Convex polytopes and linear programs

Schnappschüsse moderner Mathematik aus Oberwolfach

Convex polytopes and linear programs

Convex polytopes are geometric objects that look deceptively simple. They occur everywhere in mathematics and have practical applications in everyday life – like organizing your grocery shopping list. In this snapshot, you get into contact with a long-standing, unsolved question in mathematics, which you can explore interactively.

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Mathematisches Fachgebiet

Diskrete Mathematik und Grundlagen

Geometrie und Topologie

Verbindung zu anderen Gebieten

Informatik

Autor(en)

Michael Joswig

Lizenz

CC BY-SA-4.0

DOI (Digital Object Identifier)

10.14760/SNAP-2025-002-EN

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snapshots: overview

Convex polytopes and linear programs

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Truncated fusion rules for supergroups

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Cutoff phenomenon: Surprising behaviour in card shuffling and other Markov chains

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Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften

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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Route planning for bacteria

Characterizations of intrinsic volumes on convex bodies and convex functions

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A tale of three curves

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What is Pattern?

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Biological Shape Analysis with Geometric Statistics and Learning

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Representations and degenerations

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Solving inverse problems with Bayes’ theorem

Jewellery from tessellations of hyperbolic space

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Seeing through rock with help from optimal transport

David A. Craven

Searching for the Monster in the Trees

The Robinson–Schensted algorithm

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Emergence in biology and social sciences

Lagrangian mean curvature flow

Finite geometries: pure mathematics close to applications

Francesca Arici, Bram Mesland

Describing distance: from the plane to spectral triples

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Quantum symmetry

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The Enigma behind the Good–Turing formula

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

Searching for structure in complex data: A modern statistical quest

C∗-algebras: structure and classification

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From the dollar game to the Riemann-Roch Theorem

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Higgs bundles without geometry

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Shape space - a paradigm for character animation in computer graphics

Rotating needles, vibrating strings, and Fourier summation

Quantum symmetry

Determinacy versus indeterminacy

Jayadev S. Athreya, David Aulicino

Vertex-to-Self Trajectories on the Platonic Solids

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Random matrix theory: Dyson Brownian motion

Holger Kammeyer, Roman Sauer

From Betti numbers to l2-Betti numbers

Martin J. Gander

Is it possible to predict the far future before the near future is known accurately?

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The Interaction of Curvature and Topology

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The Mathematics of Fluids and Solids

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A surprising connection between quantum mechanics and shallow water waves

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Formation Control and Rigidity Theory

Expander graphs and where to find them

Simon Arridge, Maarten de Hoop, Peter Maass, Ozan Öktem, Carola Schönlie, Michael Unser

Deep Learning and Inverse Problems

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Mixed-dimensional models for real-world applications

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Limits of graph sequences

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Nonlinear Acoustics

Random permutations

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Counting self-avoiding walks on the hexagonal lattice

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Algebra, matrices, and computers

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Number theory in quantum computing

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Topological Complexity, Robotics and Social Choice

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Computing with symmetries

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Topological recursion

The Algebraic Statistics of an Oberwolfach Workshop

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Solving quadratic equations in many variables

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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

Computational Optimal Transport

A few shades of interpolation

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Molecular quantum dynamics

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

Winkeltreue zahlt sich aus

Jacob Bedrossian

Towards a Mathematical Theory of Turbulence in Fluids

Laurent Bartholdi

Profinite groups

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The adaptive finite element method

Footballs and donuts in four dimensions

Nikolai Nowaczyk

The Willmore Conjecture

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Prime Tuples in Function Fields

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Polyhedra and commensurability

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High performance computing on smartphones

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Symmetry and characters of finite groups

Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes

Das Problem der Kugelpackung

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On the containment problem

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Zero-dimensional symmetry

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The Kadison-Singer problem

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Brian Harbourne, Thomas Szemberg

Arrangements of lines

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The ternary Goldbach Problem

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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

Verbindung zu anderen Gebieten

Chemie und Geowissenschaft

Informatik

Ingenieurwissenschaft und Technik

Finanzwesen

Geistes- und Sozialwissenschaft

Biowissenschaft

Physik

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