1 - Oberwolfach Preprints (OWP)
http://publications.mfo.de/handle/mfo/19
The Oberwolfach Preprints (OWP) mainly contain research results related to a longer stay in Oberwolfach. In particular, this concerns the Research in Pairs program and the Oberwolfach Leibniz Fellows, but this can also include an Oberwolfach Lecture, for example.Fri, 18 Sep 2020 10:26:52 GMT2020-09-18T10:26:52ZThe Pelletier-Ressayre Hidden Symmetry for Littlewood-Richardson Coefficients
http://publications.mfo.de/handle/mfo/3773
The Pelletier-Ressayre Hidden Symmetry for Littlewood-Richardson Coefficients
Grinberg, Darij
We prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield.
Tue, 08 Sep 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37732020-09-08T00:00:00ZGrinberg, DarijWe prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield.Braidoids
http://publications.mfo.de/handle/mfo/3771
Braidoids
Gügümcü, Neslihan; Lambropoulou, Sofia
Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in $\mathbb{R}^2$, a closure operation for braidoids, we prove an analogue of the Alexander theorem, namely an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the $L$-moves.
Thu, 03 Sep 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37712020-09-03T00:00:00ZGügümcü, NeslihanLambropoulou, SofiaBraidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in $\mathbb{R}^2$, a closure operation for braidoids, we prove an analogue of the Alexander theorem, namely an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the $L$-moves.Maximal Quaternion Orders in Quadratic Extensions - in Hurwitz’s Diaries
http://publications.mfo.de/handle/mfo/3768
Maximal Quaternion Orders in Quadratic Extensions - in Hurwitz’s Diaries
Oswald, Nicola; Steuding, Jörn
We present and comment on some unpublished work of Adolf Hurwitz on quaternion arithmetic from his diaries.
Mon, 03 Aug 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37682020-08-03T00:00:00ZOswald, NicolaSteuding, JörnWe present and comment on some unpublished work of Adolf Hurwitz on quaternion arithmetic from his diaries.Hopf Algebras in Combinatorics, Volume 2
http://publications.mfo.de/handle/mfo/3767
Hopf Algebras in Combinatorics, Volume 2
Grinberg, Darij; Reiner, Victor
Thu, 30 Jul 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37672020-07-30T00:00:00ZGrinberg, DarijReiner, VictorHopf Algebras in Combinatorics, Volume 1
http://publications.mfo.de/handle/mfo/3766
Hopf Algebras in Combinatorics, Volume 1
Grinberg, Darij; Reiner, Victor
Wed, 29 Jul 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37662020-07-29T00:00:00ZGrinberg, DarijReiner, VictorHow Quantum Information Can Improve Social Welfare
http://publications.mfo.de/handle/mfo/3765
How Quantum Information Can Improve Social Welfare
Groisman, Berry; Mc Gettrick, Michael; Mhalla, Mehdi; Pawlowski, Marcin
In [2, 18, 5, 19, 4] it has been shown that quantum resources can allow us
to achieve a family of equilibria that can have sometimes a better social welfare,
while guaranteeing privacy. We use graph games to propose a way to build non-
cooperative games from graph states, and we show how to achieve an unlimited
improvement with quantum advice compared to classical advice.
Thu, 16 Jul 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37652020-07-16T00:00:00ZGroisman, BerryMc Gettrick, MichaelMhalla, MehdiPawlowski, MarcinIn [2, 18, 5, 19, 4] it has been shown that quantum resources can allow us
to achieve a family of equilibria that can have sometimes a better social welfare,
while guaranteeing privacy. We use graph games to propose a way to build non-
cooperative games from graph states, and we show how to achieve an unlimited
improvement with quantum advice compared to classical advice.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.On Weakly Complete Universal Enveloping Algebras of pro-Lie Algebras
http://publications.mfo.de/handle/mfo/3740
On Weakly Complete Universal Enveloping Algebras of pro-Lie Algebras
Hofmann, Karl Heinrich; Kramer, Linus
Mon, 27 Apr 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37402020-04-27T00:00:00ZHofmann, Karl HeinrichKramer, LinusTheoretical Analysis and Simulation Methods for Hawkes Processes and their Diffusion Approximation
http://publications.mfo.de/handle/mfo/3719
Theoretical Analysis and Simulation Methods for Hawkes Processes and their Diffusion Approximation
Chevallier, Julien; Melnykova, Anna; Tubikanec, Irene
Oscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen and Löcherbach (2017). They are piecewise deterministic Markov processes (PDMP) and can be approximated by a stochastic diffusion. First, a strong error bound between the PDMP and the diffusion is proved. Second, moment bounds for the resulting diffusion are derived. Third, approximation schemes for the diffusion, based on the numerical splitting approach, are proposed. These schemes are proved to converge with meansquare order 1 and to preserve the properties of the diffusion, in particular the hypoellipticity, the ergodicity and the moment bounds. Finally, the PDMP and the diffusion are compared through numerical experiments, where the PDMP is simulated with an adapted thinning procedure.
Mon, 30 Mar 2020 00:00:00 GMThttp://publications.mfo.de/handle/mfo/37192020-03-30T00:00:00ZChevallier, JulienMelnykova, AnnaTubikanec, IreneOscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen and Löcherbach (2017). They are piecewise deterministic Markov processes (PDMP) and can be approximated by a stochastic diffusion. First, a strong error bound between the PDMP and the diffusion is proved. Second, moment bounds for the resulting diffusion are derived. Third, approximation schemes for the diffusion, based on the numerical splitting approach, are proposed. These schemes are proved to converge with meansquare order 1 and to preserve the properties of the diffusion, in particular the hypoellipticity, the ergodicity and the moment bounds. Finally, the PDMP and the diffusion are compared through numerical experiments, where the PDMP is simulated with an adapted thinning procedure.