Timeline for Gromov-Witten and integrability.

6 events

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Dec 13, 2016 at 21:12	comment	added	Di Yang		Then due to tau symmetry + the Hamiltonian structure, one can show existence of tau function of an arbitrary solution. The tau function of the solution is uniquely determined up to an exponential of a linear function in the couplings. This linear function can be further fixed by the string equation. Now take the solution to be the so-called topological solution, then from the above way one obtains the ``partition function" (as the tau function).
Dec 13, 2016 at 21:10	comment	added	Di Yang		Existence of a Hirota-type formulation is still an open question for the Dubrovin--Zhang integrable hierarchy. Tau function of the Dubrovin--Zhang hierarchy comes from tau-symmetry. Dubrovin--Zhang's construction uses loop equation and quasi-triviality transformation in the principal hierarchy. Their construction keeps the Hamiltonian structure and tau symmetry property. However, one needs to check ``polynomiality" of the Hamiltonian structure which was later proved by Buryak--Posthuma--Shadrin.
Dec 5, 2016 at 21:52	comment	added	Sasha		Thank you for the answer. Is a bilinear Hirota-type formulation of the Dubrovin--Zhang integrable hierarchy known?
Nov 21, 2016 at 22:15	review	Late answers
Nov 21, 2016 at 22:22
Nov 21, 2016 at 22:00	review	First posts
Nov 21, 2016 at 22:42
Nov 21, 2016 at 21:58	history	answered	Di Yang	CC BY-SA 3.0