Department of Mathematics

Algebra

  •  Leonid Chekov, MSU
  •  Topogical Recursion 3
  •  04/05/2017
  •  3:00 PM - 3:50 PM
  •  C304 Wells Hall

I will descirbe the newly developed abstract TR authored by Kontsevich and Soibelman in 2017. The main statement of the abstract TR (as presnted in the very recent paper by Andersen, Borot, L.Ch. and Orantin) is the inverse of TR for $W_s^{(g)}$: given a TR based on the set of abstract variables $\xi_k$ (which in the geometrical case can be identified with Krichever-Whitham 1-differentials based at zeros of $dx$) and imposing a single additional restriction of a total symmetricity of $W_s^{(g)}$ for all $g$ and $s$ we have a set of operators $L_k$ linear-quadratic in $\{\xi_r, \partial_{\xi_r}\}$ (one operator per one variable) all of which annihilate the partition function $Z=e^F$ that is the generating function for $W_S^{(g)}$. I present different examples of this construction including those not based on geometrical spectral curves.

 

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