Hamiltonian Systems

I will introduce triple crossing diagram (TCD) maps-certain projective configurations of points and lines-which provide a unifying framework for a range of constructions in discrete differential geometry, discrete integrable systems, total positivity and graph embeddings. As an application, I will show how this framework can be used to show that various geometric discrete integrable systems such as the pentagram map are cluster integrable systems. Based on joint works with Niklas Affolter (TU Wien), Max Glick (Google) and Sanjay Ramassamy (CNRS).