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Now showing items 101-110 of 161
What is pattern?
[SNAP-2022-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.
Quantum symmetry
[SNAP-2020-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-12-31)
The symmetry of objects plays a crucial role in many
branches of mathematics and physics. It allowed, for
example, the early prediction of the existence of new
small particles. “Quantum symmetry” concerns a
generalized ...
Curriculum development in university mathematics: where mathematicians and education collide
[SNAP-2015-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can ...
Mixed-dimensional models for real-world applications
[SNAP-2019-014-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
We explore mathematical models for physical problems
in which it is necessary to simultaneously consider
equations in different dimensions; these are called
mixed-dimensional models. We first give several examples,
and ...
The Kadison-Singer problem
[SNAP-2014-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
In quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to ...
Formation Control and Rigidity Theory
[SNAP-2019-017-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-11)
Formation control is one of the fundamental coordination
tasks for teams of autonomous vehicles. Autonomous
formations are used in applications ranging
from search-and-rescue operations to deep space
exploration, with ...
From computer algorithms to quantum field theory: an introduction to operads
[SNAP-2015-017-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
An operad is an abstract mathematical tool encoding operations on specific mathematical structures. It finds applications in many areas of mathematics and related fields. This snapshot explains the concept of an operad and ...
Solving inverse problems with Bayes' theorem
[SNAP-2022-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-09-05)
The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as ...
Tropical geometry
[SNAP-2018-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-19)
What kind of strange spaces hide behind the enigmatic
name of tropical geometry? In the tropics, just
as in other geometries, one of the simplest objects is
a line. Therefore, we begin our exploration by considering
tropical ...
Polyhedra and commensurability
[SNAP-2016-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it ...