Ricci Flow, Nash Entropy, Cigar Soliton, Lie groups, Sobolev inequality

Hey readers,

Its 3 AM.. Friday Night... dark outside.. I miss Sweet-greens, Joes and Juice, Roti in Chicago.. Wait.. actually I miss everything and everyone in Chicago. Coming back to Ricci Flow... If my fans/followers/readers remember from 2011.. I had written a lot of orchestrations on 

• Lie groups, 
• Ricci Flow, 
• Nash Entropy of Ricci Flow & 
• Convergence

..And also possibility of applying machine learning methods such as CNNs on or on Calabi Yau & Sasaki-Einstein base manifolds.. (Yeah Yeah.. just like Geoff Hinton's Boltzmann Machine's 1970s paper, I wanted to apply in drug discovery in 2006..which was a great project btw..)... 

Here are few papers which my readers might like -

1. One the Diagonalization of the Ricci Flow on Lie Groups ( https://arxiv.org/abs/1110.4003 ) - This is an amazing paper by Cynthia Will on Nilpotent Lie algebra which finally provides a good example on a left-invariant metric on a 4-dimensional nilpotent Lie group whose Ricci flow is not diagonal. Also, please see a special mention of

• Asymptotic behavior of some nil-solitons
• Ricci operator & Jacobi identity

2. On the Chern-Ricci Flow and Its Solitons for Lie Groups ( https://arxiv.org/pdf/1311.0832.pdf )- One of the best things about this paper is use of Levi Civita connection & Chern connection 

By the way, Just to show how important Levi Civita was - One day Einstein wrote to Levi Civita - I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot). Off course, The opinion expressed by Einstein was not shared by many of the Levi-Civita contemporaries and also by many scientists nowadays. Indeed many do not believe that the abstraction required to use the absolute tensor calculus is justified by the obtained results, as these last can be deduced by classical and simpler procedures.. 

• Book - When Einstein Walked with Godel - https://www.goodreads.com/book/show/36794489-when-einstein-walked-with-g-del
• Levi-Civita,Tullio Francesco Dell’Isola, Emilio Barchiesi, Luca Placidi - https://hal.archives-ouvertes.fr/hal-02099661/document

3. A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy - Special thing about this paper is ( https://arxiv.org/pdf/2107.01419v1.pdf )-

- Lie derivative
- Nash Entropy of Ricci Flow
- Convergence of Nash Entropy
- Cigar Soliton - Witten's black hole 

(if you remember Perelman's 2nd paper on Poincare conjecture in the series of 3 papers which mentioned blackholes in the Notes.. this is what has happened in last 9 years - Cigar Soliton & Witten's black hole)..