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Welcome! I'm an independent postdoc at the University of Graz (via an Austrian Science Fund grant), and my research is in the intersection of algebra, geometry, and physics.

A central theme of my research is a new theory of geometry for nonnoetherian coordinate rings in algebraic geometry.  I have shown that algebraic varieties with such coordinate rings contain positive dimensional 'smeared-out' points.  This strange geometry arises in the context of spacetime by incorporating the idea that time passes if and only if something changes into general relativity.  I am currently investigating the possibility that certain quantum phenomena -- such as spin, entanglement, and state reduction -- are geometric features of a nonnoetherian spacetime.  My motivation for introducing this new geometry lies in three areas of research:

I gave a course on dimer algebras for the program “Cluster algebras and representation theory” at the Isaac Newton Institute for Mathematical Sciences in Cambridge in September.

Dimer/ghor algebras 1

Dimer/ghor algebras 2

Dimer/ghor algebras 3

Dimer/ghor algebras 4

(Videos of my lectures are here.)

While at the University of Graz, I have co-taught two graduate courses:

- Algebraic Geometry (using Bosch's book and CoxLittleSchenckJan2010.pdf (mimuw.edu.pl))

- Cluster Algebras and Categories (using 1-3 and 4-5, by Fomin, Williams, and Zelevinsky).