http://publications.mfo.de/handle/mfo/3930 Tue, 07 Apr 2026 06:22:38 GMT 2026-04-07T06:22:38Z http://publications.mfo.de/handle/mfo/4127 Charakterisierungen von inneren Volumina auf konvexen Körpern und konvexen Funktionen Mussnig, Fabian Wenn wir die Größe einer zweidimensionalen Form mittels einer Zahl ausdrücken wollen, dann denken wir gewöhnlich an ihren Flächeninhalt oder ihren Umfang. Aber was macht diese Kennzahlen so besonders? Wir beantworten diese Frage anhand klassischer mathematischer Resultate und werfen einen Blick auf Anwendungen und Verallgemeinerungen dieser Theorie. Sun, 01 Jan 2023 00:00:00 GMT http://publications.mfo.de/handle/mfo/4127 2023-01-01T00:00:00Z Mussnig, Fabian Wenn wir die Größe einer zweidimensionalen Form mittels einer Zahl ausdrücken wollen, dann denken wir gewöhnlich an ihren Flächeninhalt oder ihren Umfang. Aber was macht diese Kennzahlen so besonders? Wir beantworten diese Frage anhand klassischer mathematischer Resultate und werfen einen Blick auf Anwendungen und Verallgemeinerungen dieser Theorie. http://publications.mfo.de/handle/mfo/3998 Closed geodesics on surfaces Dozier, Benjamin 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 paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces. Thu, 08 Dec 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3998 2022-12-08T00:00:00Z Dozier, Benjamin 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 paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces. http://publications.mfo.de/handle/mfo/3997 Route planning for bacteria Hellmuth, Kathrin; Klingenberg, Christian 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 these models to real situations can be challenging, because the model coefficients cannot be observed directly. In this snapshot, we study this question mathematically and explain how the idea of “route planning” can be used to determine these model coefficients. Thu, 08 Dec 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3997 2022-12-08T00:00:00Z Hellmuth, Kathrin Klingenberg, Christian 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 these models to real situations can be challenging, because the model coefficients cannot be observed directly. In this snapshot, we study this question mathematically and explain how the idea of “route planning” can be used to determine these model coefficients. http://publications.mfo.de/handle/mfo/3996 Characterizations of intrinsic volumes on convex bodies and convex functions Mussnig, Fabian 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 classical mathematical results. We also take a look at applications and new generalizations to the setting of functions.; [Also available in German] Thu, 08 Dec 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3996 2022-12-08T00:00:00Z Mussnig, Fabian 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 classical mathematical results. We also take a look at applications and new generalizations to the setting of functions. [Also available in German] http://publications.mfo.de/handle/mfo/3986 A tale of three curves Balakrishnan, Jennifer S. 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 century. To answer these questions, we describe a selection of techniques in modern number theory that can be used to determine the set of rational points on a curve. Thu, 27 Oct 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3986 2022-10-27T00:00:00Z Balakrishnan, Jennifer S. 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 century. To answer these questions, we describe a selection of techniques in modern number theory that can be used to determine the set of rational points on a curve. http://publications.mfo.de/handle/mfo/3983 What is pattern? Baake, Michael; Grimm, Uwe; Moody, Robert V. 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. Tue, 25 Oct 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3983 2022-10-25T00:00:00Z Baake, Michael Grimm, Uwe Moody, Robert V. 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. http://publications.mfo.de/handle/mfo/3985 Biological shape analysis with geometric statistics and learning Utpala, Saiteja; Miolane, Nina 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 the key to unlocking outstanding mysteries in biomedicine. This snapshot introduces the mathematical framework of geometric statistics and learning and its applications to biomedicine. Tue, 25 Oct 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3985 2022-10-25T00:00:00Z Utpala, Saiteja Miolane, Nina 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 the key to unlocking outstanding mysteries in biomedicine. This snapshot introduces the mathematical framework of geometric statistics and learning and its applications to biomedicine. http://publications.mfo.de/handle/mfo/3984 Representations and degenerations Dumanski, Ilya; Kiritchenko, Valentina 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. Tue, 25 Oct 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3984 2022-10-25T00:00:00Z Dumanski, Ilya Kiritchenko, Valentina 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. http://publications.mfo.de/handle/mfo/3972 Solving inverse problems with Bayes' theorem Latz, Jonas; Sprungk, Björn 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 the Bayesian approach. In this approach, the unknown parameter is modelled as a random variable to reflect its uncertain value. Bayes’ theorem is applied to update our knowledge given new information from noisy data. Mon, 05 Sep 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3972 2022-09-05T00:00:00Z Latz, Jonas Sprungk, Björn 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 the Bayesian approach. In this approach, the unknown parameter is modelled as a random variable to reflect its uncertain value. Bayes’ theorem is applied to update our knowledge given new information from noisy data. http://publications.mfo.de/handle/mfo/3952 Jewellery from tessellations of hyperbolic space Gangl, Herbert 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 hyperbolic space. Many of the building blocks of these tessellations exhibit beautiful symmetry and have inspired the design of 3D printed jewellery. Thu, 02 Jun 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/3952 2022-06-02T00:00:00Z Gangl, Herbert 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 hyperbolic space. Many of the building blocks of these tessellations exhibit beautiful symmetry and have inspired the design of 3D printed jewellery.