Speaker: V.E. Adler (L.D. Landau ITP)

Title: Around 3D-consistency

Date and time:  11.12.2024, 17:00 (GMT +03:00)

Abstract: The 3D-consistency property is usually formulated as the Consistency-Around-a-Cube for discrete equations on a square lattice (quad-equations). However, this property can be extended to some other types of equations, including continuous ones. In my talk, I will show that a multidimensional lattice governed by consistent quad-equations can carry some derivations that preserve this lattice and commute with each other. They are described by continuous equations of the KdV type and differential-difference equations of the Volterra lattice and dressing chain types, which are no less important objects than quad-equations. In principle, these equations can be obtained from quad-equations by continuous limits, but in my talk I will move in the opposite direction, interpreting quad-equations as the superposition formula for B\"acklund transformations. Particular attention will be paid to the interpretation of Volterra-type equations as negative symmetries for KdV-type equations and to the definition of 3D-consistency property for these symmetries.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com