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

Abstract: 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 curves. In this report, the first examples of operators of rank 2 corresponding to trigonal spectral curves of genus 3 will be described.