Browsing 2 - Snapshots of Modern Mathematics from Oberwolfach by Author "Munday, Sara"

Now showing items 21-39 of 39

    • 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 ...

    • Lagrangian mean curvature flow 

      [SNAP-2021-011-EN] Lotay, Jason D. (Mathematisches Forschungsinstitut Oberwolfach, 2021-09-16)
      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 ...

    • Limits of graph sequences 

      [SNAP-2019-010-EN] Klimošová, Tereza (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
      Graphs are simple mathematical structures used to model a wide variety of real-life objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent ...

    • The Mathematics of Fluids and Solids 

      [SNAP-2019-019-EN] Kaltenbacher, Barbara; Kukavica, Igor; Lasiecka, Irena; Triggiani, Roberto; Tuffaha, Amjad; Webster, Justin (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
      Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ...

    • Mixed-dimensional models for real-world applications 

      [SNAP-2019-014-EN] Nordbotten, Jan Martin (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
      We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and ...

    • Nonlinear Acoustics 

      [SNAP-2019-008-EN] Kaltenbacher, Barbara; Brunnhuber, Rainer (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
      Nonlinear acoustics has been a topic of research for more than 250 years. Driven by a wide range and a large number of highly relevant industrial and medical applications, this area has expanded enormously in the last ...

    • On Logic, Choices and Games 

      [SNAP-2019-009-EN] Oliva, Paulo (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
      Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ...

    • On radial basis functions 

      [SNAP-2019-002-EN] Buhmann, Martin; Jäger, Janin (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-13)
      Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a ...

    • 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 ...

    • Positive Scalar Curvature and Applications 

      [SNAP-2019-004-EN] Rosenberg, Jonathan; Wraith, David (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-25)
      We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar curvature. We discuss why ...

    • Quantum symmetry 

      [SNAP-2020-009-EN] Caspers, Martijn (Mathematisches Forschungsinstitut Oberwolfach, 2020-12-31)
      The symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized ...

    • Random matrix theory: Dyson Brownian motion 

      [SNAP-2020-002-EN] Finocchio, Gianluca (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
      The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John ...

    • 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 ...

    • Searching for structure in complex data: a modern statistical quest 

      [SNAP-2021-003-EN] Loh, Po-Ling (Mathematisches Forschungsinstitut Oberwolfach, 2021-03-29)
      Current research in statistics has taken interesting new directions, as data collected from scientific studies has become increasingly complex. At first glance, the number of experiments conducted by a scientist must ...

    • Shape space – a paradigm for character animation in computer graphics 

      [SNAP-2020-007-EN] Heeren, Behrend; Rumpf, Martin (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-07)
      Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions ...

    • Snake graphs, perfect matchings and continued fractions 

      [SNAP-2019-001-EN] Schiffler, Ralf (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-13)
      A continued fraction is a way of representing a real number by a sequence of integers. We present a new way to think about these continued fractions using snake graphs, which are sequences of squares in the plane. You ...

    • Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives 

      [SNAP-2019-013-EN] Milici, Pietro (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
      When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century ...

    • Vertex-to-self trajectories on the platonic solids 

      [SNAP-2020-003-EN] Athreya, Jayadev S.; Aulicino, David (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
      We consider the problem of walking in a straight line on the surface of a Platonic solid. While the tetrahedron, octahedron, cube, and icosahedron all exhibit the same behavior, we find a remarkable difference with the ...