Introduction to random plane geometry

Virág Bálint (University of Toronto)


If lengths 1 and 2 are assigned randomly to each edge in Z2, what are the fluctuations of distances between far away points?

This problem is open, yet we know, in great detail, what to expect.

The directed landscape, a universal random plane geometry, provides the answer to such questions.

What is the directed landscape? What does it teach us about longest increasing subsequences in random permutations, about random polymers,
about models for spread of infection, about tetris, about random Schrodinger operators, and about cell biology?