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The Warriors Grow Up
‘No great mathematician is so difficult to study as Newton.’ wrote Clifford Truesdell at the beginning of the 1960s [Truesdell 1984, S. 269]. This is...
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The holomorphic couch theorem
We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal...
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Homotopy Invariant Commutative Algebra over Fields
This article grew out of lectures given in the programme “Interactions between Representation Theory, Algebraic Topology, and Commutative Algebra”...
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Puzzles and Mathematics
The English word puzzle covers a broad range of meanings, alluding to everything from riddles and crosswords to Sudoku, optical illusions, and...
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Categorical Logic
The Arabic logiciansCategorical logic traditionallyAssent divideTraditional logic into two parts as witnessed by Tony Street[aut]Street (Tony) in his...
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Klein, Mittag-Leffler, and the Klein-Poincaré Correspondence of 1881–1882
If a modern-day Plutarch were to set out to write the “Parallel lives” of some famous modern-day mathematicians, he could hardly do better than to...
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Connecting orbits of Lagrangian systems in a nonstationary force field
We study connecting orbits of a natural Lagrangian system defined on a complete Riemannian manifold subjected to the action of a nonstationary force...
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Applying Random Forests to the Problem of Dense Non-rigid Shape Correspondence
We introduce a novel dense shape matching method for deformable, three-dimensional shapes. Differently from most existing techniques, our approach is...
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On some simple examples of mechanical systems with hyperbolic chaos
Examples of mechanical systems with hyperbolic chaos are discussed, including the Thurston–Weeks–Hunt–MacKay hinge mechanism, in which conservative...
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Statistics and probability calculus
The word statistics was first employed as a synonym for “numerical descriptions of societies” in 19th century England and France. In those times, no...
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Proportions and similar objects
In this chapter, we deal with similar objects and other proportions. The insights thus won have many practical applications and benefit the...
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Spatial Models
Before IPMs were used for size-structured populations, they had a long history as models for spatially structured populations and for spatial spread...
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Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics
Computer verification of hyperbolicity is provided based on statistical analysis of the angles of intersection of stable and unstable manifolds for...
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From the Perspective of Artificial Intelligence: A New Approach to the Nature of Consciousness
Consciousness is not only a philosophical but also a technological issue, since a conscious agent has evolutionary advantages. Thus, to replicate a...
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Non-rigid Shape Correspondence Using Surface Descriptors and Metric Structures in the Spectral Domain
Finding correspondence between non-rigid shapes is at the heart of three-dimensional shape processing. It has been extensively addressed over the...
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Optimal Control
Given optimal control a set of nonholonomic constraints, there are two interesting associated problems. One of these...
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Distances in Physics and Chemistry
Physics studies the behavior and properties of matter in a wide variety of contexts, ranging from the submicroscopic particles from which all...
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The Nature and Challenges of Mathematics Research
Sylvestre Huet: Now I would like us to address aspects connected with the nature and the challenges of mathematics research. Today, what are its...