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Now showing items 71-80 of 161
Rotating needles, vibrating strings, and Fourier summation
[SNAP-2020-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-09-21)
We give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis.
Random sampling of domino and lozenge tilings
[SNAP-2016-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different ...
Solving quadratic equations in many variables
[SNAP-2017-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-30)
Fields are number systems in which every linear equation
has a solution, such as the set of all rational
numbers Q or the set of all real numbers R. All fields
have the same properties in relation ...
Dirichlet Series
[SNAP-2014-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them.
Counting self-avoiding walks on the hexagonal lattice
[SNAP-2019-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-06-04)
In how many ways can you go for a walk along a
lattice grid in such a way that you never meet your
own trail? In this snapshot, we describe some combinatorial
and statistical aspects of these so-called
self-avoiding ...
Das Problem der Kugelpackung
[SNAP-2016-004-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3-dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen ...
Topological recursion
[SNAP-2018-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-05)
In this snapshot we present the concept of topological
recursion – a new, surprisingly powerful formalism
at the border of mathematics and physics, which has
been actively developed within the last decade. After
introducing ...
Reflections on hyperbolic space
[SNAP-2021-007-EN] (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'', ...
Route planning for bacteria
[SNAP-2022-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-08)
Bacteria have been fascinating biologists since their discovery in the late 17th century. By analysing their movements, mathematical models have been developed as a tool to understand their behaviour. However, adapting ...
Snake graphs, perfect matchings and continued fractions
[SNAP-2019-001-EN] (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 ...