Local to global principle in discrete mathematics

Seminar in Mathematics

Local to global principle refers to the idea that sometimes one can obtain a global understanding of a structure through local considerations. Local to global ideas are ubiquitous across discrete mathematics and beyond and are often useful in unexpected situations. We will discuss two such, very different topics where a certain local to global idea, namely the use of sublinear expansion, proved useful. The first concerns recent progress towards the classical Erdős-Gallai cycle decomposition conjecture, the second an essentially tight answer to the classical Erdős unit distance problem for "most" real normed spaces.