Office 209, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, CANADA

rayan (at) math.usask.ca | 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**

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**.

**Papers**

- June 2018: My recent paper,
**Geodesics on a Kerr-Newman-(anti-)de Sitter instanton**, written with my student A. Lindberg, now appears in*Journal of Geometry and Physics*. - May 2018: My recent paper,
**Twisted argyle quivers and Higgs bundles**, written with my student E. Sundbo, now appears in*Bulletin des Sciences Mathématiques*. - November 2017: My recent paper,
**Abstract integrable systems on hyperkähler manifolds arising from Slodowy slices**, written with P. Crooks, has been accepted by*Mathematical Research Letters*. - August 2017: A new preprint,
**Spectral curves for the triple reduced product of coadjoint orbits for SU(3)**, written with J. Hurtubise, L. Jeffrey, P. Selick, and J. Weitsman, is online. This paper has been refereed and accepted for the Hitchin Festschrift. - May 2017: A recent paper,
**A vanishing theorem for co-Higgs bundles on the moduli space of bundles**, written with I. Biswas, now appears in*Geometriae Dedicata*. - April 2017: A new preprint,
**Ginzburg-Landau equations on Riemann surfaces of higher genus**, written with D. Chouchkov, N. Ercolani, and I. M. Sigal, is online. - March 2017: My recent paper,
**The quiver at the bottom of the twisted nilpotent cone on**, has appeared in**P**^{1}*European Journal of Mathematics*.

**Talks**

- November 2018: I spoke in the
**Geometry & Analysis Seminar**in the University of Oxford's Mathematical Institute. The topic was the hyperkähler geometry of hyperpolygon spaces, including the problem of how to extend the McKay correspondence for certain non-ADE quivers. - June 2018: I gave the
**Ethel Raybould Colloquium**in the School of Mathematics & Physics at the University of Queensland. The talk was titled "Hitchin Systems in Mathematics and Beyond". - May 2018: I gave a talk in the
**Geometry Seminar**at Stanford University and two in the**Geometry and Topology Seminar**at Caltech. The talk at Stanford described a new construction of solutions to twisted**t=0**Kapustin-Witten equations on a compact Kaehler surface. The second talk at Caltech was similar, but was preceded by an introductory talk on Higgs bundles and Hitchin systems. - April 2018: I gave a talk in the
**Geometry / Topology Seminar**at Duke University and a talk in the**Analysis and Geometry Seminar**at Central Michigan University. Both were on asymptotics of hyperpolygon spaces. I also gave the**Colloquium**at SNOLab on what I consider to be spectacular interactions between geometry and physics in the 20th and 21st centuries! - 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 infiniite dimensional hyperkähler quotients, with a particular focus on hyperpolygons. - 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.