Seminario “The MST-Ratio: A New Measure of Mixedness for Colorful Point Sets”

Dettagli

Mercoledì 5 febbraio 2025 ore 12 - Sala Alessandri del Dipartimento di Ingegneria

short Bio

Dr. Morteza Saghafian,
Institute of Science and Technology, Austria
Morteza Saghafian is a postdoctoral researcher in the Edelsbrunner Group at IST Austria, working in discrete geometry and computational topology, especially on geometric graph theory and generalizations of Delaunay triangulations. He earned his Ph.D. in Computer Science from Sharif University of Technology, focusing on clustering algorithms and higher order Voronoi tessellations. Moreover, since winning a gold medal at the International Mathematical Olympiad (IMO), he has been active in math education, contributing creative problems to competitions and Olympiads.

Title

The MST-Ratio: A New Measure of Mixedness for Colorful Point Sets

Abstract

Recently, motivated by applications in spatial biology, we explored the interactions between color classes in a colored point set from a topological perspective. We introduced MST-ratio as a measure for quantifying the mingling of points with different colors. Investigating this measure raises intriguing questions in discrete geometry, which is the primary focus of this talk.
In this talk, I will introduce the concept of the MST-ratio, present the best-known bounds and key complexity results for computing its maximum, and share new findings on its behavior in both random and arbitrary point sets. Finally, I will highlight several open questions in discrete and stochastic geometry that arise from this work.

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