Assistant Professor, Department of Mathematics & Statistics, University of Saskatchewan
Office 209, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, CANADA

rayan (at) | Dept of Math & Stats | U of S


I am an Assistant Professor in the Department of Mathematics & Statistics at the University of Saskatchewan. My primary areas of research are:

  • algebraic geometry and topology of moduli spaces
  • geometric and topological techniques in mathematical physics
In particular, I am interested in moduli spaces of vector bundles and Higgs bundles on complex varieties, and in using these objects as tools for understanding other geometric structures. Wherever possible, I seek to reduce geometric and topological questions to combinatorial ones. For moduli spaces of Higgs bundles, this can be achieved by viewing Higgs bundles as representations of "quivers".

You can learn more about my research by clicking on the appropriate tab above, or you can go directly to my papers.

I am a member of the GEAR Network.


Recent Activity



  • February 2018: I gave the Colloquium in the Department of Mathematics at the University of Manitoba on the problem of finding finite-dimensional presentations of infinite dimensional hyperkähler quotients.
  • January 2018: I gave a talk in the Algebra & Geometry Seminar at the University of British Columbia on moduli spaces of hyperpolygons.
  • October 2017: I gave a talk at the Singular Geometry and Higgs Bundles in Sring Theory workshop at AIM in San Jose. The topic was the C*-action on the global nilpotent cone.
  • August 2017: I gave a talk at the Analysis of Gauge-Theoretic Moduli Spaces workshop at BIRS in Banff. The topic was the large-scale geometry of hyperpolygon spaces.
  • July 2017: I spent a week at the Mathematical Congress of the Americas in Montréal, where I gave talks in two scientific sessions.
  • June 2017: Together with H. Weiss, I gave a Master Class titled "Asymptotics of Higgs Bundles and Hyperpolygons" at the Centre for the Quantum Geometry of Moduli Spaces in Aarhus, Denmark. We gave six lectures each.
  • June 2017: I gave the Colloquium in the Department of Mathematics at the Christian-Albrechts Universität in Kiel, Germany. The topics were Higgs bundles and the Hitchin system.
  • February 2017: I gave the Colloquium at the Center for Mathematical Sciences and Applications at Harvard University. The topics were Higgs bundles and the Hitchin system.