopf algebras
and tensor categories.
Questions included whether the cohomology ring
of a finite dimensional Hopf algebra or a finite tensor category is
finitely generated, questions about corresponding
geometric methods in representation theory, and
questions about noetherian Hopf algebras.
The workshop brought together mathematicians currently
working on these and other open problems.