Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Snapshot Mathematical Subject "Analysis"
Now showing items 120 of 42

4 = 2 × 2, or the Power of Even Integers in Fourier Analysis
[SNAP2023006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20231230)We describe how simple observations related to vectors of length 1 recently led to the proof of an important mathematical fact: the sharp Stein–Tomas inequality from Fourier restriction theory, a pillar of modern harmonic ... 
Algebras and Quantum Games
[SNAP2023004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20231128)Everyone loves a good game, but when the players can access the counterintuitive world of quantum mechanics, watch out! 
Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
[SNAP2019012EN] (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 ... 
Aperiodic Order and Spectral Properties
[SNAP2017003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20170914)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 ... 
Braid groups, the Yang–Baxter equation, and subfactors
[SNAP2021005EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021)The Yang–Baxter equation is a fascinating equation that appears in many areas of physics and mathematics and is best represented diagramatically. This snapshot connects the mathematics of braiding hair to the Yang–Baxter ... 
$C^*$algebras: structure and classification
[SNAP2021002EN] (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
[SNAP2022011EN] (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 ... 
Charakterisierungen von inneren Volumina auf konvexen Körpern und konvexen Funktionen
[SNAP2022011DE] (Mathematisches Forschungsinstitut Oberwolfach, 2023)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 ... 
Curriculum development in university mathematics: where mathematicians and education collide
[SNAP2015011EN] (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
[SNAP2015007EN] (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
[SNAP2019015EN] (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 ... 
Determinacy versus indeterminacy
[SNAP2020004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200422)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
[SNAP2014001EN] (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
[SNAP2022001EN] (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 ... 
Expander graphs and where to find them
[SNAP2019016EN] (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 ... 
Geometry behind one of the Painlevé III differential equations
[SNAP2018010EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180620)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 KadisonSinger problem
[SNAP2014008EN] (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
[SNAP2019010EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Graphs are simple mathematical structures used to model a wide variety of reallife 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
[SNAP2018008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180619)Aquatic locomotion is a selfpropelled 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
[SNAP2019019EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191218)Fluidstructure 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 ...