18 results
Search Results
Now showing 1 - 10 of 18
- ItemMinimizing energy(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Breiner, ChristineWhat 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.
- ItemGeometry behind one of the Painlevé III differential equations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Hertling, ClausThe 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 solutions of one of the Painlevé equations and presents old results on the asymptotics at two singular points and new results on the global behavior.
- ItemMixed volumes and mixed integrals(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Rotem, LiranIn 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 convex geometry become thereby accessible to analytic and probabilistic tools, and we can use these tools to make progress on very difficult open problems. We discuss in this Snapshot such a functional extension of some “volumes” which measure how “big” a set is. We recall the construction of “intrinsic volumes”, discuss the fundamental inequalities between them, and explain the functional extensions of these results.
- ItemCurriculum development in university mathematics: where mathematicians and education collide(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Sangwin, Christopher J.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?
- ItemThe Kadison-Singer problem(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Valette, AlainIn 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.
- ItemMolecular Quantum Dynamics(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Hagedorn, George A.; Lasser, CarolineWe 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 interest in this exciting subject.
- ItemNews on quadratic polynomials(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Pottmeyer, LukasMany 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.
- ItemAperiodic Order and Spectral Properties(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Baake, Michael; Damanik, David; Grimm, UwePeriodic 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 going to explore highly ordered structures that are substantially nonperiodic, or aperiodic. As we construct such structures, we will discover surprising connections to various branches of mathematics, materials science, and physics. Let us catch a glimpse into the inherent beauty of aperiodic order!
- ItemMathematische Modellierung von Krebswachstum(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Engwer, Christian; Knappitsch, MarkusKrebs 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 erfolgreiche Behandlung erschwert. Mathematische Modellierung und Computersimulationen können helfen, die Mechanismen des Tumorwachstums besser zu verstehen. Sie eröffnen somit neue Chancen für zukünftige Behandlungsmethoden. In diesem Schnappschuss steht die mathematische Modellierung von Glioblastomen im Fokus, einer Klasse sehr agressiver Tumore im menschlichen Gehirn.
- ItemDirichlet Series(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) McCarthy, John E.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.