Nonholonomic Einstein systems, Perelman Entropy, Ricci Flow

Hi Readers,

Happy Diwali! I am in Mumbai these days.. I have been speaking about nonholonomic diffusion in Einstein Systems, Ricci Flow, Yang Mills Flow, topological game theory in social networks and neural networks since 2010 with some mathematicians.

Perelman's (Field Medalist in 2010 who rejected Field Medal first time in 150 years after solving Poincare Conjecture which was unsolved for 100 years) 2008 paper The entropy formula for the Ricci flow and its geometric applications says that he did not know enough about Blackholes & (pseudo)- Riemannian geometry, Ricci Flow, Black Hole Thermodynamics, etc https://arxiv.org/pdf/math/0211159.pdf

Hence, I thought a perfect way to apply Perelman's work was AI, Data Science (please see my Ricci Flow- https://www.youtube.com/watch?v=z_pjsJisdHQ&t=26s ) & Econophysics using black hole thermodynamics etc. 

Anyway......

Here comes a state of the art paper on Perelman Entropy and Quantum Information systems - Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies - https://dl.acm.org/doi/abs/10.1007/s11128-021-03287-7

Obviously CERN has produced a great paper on application of Convolutional Neural Networks in Einstein Sasaki Vol Min. - https://arxiv.org/abs/1706.03346

But this paper Quantum Geometric Information Flows changes the way, I have analyzed GANs through Perelman Entropy and Ricci Flow in my SDSU-UCSD lecture for better convergence of GANs (the original lecture was on Image and Video Analytics/Computer Vision in Healthcare). 

This paper also gives lot of room for new research on on Ricci Flow,  Yang Mills and Social Collider articles (2 articles in KDnuggets). Twitter has recently published a blog on Ricci Curvature and Graph Neural Networks, while Univ of Cambridge has published a paper on RicciNets after my lecture.

This also changes the way I was going to apply Ricci Flow & Nash Entropy Optimized GANs to solve PDEs in Dynamical and Chaotic systems in certain way. 

More to come soon.. 

Happy Diwali again! Every Diwali brings lot of peace of mind and some good memories..