Hyperbolic Geometry and Chaos in the Complex Plane
By Prof Mahan Mj, School of Mathematics, TIFR, Mumbai
Date: Tue, 7 Mar 2017
Time: 3:45 PM
Venue: 105 (Audi), Himalaya Building, IIIT-H
Abstract: Instances of hyperbolic geometry come up in nature whenever a system starts developing fast interconnections. Examples include trees, the human brain and the internet. A tell-tale signature is the existence of a fractal in one dimension less, e.g. the surfaces of trees and brains in the above examples.
After dealing with the above examples, we shall discuss a special case where the fractals emerge in the complex plane as a result of symmetries of hyperbolic 3-space. These symmetries act on the complex plane as well; however the dynamics being chaotic, it is hard to get a hold on them directly. Instead we go to hyperbolic geometry in 3 dimensions, set up a dictionary between the two and finally get a hold on the fractals in the complex plane through our study of hyperbolic geometry in 3 dimensions.
Bio: Prof Mahan Mj is a PhD from University of California, Berkeley; M.Sc (Integrated) Mathematics from IIT, Kanpur. He has nearly 45 research publications; has received several awards including the Shanti Swarup Bhatnagar Award in Mathematical Sciences, 2011, Infosys Prize for Mathematical Sciences, 2015 and J C Bose Fellowship, 2014. He was appointed Adjunct Professor at TIFR in 2012. He is a Fellow of the Indian Academy of Sciences. He has been a recipient of several fellowships and has visited many institutions across the globe.
Page last updated on 6th March, 2017