Browsing 2  Snapshots of modern mathematics from Oberwolfach by Author "Bruschi, David Edward"
Now showing items 116 of 16

Algebra, matrices, and computers
[SNAP2019005EN] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 20190503)What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that ... 
The codimension
[SNAP2018009EN] Lerario, Antonio (Mathematisches Forschungsinstitut Oberwolfach, 20180619)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. 
Computational Optimal Transport
[SNAP2017008EN] Solomon, Justin (Mathematisches Forschungsinstitut Oberwolfach, 20171221)Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; ... 
Configuration spaces and braid groups
[SNAP2019011EN] Jiménez Rolland, Rita; Xicoténcatl, Miguel A. (Mathematisches Forschungsinstitut Oberwolfach, 20191008)In this snapshot we introduce configuration spaces and explain how a mathematician studies their ‘shape’. This will lead us to consider paths of configurations and braid groups, and to explore how algebraic properties of ... 
Fast Solvers for Highly Oscillatory Problems
[SNAP2018006EN] Barnett, Alex (Mathematisches Forschungsinstitut Oberwolfach, 20180626)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 ... 
From Betti numbers to ℓ²Betti numbers
[SNAP2020001EN] Kammeyer, Holger; Sauer, Roman (Mathematisches Forschungsinstitut Oberwolfach, 20200415)We provide a leisurely introduction to ℓ²Betti numbers, which are topological invariants, by relating them to their much older cousins, Betti numbers. In the end we present an open research problem about ℓ²Betti numbers. 
The Interaction of Curvature and Topology
[SNAP2019020EN] Kordaß, JanBernhard (Mathematisches Forschungsinstitut Oberwolfach, 20191218)In this snapshot we will outline the mathematical notion of curvature by means of comparison geometry. We will then try to address questions as the ways in which curvature might influence the topology of a space, and ... 
The Mathematics of Fluids and Solids
[SNAP2019019EN] Kaltenbacher, Barbara; Kukavica, Igor; Lasiecka, Irena; Triggiani, Roberto; Tuffaha, Amjad; Webster, Justin (Mathematisches Forschungsinstitut Oberwolfach, 20191218)Fluidstructure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ... 
Molecular Quantum Dynamics
[SNAP2017006EN] Hagedorn, George A.; Lasser, Caroline (Mathematisches Forschungsinstitut Oberwolfach, 20171024)We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current ... 
News on quadratic polynomials
[SNAP2017002EN] Pottmeyer, Lukas (Mathematisches Forschungsinstitut Oberwolfach, 20170718)Many problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning ... 
Nonlinear Acoustics
[SNAP2019008EN] Kaltenbacher, Barbara; Brunnhuber, Rainer (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Nonlinear acoustics has been a topic of research for more than 250 years. Driven by a wide range and a large number of highly relevant industrial and medical applications, this area has expanded enormously in the last ... 
Number theory in quantum computing
[SNAP2018012EN] Schönnenbeck, Sebastian (Mathematisches Forschungsinstitut Oberwolfach, 20180807)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 ... 
Prony’s method: an old trick for new problems
[SNAP2018004EN] Sauer, Tomas (Mathematisches Forschungsinstitut Oberwolfach, 20180306)In 1795, French mathematician Gaspard de Prony invented an ingenious trick to solve a recovery problem, aiming at reconstructing functions from their values at given points, which arose from a specific application in ... 
Rotating needles, vibrating strings, and Fourier summation
[SNAP2020006EN] Zahl, Joshua (Mathematisches Forschungsinstitut Oberwolfach, 20200921)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. 
Searching for structure in complex data: a modern statistical quest
[SNAP2021003EN] Loh, PoLing (Mathematisches Forschungsinstitut Oberwolfach, 20210329)Current research in statistics has taken interesting new directions, as data collected from scientific studies has become increasingly complex. At first glance, the number of experiments conducted by a scientist must ... 
A short story on optimal transport and its many applications
[SNAP2018013EN] Santambrogio, Filippo (Mathematisches Forschungsinstitut Oberwolfach, 20180808)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 ...