It has traditionally strong relations to integral geometry. Here is a list of applications of other kinds of math to discrete and convex geometry there is a little overlap with other answer already given.
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Some are not as important or groundbreaking as others but I consider all of them as reasonably interesting. The list comes in no particular order. Ball, Keith Convex geometry and functional analysis. Handbook of the geometry of Banach spaces, Vol.
Convexity and Discrete Geometry Including Graph Theory
I, —, North-Holland, Amsterdam, Ball, Keith An elementary introduction to modern convex geometry. Flavors of geometry, 1—58, Math.
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- Approaching convex and discrete geometry from other disciplines - MathOverflow;
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Press, Cambridge, Ostrovskii, Mikhail I. Bilipschitz and coarse embeddings into Banach spaces. De Gruyter Studies in Mathematics, De Gruyter, Berlin, Since you mention topology In this MO answer , Ryan Budney identifies these as plumber's knots. There is quite a bit of work on modeling polymer chains in 3D lattices, e.
Workshop II: Combinatorial Geometry
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Approaching convex and discrete geometry from other disciplines Ask Question. Asked 5 years, 1 month ago. Active 5 years, 1 month ago. Viewed times. I did some MathSciNet searches, but I am not sure which papers could be interesting. Applications of topology to discrete geometry aka "Topological Combinatorics" -- Examples include the Ham Sandwich Theorem for measures, the colorful Tverberg theorem, and many more.
A good starting point is the book "Using the Borsuk-Ulam theorem" by J.
If you want to learn from the master himself, have a look at Stanley's book "Combinatorics and commutative algebra". A good starting point to learn about this might be the blog entry by Tao. Monsky's theorem -- Monsky's theorem says that you cannot dissect a square in an odd number of triangles with all triangles having the same area. The proof makes essential use of 2-adic valuations and Sperner's lemma from topology. The technqiues used stem from extremal hyper graph theory and are not difficult to understand. The book will be appreciated by specialists in the field The book can be used as a base for some special courses at universities and for further preparation of PhD students.
It is a book that should be available in any mathematical oriented library.
EMS Newsletter, December, A fascinating overview of major results, methods and ideas of convex and discrete geometry and some of their applications. All in all an impressive book, which by no means may serve only as work of reference but can be used very well as a rich source for lecturers and as graduate-level introduction to the field.
Kowol, Monatshefte fur Mathematik, Vol. Toon meer Toon minder. Betrokkenen Auteur Peter M. Gruber Uitgever Springer. Reviews Schrijf een review.
Forbidden Configurations in Discrete Geometry - David Eppstein - Google книги
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Anderen bekeken ook. Springer Polytopes , Bisztriczky Polytopes , Jacek Banasiak Volumetric Discrete Geometry , Andras Bezdek Discrete Geometry , Kg Advances in Discrete Differential Geometry 53,