Adjunct faculty, Department of Physics, University of Waterloo, Waterloo, Canada
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I am interested in a variety of different topics including cosmology, particle physics, gravitational waves, black holes, and non-standard crystals ("choreographic crystals" and quasicrystals).
Several topics particularly close to my heart have formed a running theme in my research in recent years:
1) I would like to understand where the unexplained structures and patterns in the standard model of particle physics come from. See my paper on "The Standard Model, the Exceptional Jordan Algebra, and Triality" (arxiv.org/abs/2006.16265).
2) The early universe was remarkably simple and symmetrical. What is the correct explanation? Recently, my collaborators and I proposed a new cosmological model, the "CPT-Symmetric Universe," in which the universe before the bang is the CPT mirror image of the universe after the bang. We have presented some of the observational predictions of this idea, and are currently working out others. See our original paper "CPT-Symmetric Universe" in Physical Review Letters (arxiv.org/abs/1803.08928).
3) I am fascinated by the Penrose tiling (and its less-well-known decoration by "Ammann bars") -- both because of its mathematical beauty, and because of its connections to physics (e.g. as a so-far unexploited tool for discretizing scale-invariant physical systems). To find all analogous patterns (in two dimensions or higher), I have developed a deeper perspective in which these patterns originate from special pairs of reflection groups (which I call "Coxeter pairs"). An initial version of this story is described in my paper "Coxeter Pairs, Ammann Patterns and Penrose-like Tilings" (arxiv.org/abs/1608.08215), and a more complete version will be described in a forthcoming paper.