Game-theoretic statistics

Snapshots of modern mathematics from Oberwolfach

Game-theoretic statistics

Statistical modeling is the art of connecting abstract models with scientific or practical questions, so that the models’ probabilities throw light on these questions. Standard statistical theory summarizes the results with p-values. Unfortunately, p-values are widely misunderstood. Game-theoretic statistics replace them with e-values, also called betting scores. The model makes a forecast, the statistician makes an imaginary bet against it, and the value is the factor by which she multiplies her stake.

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Mathematical subjects

Probability Theory and Statistics

Connections to other fields

Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science

Author(s)

Glenn Shafer

License

DOI (Digital Object Identifier)

10.14760/SNAP-2026-009-EN

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snapshot-2026-009.pdf

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snapshots: overview

Bas Lodewijks
Do the rich get richer? Mathematical models for real-world networks
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Game-theoretic statistics
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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
Jason J. Bramburger
Patterns and waves in theory, experiment, and application
Benjamin Dozier
Closed geodesics on surfaces
Kathrin Hellmuth, Christian Klingenberg
Route planning for bacteria
Fabian Mussnig
Characterizations of intrinsic volumes on convex bodies and convex functions
Jennifer S. Balakrishnan
A tale of three curves
Michael Baake, Uwe Grimm, Robert V. Moody
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Reflections on hyperbolic space
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David Kerr
C∗-algebras: structure and classification
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Quantum symmetry
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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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Formation Control and Rigidity Theory
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Algebra, matrices, and computers
Jonathan Rosenberg, David Wraith
Positive Scalar Curvature and Applications
Hector Pasten
Diophantine equations and why they are hard
Martin Buhmann, Janin Jäger
On radial basis functions
Ralf Schiffler
Snake graphs, perfect matchings and continued fractions
Nicolai Baldin
Estimating the volume of a convex body
Liran Rotem
Mixed volumes and mixed integrals
Filippo Santambrogio
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
Claus Hertling
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The codimension
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Erwan Brugallé, Ilia Itenberg, Kristin Shaw, Oleg Viro
Tropical geometry
Alex Barnett
Fast Solvers for Highly Oscillatory Problems
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Topological Complexity, Robotics and Social Choice
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Topological recursion
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Justin Solomon
Computational Optimal Transport
Justyna Szpond
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
Laurent Bartholdi
Profinite groups
Dietmar Gallistl
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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Robert Altmann, Jan Heiland
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Anthony T Patera, Karsten Urban
High performance computing on smartphones
Eugenio Giannelli, Jay Taylor
Symmetry and characters of finite groups
Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
Das Problem der Kugelpackung
Tomasz Szemberg, Justyna Szpond
On the containment problem
Éric Fusy
Random sampling of domino and lozenge tilings
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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J. Marron
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Christopher Sangwin
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Jürg Kramer, Anna-Maria Pippich
Special values of zeta functions and areas of triangles
Victoria Powers
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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
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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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