Algebra Seminar: Dimer models, their stability spaces and matching cones

Abstract: Dimer models on the torus encode birational geometric information over 3-dimensional Gorenstein toric singularities. This geometry is explicitly recovered via moduli of \theta-stable representations of the dimer algebra A. Understanding the space of stability conditions and how changes in stability affect the geometry is therefore an important task.

In this talk, I will give an overview of the background, including dimer models and quiver GIT. The main focus will be a new approach to construct the wall-and-chamber structure of the stability space. For this, we use certain lattice cones arising from perfect matchings in the dimer model. I will show some applications of this construction, and present many open problems.

This talk is based on work in progress with Yusuke Nakajima.

This seminar is held on Zoom: https://uu-se.zoom.us/j/64555726999, (please contact the organiser for passcode)

This is a seminar in our algebra seminar series.