2 - Snapshots of modern mathematics from Oberwolfach
http://publications.mfo.de/handle/mfo/20
The snapshot project is designed to promote the understanding and appreciation of modern mathematics and mathematical research in the general public world-wide. It is part of the project "Oberwolfach meets IMAGINARY“, supported by the Klaus Tschira Foundation.Wed, 30 Nov 2022 14:25:04 GMT2022-11-30T14:25:04ZA tale of three curves
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 GMThttp://publications.mfo.de/handle/mfo/39862022-10-27T00:00:00ZBalakrishnan, 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.What is pattern?
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 GMThttp://publications.mfo.de/handle/mfo/39832022-10-25T00:00:00ZBaake, MichaelGrimm, UweMoody, 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.Biological shape analysis with geometric statistics and learning
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 GMThttp://publications.mfo.de/handle/mfo/39852022-10-25T00:00:00ZUtpala, SaitejaMiolane, NinaThe 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.Representations and degenerations
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 GMThttp://publications.mfo.de/handle/mfo/39842022-10-25T00:00:00ZDumanski, IlyaKiritchenko, ValentinaIn 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.Solving inverse problems with Bayes' theorem
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 GMThttp://publications.mfo.de/handle/mfo/39722022-09-05T00:00:00ZLatz, JonasSprungk, BjörnThe 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.Jewellery from tessellations of hyperbolic space
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 GMThttp://publications.mfo.de/handle/mfo/39522022-06-02T00:00:00ZGangl, HerbertIn 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.Seeing through rock with help from optimal transport
http://publications.mfo.de/handle/mfo/3941
Seeing through rock with help from optimal transport
Frederick, Christina; Yang, Yunan
Geophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the mathematics of wave propagation, but we will see that a different mathematical theory – optimal transport – also turns out to be very useful.
Fri, 06 May 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39412022-05-06T00:00:00ZFrederick, ChristinaYang, YunanGeophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the mathematics of wave propagation, but we will see that a different mathematical theory – optimal transport – also turns out to be very useful.The Robinson–Schensted algorithm
http://publications.mfo.de/handle/mfo/3940
The Robinson–Schensted algorithm
Thomas, Hugh
I am going to describe the Robinson–Schensted algorithm which transforms a permutation of the numbers from 1 to n into a pair of combinatorial objects called “standard Young tableaux”. I will then say a little bit about a few of the fascinating properties of this transformation, and how it connects to current research.
Fri, 06 May 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39402022-05-06T00:00:00ZThomas, HughI am going to describe the Robinson–Schensted algorithm which transforms a permutation of the numbers from 1 to n into a pair of combinatorial objects called “standard Young tableaux”. I will then say a little bit about a few of the fascinating properties of this transformation, and how it connects to current research.Searching for the monster in the trees
http://publications.mfo.de/handle/mfo/3935
Searching for the monster in the trees
Craven, David A.
The Monster finite simple group is almost unimaginably large, with about 8 × 1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite groups, representations, and finally Brauer trees, which offer some new understanding of this vast and intricate structure.
Wed, 13 Apr 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39352022-04-13T00:00:00ZCraven, David A.The Monster finite simple group is almost unimaginably large, with about 8 × 1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite groups, representations, and finally Brauer trees, which offer some new understanding of this vast and intricate structure.Emergence in biology and social sciences
http://publications.mfo.de/handle/mfo/3931
Emergence in biology and social sciences
Hoffmann, Franca; Merino-Aceituno, Sara
Mathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf venation, opinion dynamics, and network formation, to name a few. In this article, we explore how mathematics is able to traverse scales, and in particular its application in modelling collective motion of bacteria driven by chemical signalling.
Thu, 31 Mar 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39312022-03-31T00:00:00ZHoffmann, FrancaMerino-Aceituno, SaraMathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf venation, opinion dynamics, and network formation, to name a few. In this article, we explore how mathematics is able to traverse scales, and in particular its application in modelling collective motion of bacteria driven by chemical signalling.