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

Schnappschüsse moderner Mathematik aus 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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Mathematisches Fachgebiet

Algebra und Zahlentheorie
Analysis

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Informatik
Ingenieurwissenschaft und Technik
Physik

Autor(en)

Rajula Srivastava

Lizenz

DOI (Digital Object Identifier)

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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Quantum symmetry
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Reflections on hyperbolic space
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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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The Mathematics of Fluids and Solids
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Topological recursion
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Molecular quantum dynamics
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Closed geodesics on surfaces and Riemannian manifolds
Christian Engwer, Markus Knappitsch
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Profinite groups
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Tom Solomon
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Zero-dimensional symmetry
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Billiards and flat surfaces
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Operator theory and the singular value decomposition
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The Kadison-Singer problem
Ragnar-Olaf Buchweitz, Eleonore Faber
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Howell Tong
Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
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The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Mathematisches Fachgebiet

Algebra und Zahlentheorie
Analysis
Didaktik und Bildung
Diskrete Mathematik und Grundlagen
Geometrie und Topologie
Numerik und Wissenschaftliches Rechnen
Wahrscheinlichkeitstheorie und Statistik

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