Combinatorial positive valuations
Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017
Location: SLMath: Eisenbud Auditorium
combinatorial positivity
valuations
lattice polytopes
Ehrhart polynomial
49L25 - Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
05C69 - Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
49K45 - Optimality conditions for problems involving randomness [See also 93E20]
5-Jochemko
In the continuous setting, valuations are well-studied and the volume plays a prominent role in many classical and structural results. It has various desirable properties such as homogeneity, monotonicity and translation-invariance. In the less examined discrete setting, the number of lattice points in a polytope - its discrete volume - takes a fundamental role. Although homogeneity and continuity are lost, some striking parallels to the continuous setting can be drawn. The central notion here is that of combinatorial positivity. In this talk, I will discuss similarities, analogies and differences between the continuous and discrete world of translation-invariant valuations as well as applications to Ehrhart theory
Jochemko Notes
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5-Jochemko
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