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
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
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