2022
2022
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Convolution in Dual Cesàro Sequence Spaces
[OWP-2022-20] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-16)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 Laguerre-Pólya Class
[OWP-2022-19] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-12)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_{k-1}^2}{ ... -
Quasi-Equilibria and Click Times for a Variant of Muller's Ratchet
[OWP-2022-18] (Mathematisches Forschungsinstitut Oberwolfach, 2022-11-30)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
[OWP-2022-17] (Mathematisches Forschungsinstitut Oberwolfach, 2022-09-20)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
[OWP-2022-16] (Mathematisches Forschungsinstitut Oberwolfach, 2022-09-15)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
[OWP-2022-15] (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-25)The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes 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
[OWP-2022-14] (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-02)We prove a no-go 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
[OWP-2022-13] (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-01)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 semi-simplicial ... -
Shock-avoiding Slicing Conditions: Tests and Calibrations
[OWP-2022-12] (Mathematisches Forschungsinstitut Oberwolfach, 2022-07-19)While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop "gauge-shocks" in some examples. Alternative "shockavoiding" slicing conditions ... -
On the Enumeration of Finite $L$-Algebras
[OWP-2022-11] (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-29)We use Constraint Satisfaction Methods to construct and enumerate finite L-algebras 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
[OWP-2022-10] (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-08)Discretization methods for differential-algebraic 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
[OWP-2022-09] (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-30)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 Quasi-Banach Case
[OWP-2022-08] (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-27)This paper provides a self-contained exposition of coorbit spaces associated with integrable group representations and quasi-Banach function spaces. It extends the theory in [Studia Math., 180(3):237–253, 2007] to locally ... -
Deciding Non-Freeness of Rational Möbius Groups
[OWP-2022-07] (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-22)We explore a new computational approach to a classical problem: certifying non-freeness of (2-generator, 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
[OWP-2022-06] (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-16)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 Differential-Algebraic Equations with Symmetries
[OWP-2022-05] (Mathematisches Forschungsinstitut Oberwolfach, 2022-02-21)Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented ... -
Aeppli-Bott-Chern-Massey Products, Bigraded Notions of Formality, and Non-Zero Degree Maps
[OWP-2022-04] (Mathematisches Forschungsinstitut Oberwolfach, 2022-02-15)We introduce and study notions of bigraded formality for the algebra of forms on a complex manifold, along with their relation to higher Aeppli-Bott-Chern-Massey products which extend, in an augmented setting, the case of ... -
Some Homological Properties of Borel Type Ideals
[OWP-2022-03] (Mathematisches Forschungsinstitut Oberwolfach, 2022-02-01)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)
[OWP-2022-02] (Mathematisches Forschungsinstitut Oberwolfach, 2022-01-28)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 Non-Homogeneous Poisson Structures
[OWP-2022-01] (Mathematisches Forschungsinstitut Oberwolfach, 2022-01-20)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 Darboux-Poisson and non-degenerate, and study the Poisson ...
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