Timeline for Why is there a connection between enumerative geometry and nonlinear waves?
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 23:28 | comment | added | Tom Copeland | The viscous Burgers and the KdV equations are intimately related as noted in The Elliptic Lie Triad tcjpn.wordpress.com/2015/10/12/… | |
| Mar 19, 2021 at 21:52 | comment | added | Tom Copeland | See also "Algebro-Geometric Solutions of the Generalized Virasoro Constraints" by Martin (arxiv.org/abs/1110.0729) and "Enumerative geometry, tau-functions and Heisenberg-Virasoro algebra" by Alexandrov (arxiv.org/abs/1404.3402). | |
| Sep 30, 2020 at 19:44 | comment | added | Tom Copeland | From "The Magic Wand Theorem of A. Eskin and M. Mirzakhani" by Zorich (arxiv.org/abs/1502.05654): In hyperbolic geometry, Mirzakhani established asymptotic formulas and statistics for the number of simple closed geodesics on a Riemann surface of genus g. She next used these results to give a new and completely unexpected proof of Witten’s conjecture, a formula for characteristic classes for the moduli spaces of Riemann surfaces with marked points. | |
| Sep 17, 2020 at 21:33 | comment | added | Tom Copeland | It's always interesting to monitor the social dynamics at MO if only to keep grounded in reality. It has been more than five years since I've updated this entry yet someone/thing has just this day upvoted Yuan's comment. Just a word of advice to the creature: Avoid the daylight. Hope you can find a big enough bridge, and LMK which one that is cuz you must be extra 'special'. | |
| Feb 25, 2020 at 17:40 | comment | added | Tom Copeland | See also "Remarks on intersection numbers and integrable hierarchies. I. Quasi-triviality" by Dubrovin and Yang arxiv.org/abs/1905.08106 | |
| Nov 12, 2018 at 17:15 | comment | added | Tom Copeland | See also "Catalan Numbers and Branched Coverings by the Riemann Sphere" by Goldberg, "Rational functions with prescribed critical points" by Scherbak, and "Enumerative Real Algebraic Geometry" by Sottile. | |
| Oct 27, 2018 at 18:29 | comment | added | Tom Copeland | From the article on Mirzakhani in the Nov AMS Notices (pg. 1239): Witten’s posited relations are expressed in terms of the Virasoro Lie algebra generated by differential operators $ L_n= -x^{n+1} \frac{d}{dx}$ for $n > −2$, with commutators $[L_n,L_m] = (n-m) L_{n+m}$. ... Mirzakhani was able to decipher the mystery ... . Theorem 6 (The Witten-Kontsevich conjecture). The moduli volume recursion gives the Virasoro constraints. | |
| Oct 22, 2015 at 17:22 | comment | added | Qiaochu Yuan | Tom, please stop constantly editing this answer; you bump it to the top every time you do so. If you have so much to say about this topic then write a blog post and constantly edit that instead. | |
| Oct 22, 2015 at 16:59 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Elimunated last paragraph due to error in ref or interpretation
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| Oct 18, 2015 at 22:57 | history | edited | Tom Copeland | CC BY-SA 3.0 |
A little history,reduction of KdV to Burgers, and another link to Grassmannians
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| Oct 17, 2015 at 16:25 | comment | added | Tom Copeland | A similar situation occurs with the hypercubes (oeis.org/A038207) and a Fokker-Planck equation. | |
| Oct 16, 2015 at 22:00 | history | edited | Tom Copeland | CC BY-SA 3.0 |
General connection to Eulerians
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| Oct 12, 2015 at 21:50 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Another example
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| Jun 5, 2015 at 19:41 | history | edited | Tom Copeland | CC BY-SA 3.0 |
author's name corrected
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| May 1, 2015 at 0:53 | history | edited | Tom Copeland | CC BY-SA 3.0 |
corrected ODE and alternative formula for g(z)
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| Apr 13, 2015 at 21:14 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Corrected notation
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| Dec 26, 2014 at 23:22 | comment | added | Tom Copeland | See also Friedrich and McKay, "Formal groups, Witt vectors and free probability" (page 5). | |
| Nov 27, 2014 at 11:28 | comment | added | Tom Copeland | Also see "Bernoulli numbers and solitons" by G Rzadkowski tandfonline.com/doi/pdf/10.1142/S1402925110000635 The connections of the Bernoulli numbers to topology are well-known. | |
| Sep 23, 2014 at 2:58 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Elaboration
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| Sep 22, 2014 at 14:56 | history | answered | Tom Copeland | CC BY-SA 3.0 |