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Combinatorial positive valuations

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 10, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Katharina Jochemko (Royal Institute of Technology (KTH))
Location: MSRI: Simons Auditorium
Video

5-Jochemko

Abstract

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

Supplements
29703?type=thumb Jochemko Notes 2.21 MB application/pdf Download
Video/Audio Files

5-Jochemko

H.264 Video 5-Jochemko.mp4 112 MB video/mp4 rtsp://videos.msri.org/data/000/029/579/original/5-Jochemko.mp4 Download
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