Billiards and flat surfaces

Snapshots of modern mathematics from Oberwolfach

Billiards and flat surfaces

Billiards, the study of a ball bouncing around on a table, is a rich area of current mathematical research. We discuss questions and results on billiards, and on the related topic of flat surfaces.

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Mathematical subjects

Geometry and Topology

Connections to other fields

Physics

Author(s)

Diana Davis

License

DOI (Digital Object Identifier)

10.14760/SNAP-2015-001-EN

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snapshot-2015-001.pdf

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snapshots: overview

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The periodic tables of algebraic geometry
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Patterns and waves in theory, experiment, and application
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Closed geodesics on surfaces
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Route planning for bacteria
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Characterizations of intrinsic volumes on convex bodies and convex functions
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A tale of three curves
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Representations and degenerations
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Solving inverse problems with Bayes’ theorem
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Jewellery from tessellations of hyperbolic space
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Seeing through rock with help from optimal transport
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The Robinson–Schensted algorithm
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Emergence in biology and social sciences
Jason D. Lotay
Lagrangian mean curvature flow
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Finite geometries: pure mathematics close to applications
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Describing distance: from the plane to spectral triples
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Quantum symmetry
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The Enigma behind the Good–Turing formula
Anna Haensch
Reflections on hyperbolic space
Isaac Goldbring
Ultrafilter methods in combinatorics
Gandalf Lechner
Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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Invitation to quiver representation and Catalan combinatorics
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Searching for structure in complex data: A modern statistical quest
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C∗-algebras: structure and classification
Sara Lamboglia, Martin Ulirsch
From the dollar game to the Riemann-Roch Theorem
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Higgs bundles without geometry
Behrend Heeren, Martin Rumpf
Shape space - a paradigm for character animation in computer graphics
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Rotating needles, vibrating strings, and Fourier summation
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Quantum symmetry
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Determinacy versus indeterminacy
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Vertex-to-Self Trajectories on the Platonic Solids
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Random matrix theory: Dyson Brownian motion
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From Betti numbers to l2-Betti numbers
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Is it possible to predict the far future before the near future is known accurately?
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The Interaction of Curvature and Topology
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The Mathematics of Fluids and Solids
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A surprising connection between quantum mechanics and shallow water waves
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Formation Control and Rigidity Theory
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Expander graphs and where to find them
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Touching the transcendentals: tractional motion from the birth of calculus to future perspectives
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Limits of graph sequences
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Nonlinear Acoustics
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Random permutations
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Counting self-avoiding walks on the hexagonal lattice
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Positive Scalar Curvature and Applications
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Diophantine equations and why they are hard
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On radial basis functions
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Snake graphs, perfect matchings and continued fractions
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Estimating the volume of a convex body
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Mixed volumes and mixed integrals
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A short story on optimal transport and its many applications
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Number theory in quantum computing
Matthias Morzfeld, Sebastian Reich
Data assimilation: mathematics for merging models and data
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Geometry behind one of the Painlevé III differential equations
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The codimension
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The mathematics of aquatic locomotion
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Tropical geometry
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Topological Complexity, Robotics and Social Choice
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Prony’s method: an old trick for new problems
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Computing with symmetries
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Topological recursion
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The Algebraic Statistics of an Oberwolfach Workshop
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Solving quadratic equations in many variables
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Mathematics plays a key role in scientific computing
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Spaces of Riemannian metrics
Shaula Fiorelli Vilmart, Gilles Vilmart
Computing the long term evolution of the solar system with geometric numerical integrators
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Computational Optimal Transport
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A few shades of interpolation
George Hagedorn, Caroline Lasser
Molecular quantum dynamics
Marco Radeschi
Closed geodesics on surfaces and Riemannian manifolds
Christian Engwer, Markus Knappitsch
Mathematische Modellierung von Krebswachstum
Michael Baake, David Damanik, Uwe Grimm
Aperiodic Order and Spectral Properties
Lukas Pottmeyer
News on quadratic polynomials
Felix Günther
Winkeltreue zahlt sich aus
Jacob Bedrossian
Towards a Mathematical Theory of Turbulence in Fluids
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Profinite groups
Dietmar Gallistl
The adaptive finite element method
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Footballs and donuts in four dimensions
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The Willmore Conjecture
Lior Bary-Soroker
Prime Tuples in Function Fields
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Polyhedra and commensurability
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High performance computing on smartphones
Eugenio Giannelli, Jay Taylor
Symmetry and characters of finite groups
Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
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On the containment problem
Éric Fusy
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Magnus Egerstedt
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Ulrich Krähmer
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Juanjo Rué
Domino tilings of the Aztec Diamond
Sebastian Funk
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Antti Knowles
Quantum diffusion
Amanda Swan, Albert Murtha
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Special values of zeta functions and areas of triangles
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Ben Schweizer
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Raluca Eftimie
Modelling communication and movement: from cells to animals and humans
Tom Solomon
Chaos and chaotic fluid mixing
Thorsten Holm
Friezes and tilings
George Willis
Zero-dimensional symmetry
Christine Breiner
Minimizing energy
Diana Davis
Billiards and flat surfaces
Peter Benner, Hermann Mena, René Schneider
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Gregory Knese
Operator theory and the singular value decomposition
Alain Valette
The Kadison-Singer problem
Ragnar-Olaf Buchweitz, Eleonore Faber
Swallowtail on the shore
Howell Tong
Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
Bruce Reznick
What does ">" really mean?
Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Mathematical subjects

Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics

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