Now showing items 1-20 of 36

• #### Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964) ﻿

[SNAP-2019-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
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 ...
• #### Aperiodic Order and Spectral Properties ﻿

[SNAP-2017-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-09-14)
Periodic structures like a typical tiled kitchen floor or the arrangement of carbon atoms in a diamond crystal certainly possess a high degree of order. But what is order without periodicity? In this snapshot, we are ...
• #### $C^*$-algebras: structure and classification ﻿

[SNAP-2021-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021-02-23)
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 ﻿

[SNAP-2022-011-ENSNAP-2022-011-DE] (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 ...
• #### Curriculum development in university mathematics: where mathematicians and education collide ﻿

[SNAP-2015-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can ...
• #### Darcy's law and groundwater flow modelling ﻿

[SNAP-2015-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, ...
• #### Deep Learning and Inverse Problems ﻿

[SNAP-2019-015-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
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 ...
• #### Determinacy versus indeterminacy ﻿

[SNAP-2020-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-22)
Can a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes ...
• #### Dirichlet Series ﻿

[SNAP-2014-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them.
• #### Emergence in biology and social sciences ﻿

[SNAP-2022-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-31)
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 ...
• #### Expander graphs and where to find them ﻿

[SNAP-2019-016-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-22)
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 ...
• #### Geometry behind one of the Painlevé III differential equations ﻿

[SNAP-2018-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-20)
The Painlevé equations are second order differential equations, which were first studied more than 100 years ago. Nowadays they arise in many areas in mathematics and mathematical physics. This snapshot discusses the ...
• #### The Kadison-Singer problem ﻿

[SNAP-2014-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
In quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to ...
• #### Limits of graph sequences ﻿

[SNAP-2019-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
Graphs are simple mathematical structures used to model a wide variety of real-life objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent ...
• #### The mathematics of aquatic locomotion ﻿

[SNAP-2018-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)
Aquatic locomotion is a self-propelled motion through a liquid medium. It can be of biological nature (fish, microorganisms,. . .) or performed by robotic swimmers. This snapshot aims to introduce the reader to some ...
• #### The Mathematics of Fluids and Solids ﻿

[SNAP-2019-019-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ...
• #### Mathematische Modellierung von Krebswachstum ﻿

[SNAP-2017-004-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-17)
Krebs ist eine der größten Herausforderungen der modernen Medizin. Der WHO zufolge starben 2012 weltweit 8,2 Millionen Menschen an Krebs. Bis heute sind dessen molekulare Mechanismen nur in Teilen verstanden, was eine ...
• #### Minimizing energy ﻿

[SNAP-2015-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area bounded by a simple closed planar curve of fixed length? We consider the answer ...
• #### Mixed volumes and mixed integrals ﻿

[SNAP-2018-014-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-29)
In recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from ...
• #### Molecular Quantum Dynamics ﻿

[SNAP-2017-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-24)
We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current ...