ICM 2018, Hodge theory of Teichmuller curves, CurvGAN, Hodge Loci, Schrodinger Flows, ColombGAN, Yang Mill Connections

Hey Readers,

I used to write a lot about Teichmuller Curves, Hodge Theory, Machine Learning, Schrodinger Flows, Nash Entropy Optimized GANs, Yang Mills & Social Collider ( https://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html ) in 2010 - 2013 on weekends. I expected the following papers/talks will come in in the coming decade using the information topology of research papers of the last 50 years.. and here they come...  

1. Here is an amazing lecture from Anna Wienhard in ICM 2018 on Teichmuller Theory (what was missing in this Field Medal - ICM lecture was mention of CurvGAN, ColombGAN & TopologyGAN for analyzing Hodge, Teichmuller Curves, and other conjectures/topological entities) - 

2. Here is a cool application of CurvGAN on Hodge theory of Teichmuller curves (which becomes really important in analyzing Teichmuller curves through AI & analyze Hodge conjecture, Hodge Loci, etc.) - https://www.uni-frankfurt.de/50569475/Generic_50569475.pdf

with some interesting insights and way to solve Hodge Conjecture.

3. Here is the coolest paper on Schrodinger Flows & Bayesian learning (which has amazing applications in social networks & learning through social networks) - https://arxiv.org/abs/2111.10510 

Another application of this is DeepWalk & learning across the networks through optimized navigation (check out some amazing applications of DeepWalk by IIT Roorkee). 

4. Why are we not using TopologyGAN, CurvGAN & ColombGAN to analyze  Yang-Mills?  

So far the latest we have seen after my publication of Yang-Mills & Social Collider... - 

Hermitian–Yang-Mills Connections on Collapsing Elliptically Fibered K3 Surfaces - https://link.springer.com/article/10.1007/s12220-021-00808-9 

• Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf
• Yang-Mills theory in highly multiple-connected topologies - https://www.researchgate.net/publication/321462498_Yang-Mills_theory_in_highly_multiple-connected_topologies 
• The Hyperbolic Yang–Mills Equation for Connections in an Arbitrary Topological Class - https://link.springer.com/article/10.1007/s00220-018-3205-x 

12th May, TopologyGAN, CurvGAN..

Hey Readers,

It's Tuesday night 1 AM. It's going to be 12th May next week - Maryam Mirzakhani's Birthday & I am going to celebrate it with some cool blog on Teichmüller theory. 

First of all, Congrats Gigliola Staffilani.. Her work on Schrodinger flows in Hyperbolic spaces, Nonlinear dispersive equations is very cool & she just won the National Academy of Sciences awards. If you want to read more about data driven vector soliton solutions of coupled nonlinear vector soliton Schrödinger equation, please read my Jan 10 blog.. - https://researchcircle.blogspot.com/2022/01/interesting-case-of-schrodinger.html

Coming back to Ricci Curvature & GANs, there is a very interesting paper on
CurvGANs & Ricci Curvature by Jianxin Li - https://arxiv.org/abs/2203.01604

The importance of this paper on CurvGANs along with TopologyGAN in applied sense is as follows - 

1. Predicting link in market topology & market failure to further my concept of Ricci Curvature - https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html 

2. Predicting information flow in social networks using Ricci Curvature & Ricci Flow as explained in my previous blogs. 

3. This can also be applied on another paper on Schrödinger equation in a general curved spacetime geometry to predict curvature of the spacetime geometry, Schwarzschild black hole & solve information paradox - https://www.worldscientific.com/doi/10.1142/S0218271822500183

4. Also, to further the analysis of an old paper (1949) by Abel Prize winner John Milnor by on Total Curvature of Knots.. Yes.. at least 73 years back.  

5. There might be possible applications of TopologyGAN & CurvGAN in Pointwise Convergence of the Schrödinger Flow which is portrayed & further researched in the following paper - https://arxiv.org/abs/1907.11192