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Start date: 2020 × Type: report × Version: publishedVersion × Subject: Discrete Mathematics and Foundations × Subject: Geometry and Topology ×

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    Finite geometries: pure mathematics close to applications
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2021) Storme, Leo
    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”.
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    From the dollar game to the Riemann-Roch Theorem
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2021) Lamboglia, Sara; Ulirsch, Martin
    What is the dollar game? What can you do to win it? Can you always win it? In this snapshot you will find answers to these questions as well as several of the mathematical surprises that lurk in the background, including a new perspective on a century-old theorem.