On commuting differential operators of rank 2 corresponding to trigonal spectral curves of genus 3

Construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications to soliton theory. Operators of rank 1 in the case of smooth spectral curves were found by Krichever. The problem of constructing operators of rank $l > 1$ has not been solved in the general case. In all known examples of such operators, the spectral curves are hyperelliptic. In this report, the first examples of operators of rank 2 corresponding to trigonal spectral curves of genus 3 will be described.

The talk will be streamed through “Kontur Talk”: https://imsoran.ktalk.ru/ogsac0ijeetj.