Alex Weekes

I am a postdoctoral fellow at the Perimeter Institute. My research focuses on geometric and combinatorial representation theory. I am especially interested in the representations of reductive groups and their Lie algebras, as well as associated geometries and combinatorics - for example, relationships with affine Grassmannians and/or quiver varieties. I am also very interested in deformation quantizations of Poisson varieties and their associated module categories, and connections of all of the above to physics.

Previously, I was a graduate student in mathematics at the University of Toronto, where I received my PhD in 2016 under Joel Kamnitzer. Before that, I was an undergraduate at Carleton University where I studied under Yuly Billig.

My CV

Contact:

Email: aweekes@perimeterinstitute.ca

Office: 369

Research

My thesis can be found here.

Published and submitted articles, and preprints:

"The equations defining affine Grassmannians in type A, and a conjecture of Kreiman, Lakshmibai, Magyar and Weyman", with Dinakar Muthiah, and Oded Yacobi (available at arXiv:1708.06076)

"Crystals and monodromy of Bethe vectors", with Iva Halacheva, Joel Kamnitzer, and Leonid Rybnikov (available at arXiv:1708.05105)

"A quantum Mirkovic-Vybornov isomorphism", with Ben Webster and Oded Yacobi (available at arXiv:1706.03841)

"Reducedness of affine Grassmannian slices in type A", with Joel Kamnitzer, Dinakar Muthiah, and Oded Yacobi, to appear in Proceedings of the AMS (available at arXiv:1611.06775)

"Comultiplication for shifted Yangians and quantum open Toda lattice", with Michael Finkelberg, Joel Kamnitzer, Khoa Pham, and Leonid Rybnikov, to appear in Advances in Mathematics (available at arXiv:1608.03331)

"On a reducedness conjecture for orbit closures in the affine Grassmannian", with Joel Kamnitzer and Dinakar Muthiah, to appear in Transformation Groups (available at arXiv:1611.06775)

"Highest weights for truncated shifted Yangians and product monomial crystals", with Joel Kamnitzer, Peter Tingley, Ben Webster, and Oded Yacobi (available at arXiv:1511.09131)

"Yangians and quantizations of slices in the affine Grassmannian", with Joel Kamnitzer, Ben Webster, and Oded Yacobi, Algebra and Number Theory (2014), available from ANT (also available at arXiv:1209.0349)

Other:

Joint appendix to A. Braverman, M. Finkelberg and H. Nakajima, "Coulomb branches of 3d N=4 quiver gauge theories and slices in the affine Grassmannian", with Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, and Ben Webster (available at arXiv:1604.03625)

Some work in preparation:

"Springer theory for Coulomb branches", with Justin Hilburn, Joel Kamnitzer, and Allen Knutson

Seminars

This year I am coorganizing the Mathematical Physics seminar at PI, along with Theo Johnson-Freyd. A list of upcoming talks, as well as videos of previous talks, can be found here.