Oberwolfach Snapshots
https://www.mfo.de
daily12014-10-20T21:02:49ZArrangement of lines
https://www.mfo.de/math-in-public/snapshots/files/arrangement-of-lines
We discuss certain open problems in the context of
arrangements of lines in the plane.No publisherBrian Harbourne2015-04-28T13:38:19ZFileDirichlet Series
https://www.mfo.de/math-in-public/snapshots/files/dirichlet-series
Mathematicians are very interested in prime numbers.
In this snapshot, we will discuss some problems con-
cerning the distribution of primes and introduce some
special infinite series in order to study them.
No publisherJohn E. McCarthy2015-04-28T13:28:02ZFileThe ternary Goldbach problem
https://www.mfo.de/math-in-public/snapshots/files/the-ternary-goldbach-problem
In this snapshot, we will describe to what extent the
mathematical community has resolved Goldbach’s conjecture,
with some emphasis on recent progress.No publisherHarald Helfgott2015-04-28T13:36:46ZFileWhat does ">" really mean?
https://www.mfo.de/math-in-public/snapshots/files/what-does-really-mean
This Snapshot is about the generalization of ">"
from ordinary numbers to so-called fields. At the
end, I will touch on some ideas in recent research.No publisherBruce Reznick2015-04-29T10:29:06ZFileMatrixfaktorisierungen
https://www.mfo.de/math-in-public/snapshots/files/matrixfaktorisierungen
Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen
gegeben werden. Wir werden darlegen,
warum dieses recht simple Konzept zu erstaunlich
tiefen mathematischen Gedankengängen führt und
auch in der modernen theoretischen Physik wichtige
Anwendungen hat.No publisherWolfgang Lerche2015-04-28T13:35:27ZFileDrugs, herbicides, and numerical simulation
https://www.mfo.de/math-in-public/snapshots/files/drugs-herbicides-and-numerical-simulation
The Colombian government sprays coca fields with
herbicides in an effort to reduce drug production.
Spray drifts at the Ecuador-Colombia border became
an international issue. We developed a mathematical
model for the herbicide aerial spray drift, enabling
simulations of the phenomenon.
No publisherPeter Benner2015-04-28T13:42:44ZFileOperator theory and the singular value decomposition
https://www.mfo.de/math-in-public/snapshots/files/operator-theory-and-the-singular-value-decomposition
This is a snapshot about operator theory and one
of its fundamental tools: the singular value decomposition
(SVD). The SVD breaks up linear transformations
into simpler mappings, thus unveiling their
geometric properties. This tool has become important
in many areas of applied mathematics for its
ability to organize information. We discuss the SVD
in the concrete situation of linear transformations of
the plane (such as rotations, reflections, etc.).No publisherGreg Knese2015-04-28T13:41:43ZFileThe Kadison-Singer Problem
https://www.mfo.de/math-in-public/snapshots/files/the-kadison-singer-problem
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 determine the basic probabilities associated
with a given system. In this snapshot we will present
a recent uniqueness result concerning these probabilities.No publisherAlain Valette2015-04-28T13:41:02ZFileSwallowtail on the shore
https://www.mfo.de/math-in-public/snapshots/files/swallowtail-on-the-shore
Platonic solids, Felix Klein, H.S.M. Coxeter and a
flap of a swallowtail: The five Platonic solids tetrahedron,
cube, octahedron, icosahedron and dodecahedron
have always attracted much curiosity from
mathematicians, not only for their sheer beauty but
also because of their many symmetry properties. In
this snapshot we will start from these symmetries,
move on to groups, singularities, and finally find the
connection between a tetrahedron and a “swallowtail”.
Our running example is the tetrahedron, but
every construction can be carried out with any other
of the Platonic solids.No publisherRagnar-Olaf Buchweitz2015-04-28T13:40:09ZFileStatistics and dynamical phenomena
https://www.mfo.de/math-in-public/snapshots/files/dynamicalstatistics.pdf
In this snapshot, I will give you an insight into Sta-
tistics, the field that fascinated my friend (and my-
self) so much. I will concentrate on phenomena that
change over time, in other words, dynamical events.No publisherHowell Tong2015-04-28T13:39:14ZFileBilliards and flat surfaces
https://www.mfo.de/math-in-public/snapshots/files/billiards-and-flat-surfaces
Billiards, the study of a ball bouncing around on a
table, is a rich area of current mathematical research.
We discuss questions and results on billiards, and on
the related topic of flat surfaces.No publisherDiana Davis2015-04-28T13:44:23ZFileMinimizing energy
https://www.mfo.de/math-in-public/snapshots/files/minimizing-energy
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 to this question and others like it, making note of recent results in the same spirit.No publisherChristine Breiner2015-04-28T13:45:46ZFileZero-dimensional symmetry
https://www.mfo.de/math-in-public/snapshots/files/zero-dimensional-symmetry
This snapshot is about zero-dimensional symmetry. Thanks to recent discoveries we now understand such
symmetry better than previously imagined possible. While still far from complete, a picture of zero-dimensional symmetry is beginning to emerge.No publisherGeorge Willis2015-04-28T13:46:43ZFileFriezes and tilings
https://www.mfo.de/math-in-public/snapshots/files/friezes-and-tilings
Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such friezes have appeared in current research. We are going to describe them and explain how they can be classified using some nice geometric pictures.No publisherThorsten Holm2015-04-28T13:47:25ZFileChaos and chaotic fluid mixing
https://www.mfo.de/math-in-public/snapshots/files/chaos-and-chaotic-fluid-mixing
Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small deviations in the initial conditions. We illustrate this with a single recurrence equation that can be easily simulated, and with mixing in simple fluid flows.No publisherTom Solomon2015-04-28T13:49:12ZFileModeling communication and movement: from cells to animals and humans
https://www.mfo.de/math-in-public/snapshots/files/modeling-communication-and-movement-from-cells-to-animals-and-humans
Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species communicate via multiple mechanisms. Here, I review some mathematical results on the unexpected behaviors that can be observed in biological aggregations where individuals interact with each other via multiple communication mechanisms.No publisherRaluca Eftimie2015-05-07T09:31:02ZFileDarcy's law and groundwater flow modelling
https://www.mfo.de/math-in-public/snapshots/files/darcys-law-and-groundwater-flow-modelling
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, the French hydraulic engineer Henry Darcy performed experiments, measuring water flow through a column of sand. He discovered and described a fundamental law: the linear relation between pressure difference and flow rate – known today as Darcy’s law. We describe the law and the evolution of its modern formulation. We furthermore sketch some current mathematical research related to Darcy’s law.No publisherBen Schweizer2015-07-06T07:13:41ZFileIdeas of Newton-Okounkov bodies
https://www.mfo.de/math-in-public/snapshots/files/ideas-of-newton-okounkov-bodies
In this snapshot, we will consider the problem of finding the number of solutions to a given system of polynomial equations. This question leads to the theory of Newton polytopes and Newton-Okounkov bodies of which we will give a basic notion.No publisherValentina KiritchenkoCreative Commons Attribution-ShareAlike 4.0 International2015-07-15T06:37:14ZFileHow to choose a winner: the mathematics of social choice
https://www.mfo.de/math-in-public/snapshots/files/how-to-choose-a-winner-the-mathematics-of-social-choice
Suppose a group of individuals wish to choose among several options, for example electing one of several candidates to a political office or choosing the best contestant in a skating competition. The group might ask: what is the best method for choosing a winner, in the sense that it best reflects the individual preferences of the group members? We will see some examples showing that many voting methods in use around the world can lead to paradoxes and bad outcomes, and we will look at a mathematical model of group decision making. We will discuss Arrow's impossibility theorem, which says that if there are more than two choices, there is, in a very precise sense, no good method for choosing a winner.No publisherVictoria PowersCC-BY-SA 4.02015-08-31T11:49:02ZFileBillard und ebene Flächen
https://www.mfo.de/math-in-public/snapshots/files/billard-und-ebene-flachen
[Übersetzung aus dem Englischen von Feliks Nüske, überarbeitet von der
Redaktion der „Mitteilungen der DMV“]
Billard, die Zick-Zack-Bewegungen eines Balls auf einem Tisch, ist ein reichhaltiges Feld gegenwärtiger mathematischer Forschung. In diesem Artikel diskutieren wir Fragen und Antworten zum Thema Billard, und zu dem damit verwandten Thema ebener Flächen.No publisherDiana DavisCC-BY-NC-SA 3.02015-09-01T07:56:51ZFileSpecial values of zeta functions and areas of triangles
https://www.mfo.de/math-in-public/snapshots/files/special-values-of-zeta-functions-and-areas-of-triangles
In this snapshot we give a glimpse of the interplay of special values of zeta functions and volumes of triangles. Special values of zeta functions and their generalizations arise in the computation of volumes of moduli spaces (for example of Abelian varieties) and their universal spaces. As a first example, we compute the special value of the Riemann zeta function at s=2 and give its interpretation as the volume of the moduli space of elliptic curves. As a second example, we calculate a special value of the Mordell–Tornheim zeta function using the Stern–Brocot tree. This example allows a geometric interpretation related to current research.No publisherJürg Kramer, Anna-Maria von PippichCC-BY-SA 4.02015-09-02T07:14:14ZFileCurriculum development in university mathematics: where mathematicians and education collide
https://www.mfo.de/math-in-public/snapshots/files/curriculum-development-in-university-mathematics-where-mathematicians-and-education-collide
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 significant choices really be made? Do these choices have an effect on how people learn, and, if so, can we understand what they are?No publisherChristopher J. SangwinCC-BY-SA 4.02015-09-04T06:59:24ZFileVisual Analysis of Spanish Male Mortality
https://www.mfo.de/math-in-public/snapshots/files/visual-analysis-of-spanish-male-mortality
Statistical visualization uses graphical methods to gain insights from data. Here we show how a technique called principal component analysis is used to analyze mortality in Spain over about the last hundred years. This data decomposition both reflects expected historical events and reveals some perhaps less expected trends in mortality over the years.No publisherJ.S. MarronCC-BY-SA 4.02015-09-15T06:32:36ZFileModelling the spread of brain tumours
https://www.mfo.de/math-in-public/snapshots/files/modelling-the-spread-of-brain-tumours
The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment outcomes.No publisherAmanda Swan, Albert MurthaCC-BY-SA 4.02015-09-23T08:53:46ZFileQuantum diffusion
https://www.mfo.de/math-in-public/snapshots/files/quantum-diffusion
If you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see something that is never observed in the real world. Such diffusive and irreversible behaviour is ubiquitous in nature. Nevertheless, the fundamental equations that describe the motion of individual particles – Newton's and Schrödinger's equations – are reversible in time: a film depicting the motion of just a few particles looks as realistic when played forwards as when played backwards. In this snapshot, we discuss how one may try to understand the origin of diffusion starting from the fundamental laws of quantum mechanics.No publisherAntti KnowlesCC-BY-SA 4.02015-11-18T07:46:21ZFileThe mystery of sleeping sickness – why does it keep waking up?
https://www.mfo.de/math-in-public/snapshots/files/the-mystery-of-sleeping-sickness-2013-why-does-it-keep-waking-up
Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated.No publisherSebastian FunkCC-BY-NC-SA 4.02015-11-25T08:49:24ZFileDomino tilings of the Aztec Diamond
https://www.mfo.de/math-in-public/snapshots/files/domino-tilings-of-the-aztec-diamond
Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes? One specific paper cutout can be mathematically described as the so-called Aztec Diamond, and a way to cover it with dominoes is a domino tiling. In this snapshot we revisit some of the seminal combinatorial ideas used to enumerate the number of domino tilings of the Aztec Diamond. The existing connection with the study of the so-called alternating-sign matrices is also explored.No publisherJuanjo RuéCC-BY-SA 4.02015-11-25T10:27:34ZFileFrom computer algorithms to quantum field theory: an introduction to operads
https://www.mfo.de/math-in-public/snapshots/files/from-computer-algorithms-to-quantum-field-theory-an-introduction-to-operads
An operad is an abstract mathematical tool encoding operations on specific mathematical structures. It finds applications in many areas of mathematics and related fields. This snapshot explains the concept of an operad and of an algebra over an operad, with a view towards a conjecture formulated by the mathematician Pierre Deligne. Deligne's (by now proven) conjecture also gives deep inights into mathematical physics.No publisherUlrich KrähmerCC-BY-SA 4.02015-11-30T10:37:44ZFileSwarming robots
https://www.mfo.de/math-in-public/snapshots/files/swarming-robots
When lots of robots come together to form shapes, spread in an area, or move in one direction, their motion has to be planned carefully. We discuss how mathematicians devise strategies to help swarms of robots behave like an experienced, coordinated team.No publisherMagnus EgerstedtCC-BY-NC-SA 4.02016-01-20T07:16:25ZFileRandom sampling of domino and lozenge tilings
https://www.mfo.de/math-in-public/snapshots/files/random-sampling-of-domino-and-lozenge-tilings
A grid region is (roughly speaking) a collection of ``elementary cells'' (squares, for example, or triangles) in the plane. One can ``tile'' these grid regions by arranging the cells in pairs. In this snapshot we review different strategies to generate random tilings of large grid regions in the plane. This makes it possible to observe the behaviour of large random tilings, in particular the occurrence of boundary phenomena that have been the subject of intensive recent research.No publisherEric FusyCC-BY-SA 4.02016-01-29T12:05:46ZFileOn the containment problem
https://www.mfo.de/math-in-public/snapshots/files/on-the-containment-problem
Mathematicians routinely speak two languages: the language of geometry and the language of algebra. When translating between these languages, curves and lines become sets of polynomials called "ideals". Often there are several possible translations. Then the mystery is how these possible translations relate to each other. We present how geometry itself gives insights into this question.No publisherTomasz Szemberg and Justyna SzpondCC-BY-SA 4.02016-03-08T14:51:57ZFileDas Problem der Kugelpackung
https://www.mfo.de/math-in-public/snapshots/files/das-problem-der-kugelpackung
Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3-dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen Kommunikation hat, hört sich einfach an, ist jedoch für Kugeln in höheren Dimensionen noch immer ungelöst. Sogar die Berechnung guter Näherungslösungen ist für die meisten Dimensionen schwierig.No publisherMaria Dostert, Stefan Krupp, Jan Hendrik RolfesCC-BY-SA 4.02016-04-11T10:23:15ZFileSymmetry and characters of finite groups
https://www.mfo.de/math-in-public/snapshots/files/symmetry-and-characters-of-finite-groups
Over the last two centuries mathematicians have developed an elegant abstract framework to study the natural idea of symmetry. The aim of this snapshot is to gently guide the interested reader through these ideas. In particular, we introduce finite groups and their representations and try to indicate their central role in understanding symmetry.No publisherEugenio Giannelli, Jay TaylorCC-BY-SA 4.02016-04-18T12:54:41ZFileHigh performance computing on smartphones
https://www.mfo.de/math-in-public/snapshots/files/high-performance-computing-on-smartphones
Nowadays there is a strong demand to simulate even real-world engineering problems on small computing devices with very limited capacity, such as a smartphone. We explain, using a concrete example, how we can obtain a reduction in complexity – to enable such computations – using mathematical methods.No publisherAnthony T. Patera, Karsten UrbanCC-BY-SA 4.02016-04-21T08:34:50ZFileWie steuert man einen Kran?
https://www.mfo.de/math-in-public/snapshots/files/wie-steuert-man-einen-kran
Die Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese Schwierigkeiten und zeigen wie man mit einem zum konventionellen Lösungsweg alternativen Optimierungsansatz die auftretenden Komplikationen teilweise umgehen kann.No publisherRobert Altmann, Jan HeilandCC-BY-SA 4.02016-04-29T10:53:03ZFileFokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse
https://www.mfo.de/math-in-public/snapshots/files/fokus-erkennung-bei-epilepsiepatienten-mithilfe-moderner-verfahren-der-zeitreihenanalyse
Viele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist die Frage nach der Lokalisation des Anfallsursprungs aus EEG-Aufzeichnungen wichtig. Wir beschreiben hier ein Verfahren zur Lokalisation des Anfallsursprungs mittels Zeitreihenanalyse, das auf der Schätzung von Spektren im EEG beruht.No publisherManfred Deistler, Andreas GraefCC-BY-SA 4.02016-05-12T06:17:30ZFilePolyhedra and commensurability
https://www.mfo.de/math-in-public/snapshots/files/polyhedra-and-commensurability
This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it subsequently. Finally, we discuss intriguing connections with other fields of mathematics.No publisherRafael Guglielmetti, Matthieu JacquemetCC-BY-NC-SA 4.02016-05-18T06:24:38ZFilePrime Tuples in Function Fields
https://www.mfo.de/math-in-public/snapshots/files/prime-tuples-in-function-fields
How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and seemingly unsolvable in the forseeable future. In this snapshot, we will discuss one such problem, the Twin Prime Conjecture, and a quantitative version of it known as the Hardy–Littlewood Conjecture. We will also see that these and other questions about prime numbers can be extended to questions about function fields, and discuss recent progress which has been made to answer them in this context.No publisherLior Bary-SorokerCC-BY-NC-SA 4.02016-07-06T14:11:08ZFileEine visuelle Analyse der Sterblichkeit männlicher Spanier
https://www.mfo.de/math-in-public/snapshots/files/eine-visuelle-analyse-der-sterblichkeit-mannlicher-spanier
[Übersetzung aus dem Englischen von Daniel Katona]
Die statistische Visualisierung benutzt graphische Methoden um Erkenntnisse aus Daten zu gewinnen. Wir zeigen wie mit dem Verfahren der Hauptkomponentenanalyse die Sterblichkeit in Spanien im Laufe der letzten hundert Jahre analysiert werden kann. Diese Datenzerlegung zeigt sowohl erwartete geschichtliche Ereignisse auf, als auch einige, teilweise überraschende Entwicklungen der Sterblichkeit im Laufe der Zeit.No publisherJ.S. MarronCC-BY-SA 4.02016-07-07T07:42:05ZFileWie man einen Sieger wählt: die Mathematik der Sozialwahl
https://www.mfo.de/math-in-public/snapshots/files/wie-man-einen-sieger-wahlt-die-mathematik-der-sozialwahl
[Übersetzt aus dem Englischen von Manfred Stern]
Angenommen, eine Gruppe von Einzelpersonen möchte unter verschiedenen Optionen wählen, zum Beispiel einen von mehreren Kandidaten für ein politisches Amt oder den besten Teilnehmer einer Eiskunstlaufmeisterschaft. Man könnte fragen: Was ist die beste Methode, einen Sieger in dem Sinne zu wählen, dass er die individuellen Präferenzen der Gruppenmitglieder am besten widerspiegelt? Wir werden anhand einiger Beispiele sehen, dass viele Wahlverfahren, die weltweit in Gebrauch sind, zu Paradoxa und nachgerade schlechten Ergebnissen führen können, und wir werden uns ein mathematisches Modell von Gruppenentscheidungen ansehen. Wir diskutieren das Unmöglichkeitstheorem von Arrow, das Folgendes besagt: Hat man mehr als zwei Wahlmöglichkeiten, dann gibt es in einem ganz exakten Sinn keine gute Methode für die Wahl eines Siegers. No publisherVictoria PowersCC-BY-SA 4.02016-07-07T07:50:21ZFileDrogen, Herbizide und numerische Simulation
https://www.mfo.de/math-in-public/snapshots/files/drogen-herbizide-und-numerische-simulation
Die kolumbianische Regierung versprüht Unkrautbekämpfungsmittel (Herbizide) über Coca-Feldern, um die Drogenproduktion im Land zu reduzieren. Sprühverwehungen entlang der Grenze Kolumbiens zu Ecuador wurden zu einem internationalen Streitfall. Wir haben ein mathematisches Modell für die Ausbreitung der Chemikalien in der Luft entwickelt, das es uns ermöglicht, das Phänomen am Computer zu simulieren.No publisherPeter Benner, Hermann Mena, René SchneiderCC-BY-NC-SA 3.02016-07-14T09:48:34ZFileThe Willmore Conjecture
https://www.mfo.de/math-in-public/snapshots/files/the-willmore-conjecture
The Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time.No publisherNikolai NowaczykCC-BY-SA 4.02016-09-07T11:40:07ZFileFootballs and donuts in four dimensions
https://www.mfo.de/math-in-public/snapshots/files/footballs-and-donuts-in-four-dimensions
In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world and then discuss the ways one may generalize these ideas into higher dimensions.No publisherSteven KleeCC-BY-SA 4.02016-09-16T09:57:57ZFileThe adaptive finite element method
https://www.mfo.de/math-in-public/snapshots/files/the-adaptive-finite-element-method
Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other hand, a larger number of unknowns can improve the precision of the simulation. The adaptive finite element method (AFEM) is an algorithm for optimizing the choice of parameters so accurate simulation results can be obtained with as little computational effort as possible.No publisherDietmar GallistlCC-BY-SA 4.02016-10-25T06:51:40ZFileProfinite groups
https://www.mfo.de/math-in-public/snapshots/files/profinite-groups
Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, and its implications for finite groups.No publisherLaurent BartholdiCC-BY-SA 4.02016-11-09T08:22:29ZFileTowards a Mathematical Theory of Turbulence in Fluids
https://www.mfo.de/math-in-public/snapshots/files/towards-a-mathematical-theory-of-turbulence-in-fluids
Fluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery to their motion. The random-looking, chaotic behavior of fluids is known as turbulence, and it lies far beyond our mathematical understanding, despite a century of intense research.No publisherJacob BedrossianCC-BY-SA 4.02016-11-22T13:38:14ZFileNews on quadratic polynomials
https://www.mfo.de/math-in-public/snapshots/files/news-on-quadratic-polynomials
Many problems in mathematics have remained unsolved
because of missing links between mathematical
disciplines, such as algebra, geometry, analysis, or
number theory. Here we introduce a recently discovered
result concerning quadratic polynomials, which
uses a bridge between algebra and analysis. We study
the iterations of quadratic polynomials, obtained by
computing the value of a polynomial for a given number
and feeding the outcome into the exact same polynomial
again. These iterations of polynomials have
interesting applications, such as in fractal theory.No publisherLukas PottmeyerCC-BY-SA 4.02017-07-25T13:00:56ZFile