Ricci Flow, Economics & a brilliant blog by Gita Gopinath

Hey readers,

It's 2:40 AM on Saturday night. Thanks for reading my DataHulk blog. I was glad to see 20,000 views in a single night on my last post - Yang Mills, Vector bundles, Quantum Information Geometry & Fisher-Bures Adversary Graph Convolutional Networks etc. And Yes, I noticed Terence Tao wrote his blog on the same day talking about Sphere Pinching paper (Smart people think alike I guess) - https://terrytao.wordpress.com/2022/02/08/perfectly-packing-a-square-by-squares-of-nearly-harmonic-sidelength/ 

I used to write this blog 12 years back to motivate everyone to learn math, data & AI folks. By the way, I have an exciting blogpost today which might change the way some of my followers look at economics (I know.. I know.. I promised to write about Spin Neural Networks, diffusion and capsule networks in my last blog.. which I will write later). 

1. Ricci Flow & Economics (And why Gita Gopinath's sentence in her blog is genius) - 

Here is an interesting paper followed by 2013-14 Ricci Flow & Poincare Conjecture in topology of Social Networks & Information Geometry article ( https://www.kdnuggets.com/2014/05/poincare-conjecture-perelman-topology-social-networks.html ).... Ricci curvature: An economic indicator for market fragility and systemic risk - https://www.researchgate.net/publication/303600815_Ricci_curvature_An_economic_indicator_for_market_fragility_and_systemic_risk which is an analysis based on geometric feature extraction on network data of daily returns from a set of stocks & market topology comprising the Standard and Poor’s 500 (S&P 500) over a 15-year span to highlight the fact that corresponding changes in Ricci curvature, is negatively correlated to increases in network fragility. 

network, is negatively correlated to increases in network fragility. To illustrate this insight, we examine daily

returns from a set of stocks comprising the Standard and Poor’s 500 (S&P 500) over a 15-year span to highlight

the fact that corresponding changes in Ricci curvature constitute a financial “crash hallmark.”

  

Average Ricci curvature over a 15-year span of the S&P 500 - Choosing a window of T = 22 days, we see that curvature captures several financial crashes and show that, on average, market behavior is fragile.

2. Gita Gopinath - 

Here is an interesting & brilliant blog (April 2021) by Gita Gopinath on divergent recovery -
Managing Divergent Recoveries - https://blogs.imf.org/2021/04/06/managing-divergent-recoveries/ speaking about 

1. Financial risks, 

2. Financial stability risks using macro-prudential tools, 

3. Cross-country gaps, global poverty reduction, 

4. Emerging markets, 

5. Divergent recovery paths, 

6. High degree of uncertainty and developing economies 

7. International liquidity

8. Liquidity protection

9. Debt restructuring 

10. financial stability risks using macro-prudential tools

11. Withdrawn loan payments, firm insolvencies

12. Cross-border profit shifting

which reminded me of network entropy, nodal entropy, geodesics curvature & divergence mentioned in the Sandhu's paper - Ricci curvature & Ricci Flow: An economic indicator for market fragility and systemic risk and my KDnuggets article on which intended to perform Ricci Flow on Social network analysis & information economics.