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Submitted by IMAGINARY on
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 analysis with surprising applications to number theory and geometric measure theory.
Submitted by IMAGINARY on
This snapshot compares two techniques of shuffling a deck of cards, asking how long it will take to shuffle the cards until a “well-mixed deck” is obtained. Surprisingly, the number of shuffles can be very different for very similar looking shuffling techniques.
Submitted by IMAGINARY on
Everyone loves a good game, but when the players can access the counterintuitive world of quantum mechanics, watch out!
“God does not play dice with the universe” – Albert Einstein
“Not only does God play dice but… he sometimes throws them where they cannot be seen.” – Stephen Hawking
Submitted by IMAGINARY on
Wir werden einige grundlegende Ideen der Eichtheorie und der dazugehörigen Differentialtopologie erkunden. Damit kann sich die Leserin ein Bild des Modulraums flacher Zusammenhänge machen und ihn mit den physikalisch motivierten Ideen dahinter in Beziehung bringen. Den Begriffen von Symmetrien und Feldern gehen wir gründlich nach. Außerdem werfen wir einen flüchtigen Blick auf unendliche Symmetrie in zwei Dimensionen und auf vor kurzem entdeckte Verallgemeinerungen.
Submitted by IMAGINARY on
To understand our world, we classify things. A famous example is the periodic table of elements, which describes the properties of all known chemical elements and gives us a classification of the building blocks we can use in physics, chemistry, and biology. In mathematics, and algebraic geometry in particular, there are many instances of similar periodic tables”, describing fundamental classification results. We will go on a tour of some of these.
Submitted by Elisabeth Schaber on
Modern global climate data started in 1880. We can discover the climate of yesterday in many different ways.
Submitted by IMAGINARY on
CO2 is a chemical that can exist as a gas in the atmosphere but also dissolves into water (as in sparkling water), into rocks, or inside living beings. Oceans store about ⅓ of the CO2 on the planet. This is due to a chemical process known as buffering.
Do you hear the climate crying? Data sonification makes changes happening on our planet audible. The numbers are not represented in tables or diagrams but in notes. Songs are created from them!
Submitted by IMAGINARY on
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 flow, some recent progress, and some major open problems.
Submitted by IMAGINARY on
The research field of finite geometries investigates structures with a finite number of objects. Classical examples include vector spaces, projective spaces, and affine spaces over finite fields. Although many of these structures are studied for their geometrical importance, they are also of great interest in other, more applied domains of mathematics. In this snapshot, finite vector spaces are introduced. We discuss the geometrical concept of partial t-spreads together with its implications for the “packing problem” and a recent application in the existence of “cooling codes”.