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Algebras and Quantum Games
[SNAP-2023-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-28)
Everyone loves a good game, but when the players can access the counterintuitive world of quantum mechanics, watch out!
Geproci Sets: a New Perspective in Algebraic Geometry
[SNAP-2023-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-12-30)
Geproci sets arise from applying the perspective of inverse scattering problems to algebraic geometry. Analogous to the reconstruction of an object from multiple X-ray images, we aim at a classification of sets with certain ...
Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
[SNAP-2023-003-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2023-09-19)
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 ...
The Periodic Tables of Algebraic Geometry
[SNAP-2023-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-09-04)
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 ...
Patterns and Waves in Theory, Experiment, and Application
[SNAP-2023-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-07-04)
In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social ...
The Geometry of Fair Division
[SNAP-2023-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-12-30)
How can we fairly divide a necklace with various types of beads? We use this problem as a motivating example to explain how geometry naturally appears in solutions of non-geometric problems. The strategy we develop to solve ...
Charakterisierungen von inneren Volumina auf konvexen Körpern und konvexen Funktionen
[SNAP-2022-011-DE] (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 ...
4 = 2 × 2, or the Power of Even Integers in Fourier Analysis
[SNAP-2023-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-12-30)
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 ...
Cutoff Phenomenon: Surprising Behaviour in Card Shuffling and other Markov Chains
[SNAP-2023-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-12-21)
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 ...