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Random matrix theory: Dyson Brownian motion
[SNAP-2020-002-EN] (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 ...
Emergence in biology and social sciences
[SNAP-2022-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-31)
Mathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf ...
Higgs bundles without geometry
[SNAP-2020-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-09-29)
Higgs bundles appeared a few decades ago as solutions to certain equations from physics and have attracted much attention in geometry as well as other areas of mathematics and physics. Here, we take a very informal stroll ...
Drugs, herbicides, and numerical simulation
[SNAP-2014-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the ...
The ternary Goldbach problem
[SNAP-2014-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur and polymath who lived and ...
Billard und ebene Flächen
[SNAP-2015-001-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Billard, die Zick-Zack-Bewegungen eines Balls auf einem Tisch, ist ein reichhaltiges Feld gegenwärtiger mathematischer Forschung. In diesem Artikel diskutieren wir Fragen und Antworten zum Thema Billard, und zu dem damit ...
Spaces of Riemannian metrics
[SNAP-2017-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-28)
Riemannian metrics endow smooth manifolds such as
surfaces with intrinsic geometric properties, for example
with curvature. They also allow us to measure
quantities like distances, angles and volumes. These
are the ...
Algebras and Quantum Games
[SNAP-2023-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-28)
Everyone loves a good game, but when the players can access the counterintuitive world of quantum mechanics, watch out!
How to choose a winner: the mathematics of social choice
[SNAP-2015-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Suppose a group of individuals wish to choose among several options, for example electing one of several candidates to a political office or choosing the best contestant in a skating competition. The group might ask: what ...