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Exploring the Size of Order-k Voronoi Tessellation and Chromatic Delaunay Mosaic

Series: Department Seminar

Speaker: Dr. Ranita Biswas, Institute of Science and Technology Austria (ISTA), Austria

Date/Time: Feb 06 14:00:00

Location: Online Seminar

Abstract:
In this presentation, we will first delve into the topic of the size of order-k Voronoi tessellations. Specifically, we will examine how Lee's inductive argument for counting cells in R^2 can be generalized to R^3, resulting in precise relations involving Morse-theoretic quantities for piecewise constant functions on planar arrangements. Additionally, we will introduce the concept of a chromatic Delaunay mosaic, which is a Delaunay mosaic in R^(s+d) that illustrates the intermixing of points of (s+1) colors within a locally finite set of points in R^d. Our primary findings include bounds on the size of this chromatic Delaunay mosaic. These results are the product of a collaborative effort with Sebastiano Cultrera, Herbert Edelsbrunner, Ondrej Draganov, and Morteza Saghafian.
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This is an online Seminar. The Teams URL for this is: <br>
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Speaker Bio:
Ranita Biswas is a postdoctoral scholar in the Edelsbrunner group at the Institute of Science and Technology Austria (ISTA) since 2019. Earlier, she was an assistant professor at IIT Roorkee. She received her PhD in 2016 at IIT Kharagpur working on Digital Geometric problems. Her current research interest is in the domain of Computational Geometry and Topology.

Host Faculty: R Govindarajan