### Mathematics Colloquium

# Yuri Suris

### (TU Berlin)

## "On integrability of variational problems"

** Date: ** |
Fri, September 18, 2015 |

** Time: ** |
15:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** After a brief introduction into the main concepts of variational (Lagrangian) systems, we discuss a recent development aiming to clarify, under what circumstances one should call a given variational system integrable (solvable). We propose a notion of a pluri-Lagrangian problem, which should be understood as an analog of multi-dimensional consistency for variational systems. This development has its remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. We discuss main features of pluri-Lagrangian systems in dimensions 1 and 2, both continuous and discrete, along with the relations of this novel structure to more standard notions of integrability.

*The colloquium is preceded by tea from 14:45 in the Resnikoff Mathematics Common Room, Research I, 127.*