Multiple cluster structures for geometric dynamics

Clusters and Geometry
Event time: 
Friday, April 9, 2021 - 1:00pm
Sanjay Ramassamy
Speaker affiliation: 
Institut de Physique Théorique (CEA Saclay)
Event description: 

Triple crossing diagrams (TCDs) arise as special cases of planar
bipartite graphs where all the black vertices have degree 3. We define
the notion of a TCD map as an assignment of a point in CP^n to every
white vertex, such that the points at the three neighbors of any black
vertex are aligned. One can associate to any TCD map two collections of
variables that both evolve as cluster X variables under some local
moves. Even more cluster structures appear when considering geometric
operations such as intersecting the lines of a TCD map with a
hyperplane. TCD maps provide a general framework for several geometric
dynamics having a cluster structure. In particular we identify a cluster
structure for Q-nets and several other objects from discrete
differential geometry.

This talk is based on joint projects with Niklas Affolter (TU Berlin),
Max Glick (Google) and Pavlo Pylyavskyy (University of Minnesota).