2022
2022
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Convolution in Dual Cesàro Sequence Spaces
[OWP202220] (Mathematisches Forschungsinstitut Oberwolfach, 20221216)We investigate convolution operators in the sequence spaces $d_p$, for 1 $\leqslant p<\infty$. These spaces, for $p$ > 1, arise as dual spaces of the Cesàro sequence spaces $ces_p$ thoroughly investigated by G. Bennett. A ... 
Hutchinson's Intervals and Entire Functions from the LaguerrePólya Class
[OWP202219] (Mathematisches Forschungsinstitut Oberwolfach, 20221212)We find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k1}^2}{ ... 
QuasiEquilibria and Click Times for a Variant of Muller's Ratchet
[OWP202218] (Mathematisches Forschungsinstitut Oberwolfach, 20221130)Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective ... 
Birational Rowmotion on a Rectangle over a Noncommutative Ring
[OWP202217] (Mathematisches Forschungsinstitut Oberwolfach, 20220920)We extend the periodicity of birational rowmotion for rectangular posets to the case when the base field is replaced by a noncommutative ring (under appropriate conditions). This resolves a conjecture from 2014. The proof ... 
Root Cycles in Coxeter Groups
[OWP202216] (Mathematisches Forschungsinstitut Oberwolfach, 20220915)For an element $w$ of a Coxeter group $W$ there are two important attributes, namely its length, and its expression as a product of disjoint cycles in its action on $\Phi$, the root system of $W$. This paper investigates ... 
Convergence and Error Analysis of Compressible Fluid Flows with Random Data: Monte Carlo Method
[OWP202215] (Mathematisches Forschungsinstitut Oberwolfach, 20220825)The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the NavierStokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a ... 
On a Conjecture of Khoroshkin and Tolstoy
[OWP202214] (Mathematisches Forschungsinstitut Oberwolfach, 20220802)We prove a nogo theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal $R$matrix, yielding a negative answer to a conjecture of Khoroshkin and Tolstoy from ... 
Embedding Spaces of Split Links
[OWP202213] (Mathematisches Forschungsinstitut Oberwolfach, 20220801)We study the homotopy type of the space $\mathcal{E}(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Inspired by work of Brendle and Hatcher, we introduce a semisimplicial ... 
Shockavoiding Slicing Conditions: Tests and Calibrations
[OWP202212] (Mathematisches Forschungsinstitut Oberwolfach, 20220719)While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop "gaugeshocks" in some examples. Alternative "shockavoiding" slicing conditions ... 
On the Enumeration of Finite $L$Algebras
[OWP202211] (Mathematisches Forschungsinstitut Oberwolfach, 20220629)We use Constraint Satisfaction Methods to construct and enumerate finite Lalgebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the ... 
Discretization of Inherent ODEs and the Geometric Integration of DAEs with Symmetries
[OWP202210] (Mathematisches Forschungsinstitut Oberwolfach, 20220608)Discretization methods for differentialalgebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization ... 
Bounded Weight Modules for Basic Classical Lie Superalgebras at Infinity
[OWP202209] (Mathematisches Forschungsinstitut Oberwolfach, 20220530)We classify simple bounded weight modules over the complex simple Lie superalgebras $\mathfrak{sl}(\infty \infty)$ and $\mathfrak{osp} (m  2n)$, when at least one of $m$ and $n$ equals $\infty$. For $\mathfrak{osp} (m  ... 
Coorbit Spaces and Dual Molecules: the QuasiBanach Case
[OWP202208] (Mathematisches Forschungsinstitut Oberwolfach, 20220527)This paper provides a selfcontained exposition of coorbit spaces associated with integrable group representations and quasiBanach function spaces. It extends the theory in [Studia Math., 180(3):237–253, 2007] to locally ... 
Deciding NonFreeness of Rational Möbius Groups
[OWP202207] (Mathematisches Forschungsinstitut Oberwolfach, 20220322)We explore a new computational approach to a classical problem: certifying nonfreeness of (2generator, parabolic) Möbius subgroups of SL(2, $\mathbb{Q}$). The main tools used are algorithms for Zariski dense groups and ... 
Characterization of Tropical Planar Curves up to Genus Six
[OWP202206] (Mathematisches Forschungsinstitut Oberwolfach, 20220316)We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six. 
Local and Global Canonical Forms for DifferentialAlgebraic Equations with Symmetries
[OWP202205] (Mathematisches Forschungsinstitut Oberwolfach, 20220221)Linear timevarying differentialalgebraic equations with symmetries are studied. The structures that we address are selfadjoint and skewadjoint systems. Local and global canonical forms under congruence are presented ... 
AeppliBottChernMassey Products, Bigraded Notions of Formality, and NonZero Degree Maps
[OWP202204] (Mathematisches Forschungsinstitut Oberwolfach, 20220215)We introduce and study notions of bigraded formality for the algebra of forms on a complex manifold, along with their relation to higher AeppliBottChernMassey products which extend, in an augmented setting, the case of ... 
Some Homological Properties of Borel Type Ideals
[OWP202203] (Mathematisches Forschungsinstitut Oberwolfach, 20220201)We study ideals of Borel type, including $k$Borel ideals and $t$spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated ... 
Trivial Source Character Tables of SL2(q)
[OWP202202] (Mathematisches Forschungsinstitut Oberwolfach, 20220128)We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic $\ell$ via ... 
Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible NonHomogeneous Poisson Structures
[OWP202201] (Mathematisches Forschungsinstitut Oberwolfach, 20220120)We consider multicomponent local Poisson structures of the form $\mathcal P_3 + \mathcal P_1$, under the assumption that the third order term $\mathcal P_3$ is DarbouxPoisson and nondegenerate, and study the Poisson ...