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

Oberwolfach'tan

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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Matematiksel konular

Cebir ve Sayılar Kuramı
Analiz

Diğer alanlarla ilişkiler

Bilgisayar Bilimeri
Mühendislik ve Teknoloji
Fizik

Yazar(lar)

Rajula Srivastava

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2025-009-EN

PDF indir

snapshot-2025-009.pdf

PDF

snapshots: overview

Rajula Srivastava
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The periodic tables of algebraic geometry
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Closed geodesics on surfaces
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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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Random matrix theory: Dyson Brownian motion
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From Betti numbers to l2-Betti numbers
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The Interaction of Curvature and Topology
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The Mathematics of Fluids and Solids
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Deep Learning and Inverse 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
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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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Aperiodic Order and Spectral Properties
Lukas Pottmeyer
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Towards a Mathematical Theory of Turbulence in Fluids
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Profinite groups
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The adaptive finite element method
Steven Klee
Footballs and donuts in four dimensions
Nikolai Nowaczyk
The Willmore Conjecture
Lior Bary-Soroker
Prime Tuples in Function Fields
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Polyhedra and commensurability
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Quantum diffusion
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Ideas of Newton-Okounkov bodies
Ben Schweizer
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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
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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
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Matrixfaktorisierungen
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Dirichlet Series

Matematiksel konular

Cebir ve Sayılar Kuramı
Analiz
Eğitim ve Eğitim Bilimi
Ayrık Matematik ve Matematiğin Temelleri
Geometri ve Topoloji
Nümerik ve Hesap Analizi
Olasılık Kuramı ve İstatistik

Diğer alanlarla ilişkiler

Kimya ve Yer Bilimler
Bilgisayar Bilimeri
Mühendislik ve Teknoloji
Finans
Beşeri ve Sosyal Bilimler
Yaşam Bilimleri
Fizik
Matematik Üzerine Düşünceler

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