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End date: 2024 × Start date: 2020 × Type: report × Version: publishedVersion × Subject: Discrete Mathematics and Foundations ×

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Now showing 1 - 5 of 5
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    Invitation to quiver representation and Catalan combinatorics
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2021) Rognerud, Baptiste
    Representation theory is an area of mathematics that deals with abstract algebraic structures and has numerous applications across disciplines. In this snapshot, we will talk about the representation theory of a class of objects called quivers and relate them to the fantastic combinatorics of the Catalan numbers.
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    The Robinson–Schensted algorithm
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Thomas, Hugh
    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 few of the fascinating properties of this transformation, and how it connects to current research.
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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.
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    Ultrafilter methods in combinatorics
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2021) Goldbring, Isaac
    Given a set X, ultrafilters determine which subsets of X should be considered as large. We illustrate the use of ultrafilter methods in combinatorics by discussing two cornerstone results in Ramsey theory, namely Ramsey’s theorem itself and Hindman’s theorem. We then present a recent result in combinatorial number theory that verifies a conjecture of Erdos known as the “B + C conjecture”.