UBC DG-MP-PDE Seminar: Rustum Choksi

  • Date: 11/23/2021
  • Time: 15:30
Lecturer(s):
Rustum Choksi (McGill)
Location: 

University of British Columbia

Topic: 

Optimal Quantization and Optimal Centroidal Voronoi Tessellations

Description: 

In this talk, we explore the simple, yet rich, paradigm of optimal quantization (alternatively, optimal centroidal Voronoi tessellations (CVT)).
The 3D Gersho's conjecture may be viewed as a crystallization conjecture and asserts the periodic structure, as the number of generators tends to infinity, of the optimal CVT. In joint work with Xin Yang Lu (Lakehead University), we present certain bounds which, combined with a 2D approach introduced by P. Gruber, reduce the resolution of the 3D Gersho's conjecture to a finite (albeit very large) computation of an explicit convex problem in finitely many variables.
We then address some current work for optimal quantization of the 2-sphere.

 

In the second part of the talk, we address the role of numerical algorithms for finding optimal (or close to optimal) CVTs on the
2D flat torus. For small numbers of generators, this will expose
some interesting observations and conjectures about defect vs perfect lattice structures. This is joint work with Ivan Gonzales and JC Nave (McGill University) and with two former undergraduates Dragos Cristian Manta and Jack Tisdell.

Other Information: 

Time: 3:30-4:30pm Pacifc

 Location: PIMS lounge: ESB 4133