Welcome! I'm an independent researcher at the University of Graz, and my research is in the intersection of algebra, geometry, 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. This strange geometry has allowed me 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. This 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.

I use this new geometry in the following research areas:​

   • To study the geometry and representation theory of dimer and ghor algebras, which are defined by oriented graphs in surfaces;

   • To merge gravity and quantum theory using the geometric features of a nonnoetherian spacetime; and

   • To generalize noncommutative resolutions (which are typically special endomorphism rings with nice homological properties) to singularities that are nonnoetherian.

Some slides and videos: 

- Slides for my recent talk "Particle masses and degenerate spacetime metrics" at the Tux Workshop on Quantum Gravity (2025)

- Slides for the Joint Theory Seminar, University of Vienna & TU Wien (2024)

- Talk at ESI (2023)

- Course on dimer algebras for "Cluster algebras and representation theory" at the Isaac Newton Institute for Mathematical Sciences in Cambridge (2021) with videos here and slides here.