SYZ conjecture, Maryam Mirzakhani - AI, Geodesics, Riemannian surfaces, Dennis Sullivan

Hey readers,

Everyone must have seen my last comment on Andrica's conjecture & Firoozbakht's conjecture and how looking at prime numbers as dynamical system is a smarter way to solve this. I also have a way to look at it further in terms of How to use GANs - Generative Adversarial Networks (with optimum convergence while leveraging Nash entropy) to solve PDEs in Dynamical & Chaotic systems generated by prime numbers.

There was this beautiful paper from Maryam Mirzakhani (field prize winner 2014) - Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces (2005) - https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/Teichmuller%20Space/Mirz3.pdf

A lot of my discussions during my evening time in 2010 happened on how to apply her paper in AI. So, I came up with an orchestration in 2011 on Geodesics CNN on Riemannian Surface (I used to write a same blog by the name of DataHulk - which I deleted in 2017 and restarted this year).

Here is a very interesting paper which got published in Switzerland on the same topic - Geodesic convolutional neural networks on Riemannian manifolds - https://arxiv.org/pdf/1501.06297.pdf . The most interesting part of this paper was heat diffusion on manifolds, Heat kernel signature etc.

This was followed by my 2 lectures & video on

1. Ricci Flow (heat diffusion equation with derivative form) in Networks ( https://www.kdnuggets.com/2014/05/poincare-conjecture-perelman-topology-social-networks.html )

2. Some part of my lecture in SDSU which focused on Pruning of Neural Networks using Ricci Flow after which University of Cambridge published a new paper on 
RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow - https://arxiv.org/abs/2007.04216

3. You might like my video on Ricci Flow & its use in use in community detection  - https://www.youtube.com/watch?v=z_pjsJisdHQ&t=23s  

Here is one way to look at SYZ conjecture -

By the way you might like the old paper - THE HOMOLOGY THEORY OF THE CLOSED GEODESIC PROBLEM MICHELINE VIGUE-POIRRIER & DENNIS SULLIVAN - https://www.math.stonybrook.edu/~dennis/publications/PDF/DS-pub-0034.pdf  ( Dennis Sullivan won Abel prize on 24th March for amazing circle packing work )

Edited - Zhiren Wang, associate professor of mathematics at Penn State, has been award the 11th Brin Prize in Dynamical Systems MAY 24, 2022