Browsing by Author "Jahns, Sophia"
Now showing items 2140 of 54

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. 
From the dollar game to the RiemannRoch Theorem
[SNAP2021001EN] Lamboglia, Sara; Ulirsch, Martin (Mathematisches Forschungsinstitut Oberwolfach, 20210223)What is the dollar game? What can you do to win it? Can you always win it? In this snapshot you will find answers to these questions as well as several of the mathematical surprises that lurk in the background, including ... 
Higgs bundles without geometry
[SNAP2020008EN] Rayan, Steven; Schaposnik, Laura P. (Mathematisches Forschungsinstitut Oberwolfach, 20200929)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 ... 
How to choose a winner: the mathematics of social choice
[SNAP2015009EN] Powers, Victoria Ann (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 ... 
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 ... 
Invitation to quiver representation and Catalan combinatorics
[SNAP2021004EN] Rognerud, Baptiste (Mathematisches Forschungsinstitut Oberwolfach, 20210408)Representation theory is an area of mathematics that deals with abstract algebraic structures and has numerous applications across disciplines. In this snapshot, we will talk about the representation theory of a class ... 
Is it possible to predict the far future before the near future is known accurately?
[SNAP2019021EN] Gander, Martin J. (Mathematisches Forschungsinstitut Oberwolfach, 20191218)It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict ... 
Lagrangian mean curvature flow
[SNAP2021011EN] Lotay, Jason D. (Mathematisches Forschungsinstitut Oberwolfach, 20210916)Lagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics. I will describe some of the key aspects of Lagrangian mean curvature ... 
Limits of graph sequences
[SNAP2019010EN] Klimošová, Tereza (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Graphs are simple mathematical structures used to model a wide variety of reallife objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent ... 
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 ... 
Mixed volumes and mixed integrals
[SNAP2018014EN] Rotem, Liran (Mathematisches Forschungsinstitut Oberwolfach, 20181229)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 ... 
Mixeddimensional models for realworld applications
[SNAP2019014EN] Nordbotten, Jan Martin (Mathematisches Forschungsinstitut Oberwolfach, 20191121)We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixeddimensional models. We first give several examples, and ... 
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 ... 
On Logic, Choices and Games
[SNAP2019009EN] Oliva, Paulo (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ... 
Positive Scalar Curvature and Applications
[SNAP2019004EN] Rosenberg, Jonathan; Wraith, David (Mathematisches Forschungsinstitut Oberwolfach, 20190425)We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar curvature. We discuss why ... 
Quantum symmetry
[SNAP2020005EN] Weber, Moritz (Mathematisches Forschungsinstitut Oberwolfach, 20200604)In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from ... 
Quantum symmetry
[SNAP2020009EN] Caspers, Martijn (Mathematisches Forschungsinstitut Oberwolfach, 20201231)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 ... 
Random matrix theory: Dyson Brownian motion
[SNAP2020002EN] Finocchio, Gianluca (Mathematisches Forschungsinstitut Oberwolfach, 20200415)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 ... 
Random permutations
[SNAP2019007EN] Betz, Volker (Mathematisches Forschungsinstitut Oberwolfach, 20190712)100 people leave their hats at the door at a party and pick up a completely random hat when they leave. How likely is it that at least one of them will get back their own hat? If the hats carry name tags, how difficult ... 
Random sampling of domino and lozenge tilings
[SNAP2016002EN] Fusy, Éric (Mathematisches Forschungsinstitut Oberwolfach, 2016)A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different ...