Welcome! I work in the intersection of geometry, algebra, and physics.

A central theme of my research is a new kind of geometry I introduced for nonnoetherian coordinate rings in algebraic geometry. In this framework, algebraic varieties with nonnoetherian coordinate rings contain positive dimensional 'smeared-out' points. 

Using this strange geometry, I have been able to find unexpected structures in the geometric representation theory of a class of well-known quiver algebras that embed in surfaces called dimer algebras, where no geometry was thought to exist. 

The geometry also arises in the context of general relativity by incorporating my proposal that the preparation and measurement of a quantum system are simultaneous events. One consequence, for example, is that tangent spaces at different points of spacetime have different dimensions, and the projection from one tangent space to another corresponds to spin wavefunction collapse.