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Invitation to quiver representation and Catalan combinatorics

Representation theory is an area of mathematics that deals with abstract algebraic structures and has nu- merous applications across disciplines. In this snap- shot, we will talk about the representation theory of a class of objects called quivers and relate them to the fantastic combinatorics of the Catalan numbers.

Shape space - a paradigm for character animation in computer graphics

Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions of triangles. The mathematical notion of a shape space allows us to effectively model, manipulate, and animate such meshes. Once an appropriate notion of dissimilarity measure between different triangular meshes is defined, various useful tools in character modeling and animation turn out to co- incide with basic geometric operations derived from this definition

Quantum symmetry

In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from spaces to quantum spaces, from groups to quantum groups, and from symmetry to quantum symmetry, following an analytical appr

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