Now showing items 1-12 of 12

• #### The Algebraic Statistics of an Oberwolfach Workshop ﻿

[SNAP-2018-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-27)
Algebraic Statistics builds on the idea that statistical models can be understood via polynomials. Many statistical models are parameterized by polynomials in the model parameters; others are described implicitly by ...
• #### Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964) ﻿

[SNAP-2019-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers ...
• #### Closed geodesics on surfaces and Riemannian manifolds ﻿

[SNAP-2017-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-07)
Geodesics are special paths in surfaces and so-called Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk ...
• #### Diophantine equations and why they are hard ﻿

[SNAP-2019-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-24)
Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. ...
• #### Finite geometries: pure mathematics close to applications ﻿

[SNAP-2021-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021-09-22)
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 ...
• #### Geometry behind one of the Painlevé III differential equations ﻿

[SNAP-2018-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-20)
The Painlevé equations are second order differential equations, which were first studied more than 100 years ago. Nowadays they arise in many areas in mathematics and mathematical physics. This snapshot discusses the ...
• #### 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'', ...
• #### 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 $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields have the same properties in relation ...
• #### Spaces of Riemannian metrics ﻿

[SNAP-2017-010-ENSNAP-2017-010-ES] (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 ...
• #### 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 ...
• #### Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives ﻿

[SNAP-2019-013-EN] (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 ...
• #### Winkeltreue zahlt sich aus ﻿

[SNAP-2017-001-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2017-08-23)
Nicht nur Seefahrerinnen, auch Computergrafikerinnen und Physikerinnen wissen Winkeltreue zu schätzen. Doch beschränkte Rechenkapazitäten und Vereinfachungen in theoretischen Modellen erfordern es, winkeltreue Abbildungen ...