Auflistung nach Erscheinungsdatum

Root Cycles in Coxeter Groups

[OWP-2022-16] Hart, Sarah; Kelsey, Veronica; Rowley, Peter (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] Grinberg, Darij; Roby, Tom (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] Utpala, Saiteja; Miolane, Nina (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] Dumanski, Ilya; Kiritchenko, Valentina (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] Baake, Michael; Grimm, Uwe; Moody, Robert V. (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] Balakrishnan, Jennifer S. (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] González Casanova, Adrian; Smadi, Charline; Wakolbinger, Anton (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] Hellmuth, Kathrin; Klingenberg, Christian (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] Dozier, Benjamin (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] Mussnig, Fabian (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] Nguyen, Thu Hien; Vishnyakova, Anna (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}{ ...

Convolution in Dual Cesàro Sequence Spaces

[OWP-2022-20] Curbera, Guillermo P.; Ricker, Werner J. (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 ...