• Patterns and Waves in Theory, Experiment, and Application 

      [SNAP-2023-001-EN] Bramburger, Jason J. (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 Periodic Tables of Algebraic Geometry 

      [SNAP-2023-002-EN] Belmans, Pieter (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 ...
    • Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften 

      [SNAP-2023-003-DE] Saberi, Ingmar (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 ...
    • Algebras and Quantum Games 

      [SNAP-2023-004-EN] Paulsen, Vern I. (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!
    • Cutoff Phenomenon: Surprising Behaviour in Card Shuffling and other Markov Chains 

      [SNAP-2023-005-EN] Baraquin, Isabelle; Lafrenière, Nadia; Schuh, Katharina (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 ...
    • Geproci Sets: a New Perspective in Algebraic Geometry 

      [SNAP-2023-008-EN] Chiantini, Luca; Harbourne, Brian (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 ...
    • The Geometry of Fair Division 

      [SNAP-2023-007-EN] Frick, Florian (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 ...
    • 4 = 2 × 2, or the Power of Even Integers in Fourier Analysis 

      [SNAP-2023-006-EN] Negro, Giuseppe; Oliveira e Silva, Diogo (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 ...