Browsing by Author "Randecker, Anja"

Now showing items 21-40 of 61

    • 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 ...

    • Finite geometries: pure mathematics close to applications 

      [SNAP-2021-010-EN] Storme, Leo (Mathematisches Forschungsinstitut Oberwolfach, 2021-09-22)
      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 ...

    • The five Platonic solids and their connection to root systems 

      [SNAP-2025-004-EN] Böhm, Sören (Mathematisches Forschungsinstitut Oberwolfach, 2025-09-05)
      Platonic solids have fascinated humans for thousands of years. In ancient times, they were associated with the elements fire, air, water, earth, and aether. These solids are completely symmetrical three-dimensional polyhedra. ...

    • Five ways to spell ADE 

      [SNAP-2025-003-EN] Kaufman, Dani (Mathematisches Forschungsinstitut Oberwolfach, 2025-07-30)
      The solutions to a surprising number of mathematical questions can be classified by the ADE Coxeter–Dynkin diagrams. This snapshot will show you a selection of these questions and how they correspond to the ADE Coxeter–Dynkin ...

    • Fracture mechanics: a nonlocal approach 

      [SNAP-2026-001-EN] Buczkowski, Nicole; Foss, Mikil; Radu, Petronela (Mathematisches Forschungsinstitut Oberwolfach, 2026-02-20)
      Nonlocal models consider interactions over a range of distances, not just at a single point. In this snapshot, we give a short introduction to nonlocal modeling, explain how it differs from its local counterpart, and present ...

    • Game-theoretic statistics 

      [SNAP-2026-009-EN] Shafer, Glenn (Mathematisches Forschungsinstitut Oberwolfach, 2026-09-11)
      Statistical modelling is the art of connecting abstract models with scientific or practical questions, so that the models' probabilities throw light on these questions. Standard statistical theory summarizes the results ...

    • Games in the matrix 

      [SNAP-2026-011-EN] Farah, Ilijas (Mathematisches Forschungsinstitut Oberwolfach, 2026-10-05)
      Do all the possible computations on very large matrices look alike? Nobody knows, but let's play a game and see how far we get!

    • Geometry behind one of the Painlevé III differential equations 

      [SNAP-2018-010-EN] Hertling, Claus (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-20)
      The 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 ...

    • 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 ...

    • 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 ...

    • How big is my slice of cheese? 

      [SNAP-2026-006-EN] Meroni, Chiara (Mathematisches Forschungsinstitut Oberwolfach, 2026-05-19)
      In this snapshot, we introduce the study of slices of polytopes – geometric shapes with flat sides – and examine the area of these slices. This is connected to combinatorics and polynomials and is surprisingly complex, ...

    • Is there a smooth lattice polytope which does not have the integer decomposition property? 

      [SNAP-2025-008-EN] Hofscheier, Johannes; Kasprzyk, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2025-12-16)
      We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the ...

    • Jewellery from tessellations of hyperbolic space 

      [SNAP-2022-005-EN] Gangl, Herbert (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-02)
      In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional ...

    • The Kakeya conjecture 

      [SNAP-2026-008-EN] Hickman, Jonathan (Mathematisches Forschungsinstitut Oberwolfach, 2026-06-19)
      The geometry of lines is a fundamental part of mathematics and the way we interact with the physical world. Core concepts such as distance and angle, and the accompanying theory of trigonometry, have been studied since ...

    • 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 ...

    • Randomness is natural - an introduction to regularisation by noise 

      [SNAP-2024-002-EN] Djurdjevac, Ana; Elad Altman, Henri; Rosati, Tommaso (Mathematisches Forschungsinstitut Oberwolfach, 2024-05-22)
      Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic ...

    • Reflections on hyperbolic space 

      [SNAP-2021-007-EN] Haensch, Anna (Mathematisches Forschungsinstitut Oberwolfach, 2021-08-24)
      In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spaces different from the usual Euclidean space in which this is not true. One of these spaces is the ''hyperbolic space'', ...

    • Representations and degenerations 

      [SNAP-2022-007-EN] Dumanski, Ilya; Kiritchenko, Valentina (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
      In this snapshot, we explain two important mathematical concepts (representation and degeneration) in elementary terms. We will focus on the simplest meaningful examples, and motivate both concepts by study of symmetry.

    • The Robinson–Schensted algorithm 

      [SNAP-2022-002-EN] Thomas, Hugh (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-06)
      I am going to describe the Robinson–Schensted algorithm which transforms a permutation of the numbers from 1 to n into a pair of combinatorial objects called “standard Young tableaux”. I will then say a little bit about a ...