An Introduction to Grassmann integrals with applications to statistical mechanics

Grassmann integrals are integrals over functions on an exterior algebra. In the "Gaussian" case they can be expressed as a determinant or Pfaffian.


These integral arise in two dimensional Ising models and random tilings or dimers. 


We review the integrable "Gaussian" case as well as the interacting case and explain some conjectures about universality and their proof.



Member, School of Mathematics