192
Compulsory

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Discrete Geometry - Hyperplanes, Matroids and Broken Circuits

In how many ways can I color the vertices of a graph so that adjacent nodes get different colors?

To answer questions like these, one is naturally led to geometric questions about a certain hyperplane arrangement associated with a graph. Generalizing even further, the structure of a matroid captures many aspects of the combinatorics of hyperplane arrangements.

In this seminar we will learn what a matroid is, what the Bergman fan and the no-broken-circuit complex of a matroid are, and what these objects tell me about colorings of graphs and regions of hyperplane arrangements.

Very recently, there have been spectacular break throughs concerning the characteristic polynomial of a matroid. By the end of the seminar we will all understand what these old conjectures -- now theorems say, and maybe even get a glimpse of the proofs.

Cross-language

Expectant Mother

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Partly dangerous
Alternative Course
Dangerous

Nursing Mother

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Partly dangerous
Alternative Course
Dangerous