Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Author "Munday, Sara"
Now showing items 120 of 37

Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
[SNAP2019012EN] Petitgirard, Loïc (Mathematisches Forschungsinstitut Oberwolfach, 20191121)Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers ... 
Biological shape analysis with geometric statistics and learning
[SNAP2022008EN] Utpala, Saiteja; Miolane, Nina (Mathematisches Forschungsinstitut Oberwolfach, 20221025)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 ... 
$C^*$algebras: structure and classification
[SNAP2021002EN] Kerr, David (Mathematisches Forschungsinstitut Oberwolfach, 20210223)The theory of $C^*$algebras traces its origins back to the development of quantum mechanics and it has evolved into a large and highly active field of mathematics. Much of the progress over the last couple of decades ... 
Characterizations of intrinsic volumes on convex bodies and convex functions
[SNAP2022011ENSNAP2022011DE] Mussnig, Fabian (Mathematisches Forschungsinstitut Oberwolfach, 20221208)If we want to express the size of a twodimensional 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 ... 
Closed geodesics on surfaces
[SNAP2022013EN] Dozier, Benjamin (Mathematisches Forschungsinstitut Oberwolfach, 20221208)We consider surfaces of three types: the sphere, the torus, and manyholed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line ... 
Computing with symmetries
[SNAP2018003EN] RoneyDougal, Colva M. (Mathematisches Forschungsinstitut Oberwolfach, 20180306)Group theory is the study of symmetry, and has many applications both within and outside mathematics. In this snapshot, we give a brief introduction to symmetries, and how to compute with them. 
Configuration spaces and braid groups
[SNAP2019011EN] Jiménez Rolland, Rita; Xicoténcatl, Miguel A. (Mathematisches Forschungsinstitut Oberwolfach, 20191008)In this snapshot we introduce configuration spaces and explain how a mathematician studies their ‘shape’. This will lead us to consider paths of configurations and braid groups, and to explore how algebraic properties of ... 
Data assimilation: mathematics for merging models and data
[SNAP2018011EN] Morzfeld, Matthias; Reich, Sebastian (Mathematisches Forschungsinstitut Oberwolfach, 20180710)When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a selfdriving car, you typically have two sources of information. The first is a mathematical model, and the ... 
Deep Learning and Inverse Problems
[SNAP2019015EN] Arridge, Simon; de Hoop, Maarten; Maass, Peter; Öktem, Ozan; Schönlieb, Carola; Unser, Michael (Mathematisches Forschungsinstitut Oberwolfach, 20191121)Big data and deep learning are modern buzz words which presently infiltrate all fields of science and technology. These new concepts are impressive in terms of the stunning results they achieve for a large variety of ... 
Describing distance: from the plane to spectral triples
[SNAP2021009EN] Arici, Francesca; Mesland, Bram (Mathematisches Forschungsinstitut Oberwolfach, 20211231)Geometry draws its power from the abstract structures that govern the shapes found in the real world. These abstractions often provide deeper insights into the underlying mathematical objects. In this snapshot, we give a ... 
Emergence in biology and social sciences
[SNAP2022001EN] Hoffmann, Franca; MerinoAceituno, Sara (Mathematisches Forschungsinstitut Oberwolfach, 20220331)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 ... 
The Enigma behind the Good–Turing formula
[SNAP2021008EN] Balabdaoui, Fadoua; Kulagina, Yulia (Mathematisches Forschungsinstitut Oberwolfach, 20210716)Finding the total number of species in a population based on a finite sample is a difficult but practically important problem. In this snapshot, we will attempt to shed light on how during World War II, two cryptanalysts, ... 
Expander graphs and where to find them
[SNAP2019016EN] Khukhro, Ana (Mathematisches Forschungsinstitut Oberwolfach, 20191122)Graphs are mathematical objects composed of a collection of “dots” called vertices, some of which are joined by lines called edges. Graphs are ideal for visually representing relations between things, and mathematical ... 
A few shades of interpolation
[SNAP2017007EN] Szpond, Justyna (Mathematisches Forschungsinstitut Oberwolfach, 20171207)The topic of this snapshot is interpolation. In the ordinary sense, interpolation means to insert something of a different nature into something else. In mathematics, interpolation means constructing new data points ... 
Formation Control and Rigidity Theory
[SNAP2019017EN] Zelazo, Daniel; Zhao, Shiyu (Mathematisches Forschungsinstitut Oberwolfach, 20191211)Formation control is one of the fundamental coordination tasks for teams of autonomous vehicles. Autonomous formations are used in applications ranging from searchandrescue operations to deep space exploration, with ... 
From the dollar game to the RiemannRoch Theorem
[SNAP2021001EN] Lamboglia, Sara; Ulirsch, Martin (Mathematisches Forschungsinstitut Oberwolfach, 20210223)What is the dollar game? What can you do to win it? Can you always win it? In this snapshot you will find answers to these questions as well as several of the mathematical surprises that lurk in the background, including ... 
The Interaction of Curvature and Topology
[SNAP2019020EN] Kordaß, JanBernhard (Mathematisches Forschungsinstitut Oberwolfach, 20191218)In this snapshot we will outline the mathematical notion of curvature by means of comparison geometry. We will then try to address questions as the ways in which curvature might influence the topology of a space, and ... 
Is it possible to predict the far future before the near future is known accurately?
[SNAP2019021EN] Gander, Martin J. (Mathematisches Forschungsinstitut Oberwolfach, 20191218)It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict ... 
Jewellery from tessellations of hyperbolic space
[SNAP2022005EN] Gangl, Herbert (Mathematisches Forschungsinstitut Oberwolfach, 20220602)In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a numbertheoretic origin give rise to a large variety of interesting tessellations of 3dimensional ... 
Lagrangian mean curvature flow
[SNAP2021011EN] Lotay, Jason D. (Mathematisches Forschungsinstitut Oberwolfach, 20210916)Lagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics. I will describe some of the key aspects of Lagrangian mean curvature ...