## PIMS-SFU Computational Math Seminar: Rustum Choksi

• Date: 11/26/2021
• Time: 15:30
Lecturer(s):
Rustum Choksi. McGill
Location:

Simon Fraser University

Topic:

Voronoi Tessellations: Optimal Quantization and Modelling Collective Behaviour

Description:

Abstract: Voronoi tessellations give rise to a wealth of analytic, geometric, and computational questions. They are also very useful in modelling.

This talk will consist of three parts.

In the first, I will address the simple, yet rich, question of optimal quantization -- or optimal centroidal Voronoi tessellations (CVT) -- on 3D torus. I will address Gersho's conjecture, a crystallization conjecture which asserts the periodic structure of the optimal CVT, as the number of generators tends to infinity.

In the second part of the talk, I present a new 2D hybrid numerical method for accessing low energy CVTs with tiny basins of attraction.

In the last part of the talk, I will present a new dynamical model for generic crowds in which individual agents are aware of their local Voronoi environment---i.e., neighbouring agents and domain boundary features---and may seek static target locations. Our model incorporates features common to many other active matter'' models like collision avoidance, alignment among agents, and homing toward targets. However, it is novel in key respects: the model combines topological and metrical features in a natural manner based upon the local environment of the agent's Voronoi diagram. With only two parameters, it captures a wide range of collective behaviours.

This talk comprises joint works with Xin Yang Lu (Lakehead University) and with Ivan Gonzalez, Jean-Christophe Nave, Jack Tisdell (all at McGill University).

Other Information:

This is an in-person presentation located at SFU, room AQ 4145.

Visit SFU Department of Mathematics for information and scroll down to see calendar listing.