LIMITS · Limits of Structures in Algebra and Combinatorics

The project is concerned with Borel and measurable combinatorics, sparsegraph limits, approximation of algebraic structures and applications tometric geometry and measured group theory. Our research will result inmajor advances in these areas, and will create new research directions incombinatorics, analysis and commutative algebra.The main research objectives are as follows.1) Study equidecompositions of sets and solve the Borel version of the Ruziewicz problem. 2) Give a new characterisation of amenable groups in terms of measurable Lovasz Local Lemma.3) Study rank approximations of infinite groups and commutative algebras.