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playground:playground [2014/08/23 15:39] FRADELIZI Matthieu |
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The course will cover several topics in combinatorial convexity, where theorems of Caratheodory, Helly, Radon, and Tverberg are the typical and classical results. We plan to investigate weak epsilons-nets, halving lines and planes, the $(p,q)$ problem and its solution, extensions to lattice convex sets, and colourful versions of the above mentioned classical theorems. Further possible topics are transversals, lattice polytopes and random polytopes. | The course will cover several topics in combinatorial convexity, where theorems of Caratheodory, Helly, Radon, and Tverberg are the typical and classical results. We plan to investigate weak epsilons-nets, halving lines and planes, the $(p,q)$ problem and its solution, extensions to lattice convex sets, and colourful versions of the above mentioned classical theorems. Further possible topics are transversals, lattice polytopes and random polytopes. | ||

The methods here use tools from linear algebra, combinatorics, topology, geometry, probability theory, and geometry of numbers. | The methods here use tools from linear algebra, combinatorics, topology, geometry, probability theory, and geometry of numbers. | ||

- | The methods here use tools from linear algebra, combinatorics, topology, geometry, probability theory, and geometry of numbers. | ||

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^ <fs larger>Jeff Kahn</fs> \\ (Rutgers University, USA)| <fs larger> | ^ <fs larger>Jeff Kahn</fs> \\ (Rutgers University, USA)| <fs larger> |