Auflistung nach Erscheinungsdatum
Anzeige der Dokumente 1881-1900 von 1987
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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 | ... -
Jewellery from tessellations of hyperbolic space
[SNAP-2022-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-02)In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
Solving inverse problems with Bayes' theorem
[SNAP-2022-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-09-05)The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as ... -
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 ... -
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 ... -
Biological shape analysis with geometric statistics and learning
[SNAP-2022-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold ... -
Representations and degenerations
[SNAP-2022-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)In this snapshot, we explain two important mathematical concepts (representation and degeneration) in elementary terms. We will focus on the simplest meaningful examples, and motivate both concepts by study of symmetry. -
What is pattern?
[SNAP-2022-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics. -
A tale of three curves
[SNAP-2022-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-27)In this snapshot, we give a survey of some problems in the study of rational points on higher genus curves, discussing questions ranging from the era of the ancient Greeks to a few posed by mathematicians of the 20th ... -
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 ... -
Route planning for bacteria
[SNAP-2022-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-08)Bacteria have been fascinating biologists since their discovery in the late 17th century. By analysing their movements, mathematical models have been developed as a tool to understand their behaviour. However, adapting ... -
Closed geodesics on surfaces
[SNAP-2022-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-08)We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line ... -
Characterizations of intrinsic volumes on convex bodies and convex functions
[SNAP-2022-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-08)If we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of ... -
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}{ ...