Why oscillation counts: Diophantine approximation, geometry, and the Fourier transform

Instantáneas de la actualidad matemática desde Oberwolfach

Why oscillation counts: Diophantine approximation, geometry, and the Fourier transform

Is it possible to approximate arbitrary points in space by vectors with rational coordinates, with which we, and computers, feel much more comfortable? If yes, can we approximate those points arbitrarily close? In this snapshot, we explore how the geometric configuration of these points influences the answers to these questions. Further, we delve into the closely related problem of counting rational vectors near surfaces. The unlikely tool which helps us in this endeavour is Fourier analysis – the study of waves and oscillations!

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Área matemática

Álgebra y Teoría de números
Análisis

Relaciones con otros campos

Informática
Ingeniería y Tecnología
Física

Autor(es)

Rajula Srivastava

Licencia

DOI (Identificador de objetos digitales)

10.14760/SNAP-2025-009-EN

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snapshot-2025-009.pdf

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snapshots: overview

Rajula Srivastava
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The geometry of fair division
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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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Lagrangian mean curvature flow
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Quantum symmetry
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Reflections on hyperbolic space
Isaac Goldbring
Ultrafilter methods in combinatorics
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Invitation to quiver representation and Catalan combinatorics
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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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The Interaction of Curvature and Topology
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The Mathematics of Fluids and Solids
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Formation Control and Rigidity Theory
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Deep Learning and Inverse Problems
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Mixed-dimensional models for real-world applications
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Random permutations
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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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Spaces of Riemannian metrics
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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
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Profinite groups
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The adaptive finite element method
Steven Klee
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Nikolai Nowaczyk
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Quantum diffusion
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J. Marron
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Jürg Kramer, Anna-Maria Pippich
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Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
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Ben Schweizer
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Tom Solomon
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Thorsten Holm
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Zero-dimensional symmetry
Christine Breiner
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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
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Howell Tong
Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
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Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
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Dirichlet Series

Área matemática

Álgebra y Teoría de números
Análisis
Didáctica y Educación
Matemática discreta y Fundamentos
Geometría y Topología
Cálculo numérico y científico
Teoría de la probabilidad y Estadística

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