Welcome! I'm an independent researcher at the University of Graz (via an Austrian Science Fund grant), and my research is in the intersection of algebra, geometry, and physics.
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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:
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Some slides and videos:
- Slides for the Joint Theory Seminar, University of Vienna & TU Wien
- Talk at ESI
- Talk with slides at the NYC noncommutative geometry seminar
- 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:
Dimer/ghor algebras 1, Dimer/ghor alg 2, Dimer/ghor alg 3, Dimer/ghor alg 4
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While at the University of Graz, I've 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).
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