Ricci Flow, Geomstats, Lie Groups on Julia & EconoPhysics (and belated Happy Valentines day)

Hey Readers,

Again... thanks for reading my blog. I have been super-busy with lot of work. But,  30,000 views in single night is pretty cool. It is 9 PM in the evening, I just came from my walk in Maryland and I am on a mission to motivate everyone to learn more about data, AI, Math, Topology and so on. I should give more guest lectures when I get time.. but, for now please have a look at wonderful lecture by Geometric Statistics in Machine Learning GeomStats with Nina Miolane - https://www.youtube.com/watch?v=3yNInHuIWlY&t=1251s 

Hence, the next blogpost in the night on Ricci Flow (the topological concept that Grigori Perelman used to prove Poincare Conjecture) and Network Geometry.

1. Network geometry and market instability -https://royalsocietypublishing.org/doi/10.1098/rsos.201734

This paper talks about Time series of log-returns over a 32-year period (1985–2016) with network of stocks with 

1. Ollivier–Ricci (ORE), 
2. Forman–Ricci (FRE), 
3. Menger–Ricci (MRE), 
4. Haantjes–Ricci (HRE) 
5. Algebraic topological aspects, such as the homology groups and Betti numbers

minimum risk Markowitz portfolio of all the stocks, to better understand tipping points, systemic risk and resilience in financial networks, and enable us to develop monitoring tools required for the highly interconnected financial systems and perhaps forecast future financial crises and market slowdowns with use of Python package NetworkX (Yeah.. I used to use a lot of R, SAS, SQL, Cytoscape, Python in 2006 but Julia became my favorite language in 2012).

You can also check out few packages such as 

1. TheanoGeometry ( https://arxiv.org/abs/1712.08364 )- Riemann, Ricci and scalar curvature & geodesics  
2. Geomstats ( https://arxiv.org/abs/2004.04667 )   
3. McTorch  - McTorch, a manifold optimization library for deep learning ( https://arxiv.org/abs/1810.01811 ) 
4. Pymanopt: A Python Toolbox for Manifold Optimization using Automatic Differentiation ( https://arxiv.org/abs/1603.03236 )
5. Topological Entropy for Geodesic Flows under a Ricci Curvature condition: Jacobi field, Ricci curvature, topological entropy, tangent bundle, Negative Ricci curvature, isometry group and Injectivity radius - ( https://www.ams.org/journals/proc/1997-125-06/S0002-9939-97-03780-5/S0002-9939-97-03780-5.pdf )
6. And how can I forget my new favorite Julia for manifold Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds - a fast and easy to use library of Riemannian manifolds and Lie groups - ( https://arxiv.org/pdf/2106.08777.pdf )