Abstract
The geometry of natural objects differs from that of ‘idealized’ objects that one studies in a geometry course. In this talk, I’ll first take a closer look at the concept of dimension of a geometrical object and will show that the dimension can be a fractional number. Then I will show how the concept of fractional dimension becomes important in characterizing not only natural objects, but also structures one encounters in the study of dynamics. The second part of the lecture will deal with the space where images (i.e., compact subsets of the $\mathbb{R}^2$ space) live. I’ll show that it is a complete metric space, and by suitably defining a contraction mapping using a set of affine transforms, one can obtain a Cauchy sequence that converges on any desired image. That gives a powerful tool to codify any image as a collection of matrices. Finally I shall illustrate a few practical applications.
About the Speaker
Prof. Soumitro Banerjee is a Professor in the Department of Physical Sciences, IISERK Kolkata.
Poster for the event, designed by Sohom Gupta and Abhisruta Maity.