Now showing items 1-10 of 15
Number theory in quantum computing
[SNAP-2018-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-07)
Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be "translated" to a series of simple steps, each of which the computer knows how to do. This task is ...
Data assimilation: mathematics for merging models and data
[SNAP-2018-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-10)
When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the ...
Topological Complexity, Robotics and Social Choice
[SNAP-2018-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-10)
Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the ...
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 ...
The mathematics of aquatic locomotion
[SNAP-2018-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)
Aquatic locomotion is a self-propelled motion through a liquid medium. It can be of biological nature (fish, microorganisms,. . .) or performed by robotic swimmers. This snapshot aims to introduce the reader to some ...
[SNAP-2018-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)
In this snapshot we discuss the notion of codimension, which is, in a sense, “dual” to the notion of dimension and is useful when studying the relative position of one object insider another one.
A short story on optimal transport and its many applications
[SNAP-2018-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-08)
We present some examples of optimal transport problems and of applications to different sciences (logistics, economics, image processing, and a little bit of evolution equations) through the crazy story of an industrial ...
Mixed volumes and mixed integrals
[SNAP-2018-014-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-29)
In recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from ...
Fast Solvers for Highly Oscillatory Problems
[SNAP-2018-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-26)
Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial for speech, mobile phones, and other communication technologies. Elastic waves propagating through the Earth bounce ...
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 ...