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- Alex Weekes

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Phd: University of Toronto 2016

Area of Research:

My research is focused on the representation theory of reductive groups and their Lie algebras, especially through associated algebraic geometry (for instance, through studying the affine Grassmannian and quiver varieties) and combinatorics (for instance, crystals and their various realizations).

I am also interested in connections between representation theory and physics, with a focus on the moduli spaces of vacua associated to 3d N=4 supersymmetric gauge theories, and their quantizations. For example, slices in the affine Grassmannian (resp. Nakajima quiver varieties) arise as Coulomb (resp. Higgs) branches for quiver gauge theories. Gauge theory thus provides a different perspective from which to view constructions and results from geometric representation theory, along with the potential for new directions of study.

- Queen Elizabeth II Graduate Scholarship, Government of Ontario
- Ontario Graduate Scholarship, Government of Ontario
- Alexander Graham Bell Canada Graduate Scholarship, NSERC

- Michael Finkelberg, Joel Kamnitzer, Khoa Pham, Leonid Rybnikov and Alex Weekes, "Comultiplication for shifted Yangians and quantum open Toda lattice", Advances in Mathematics, 1608.03331
- Joel Kamnitzer, Dinakar Muthiah, Alex Weekes and Oded Yacobi, "Reducedness of affine Grassmannian slices in type A", to appear in Proceedings of the American Mathematical Society, 1611.06775
- Joel Kamnitzer, Dinakar Muthiah and Alex Weekes, "On a reduced conjecture for spherical Schubert varieties and slices in the affine Grassmannian", to appear in Transformation Groups, 1604.00053
- Joel Kamnitzer, Ben Webster, Alex Weekes and Oded Yacobi, "Yangians and quantizations of slices in the affine Grassmannian", Algebra and Number Theory, Vol. 8, 2014, 857-893, 1209.0349
- "Crystals and monodromy of Bethe vectors", with Iva Halacheva, Joel Kamnitzer and Leonid Rybnikov, 1708.05105
- "The equations defining affine Grassmannians in type A, and a conjecture of Kreiman, Lakshmibai, Magyar and Weyman", with Dinakar Muthiah and Oded Yacobi, 1708.06076
- "A quantum Mirkovic-Vybornov isomorphism", with Ben Webster and Oded Yacobi, 1706.03841
- "Highest weights for truncated shifted Yangians and product monomial crystals", with Joel Kamnitzer, Peter Tingley, Ben Webster and Oded Yacobi, 1511.09131

- "The nonabelian Higgs and Coulomb branches", University of Oregon
- "Highest weights and cohomology rings", Ohio State University
- "A quantum Mirkovic-Vybornov isomorphism", Carleton University
- "An introduction to Nakajima quiver vareties", Australian National University
- "Introduction to Coulomb branches (3 lectures)", University of Sydney
- "Crystals and shift of argument algebras", University of Queensland
- "Cohomology of quiver varieties, and a conjecture of Hikita", Research Institute for Mathematical Sciences
- PIRSA:16090061, Shifted Yangians, loop groups, and (co)products, 2016-09-29, Mathematical Physics
- PIRSA:16010082, Symplectic duality and a presentation of the cohomology of Nakajima quiver varieties, 2016-01-28, Mathematical Physics

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