Brauer’s problems: 60 years of legacy

Instantáneas de la actualidad matemática desde Oberwolfach

Brauer’s problems: 60 years of legacy

Richard Brauer (1901–1977) was a German–American mathematician who is regarded as the founder of a highly active mathematical area known as modular representation theory. This area grew from group theory, which can be thought of as the mathematical study of symmetries. In this snapshot, we hope to impress on the reader the legacy left by Brauer and celebrate the 60th anniversary of “Brauer’s problems”, a list of 43 conjectures and objectives suggested by Brauer in 1963. These problems inspired an entire branch within character theory, studying “local-global conjectures”.

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Área matemática

Álgebra y Teoría de números

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Química y Ciencias de la Tierra
Informática
Física

Autor(es)

Noelia Rizo, Mandi Schaeffer Fry

Licencia

DOI (Identificador de objetos digitales)

10.14760/SNAP-2025-006-EN

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snapshot-2025-006.pdf

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snapshots: overview

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Brauer’s problems: 60 years of legacy
Sarah Blackwell
Trisections of four-dimensional spaces
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The five Platonic solids and their connection to root systems
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Convex polytopes and linear programs
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The geometry of fair division
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4 = 2 × 2, or the power of even integers in Fourier analysis
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Cutoff phenomenon: Surprising behaviour in card shuffling and other Markov chains
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Algebras and quantum games
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Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
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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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Characterizations of intrinsic volumes on convex bodies and convex functions
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Quantum symmetry
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The Enigma behind the Good–Turing formula
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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Invitation to quiver representation and Catalan combinatorics
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David Kerr
C∗-algebras: structure and classification
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Moritz Weber
Quantum symmetry
Christian Berg
Determinacy versus indeterminacy
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Vertex-to-Self Trajectories on the Platonic Solids
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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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Formation Control and Rigidity Theory
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Configuration spaces and braid groups
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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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Mixed volumes and mixed integrals
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Tropical geometry
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Topological Complexity, Robotics and Social Choice
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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
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Computing the long term evolution of the solar system with geometric numerical integrators
Justin Solomon
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
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News on quadratic polynomials
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Jacob Bedrossian
Towards a Mathematical Theory of Turbulence in Fluids
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Profinite groups
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The adaptive finite element method
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Prime Tuples in Function Fields
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Quantum diffusion
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Special values of zeta functions and areas of triangles
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Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
Ideas of Newton-Okounkov bodies
Ben Schweizer
Darcy’s law and groundwater flow modelling
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
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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
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

Área matemática

Álgebra y Teoría de números
Análisis
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Cálculo numérico y científico
Teoría de la probabilidad y Estadística

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