Ultrafilter methods in combinatorics
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Enviado por IMAGINARY el
Enviado por IMAGINARY el
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.
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Enviado por IMAGINARY el
Enviado por IMAGINARY el
What is the dollar game? What can you do to win it? Can you always win it? In this snapshot you will find answers to these questions as well as several of the mathematical surprises that lurk in the background, including a new perspective on a century-old theorem.
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Enviado por IMAGINARY el
Can a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes if the interval is finite, and no if the interval is infinite.
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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
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We give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis.
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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