Alex Weekes

Alex Weekes's picture
Phd: University of Toronto 2016

Area of Research:

Research Interests

My research is focused on the representation theory of reductive groups and their Lie algebras, especially through associated algebraic geometry -- for instance, through the study of the affine Grassmannian and of quiver varieties. I am also interested in related combinatorics combinatorics, for example via crystals and their various realizations.

Lately I have studied 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 provides a different perspective from which to view constructions and results from geometric representation theory, along with the potential for new directions of study.

Awards

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

Recent Publications

  • Joel Kamnitzer, Dinakar Muthiah and Alex Weekes, "On a reduced conjecture for spherical Schubert varieties and slices in the affine Grassmannian", Transformation Groups, 23, 2018, 707-722, 1604.00053
  • Michael Finkelberg, Joel Kamnitzer, Khoa Pham, Leonid Rybnikov and Alex Weekes, "Comultiplication for shifted Yangians and quantum open Toda lattice", Advances in Mathematics, 327, 2018, 349-389, 1608.03331
  • Joel Kamnitzer, Dinakar Muthiah, Alex Weekes and Oded Yacobi, "Reducedness of affine Grassmannian slices in type A", Proceedings of the American Mathematical Society, 146, 2018, 861-874, 1611.06775
  • 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
  • "On category O for affine Grassmannian slices and categorified tensor products", Joel Kamnitzer, Peter Tingley, Ben Webster, Alex Weekes, Oded Yacobi, 1806.07519
  • "The equations defining affine Grassmannians in type A, and a conjecture of Kreiman, Lakshmibai, Magyar and Weyman", Dinakar Muthiah, Alex Weekes, Oded Yacobi, 1708.06076
  • "Crystals and monodromy of Bethe vectors", Iva Halacheva, Joel Kamnitzer, Leonid Rybnikov, Alex Weekes, 1708.05105
  • "A quantum Mirkovic-Vybornov isomorphism", Ben Webster, Alex Weekes, Oded Yacobi, 1706.03841
  • Appendix to A. Braverman, M. Finkelberg and H. Nakajima, "Coulomb branches of 3d N = 4 quiver gauge theories and slices in the affine Grassmannian", Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, Alex Weekes, 1604.03625
  • "Highest weights for truncated shifted Yangians and product monomial crystals", Joel Kamnitzer, Peter Tingley, Ben Webster, Alex Weekes, Oded Yacobi, 1511.09131

Seminars

  • "The nonabelian Higgs and Coulomb branches", University of Oregon
  • "Highest weights and cohomology rings", Ohio State University
  • "A quantum Mirkovic-Vybornov isomorphism", Carleton University
  • "Crystals and shift of argument algebras", University of Queensland
  • "Introduction to Coulomb branches (3 lectures)", University of Sydney
  • "An introduction to Nakajima quiver vareties", Australian National University
  • "Cohomology of quiver varieties, and a conjecture of Hikita", Research Institute for Mathematical Sciences
  • PIRSA:18030061, PSI 2017/2018 - Quantum Integrable Models - Lecture 3, 2018-03-21, PSI 2017/2018 - Quantum Integrable Models (Costello & Weekes)
  • PIRSA:18030060, PSI 2017/2018 - Quantum Integrable Models - Lecture 2, 2018-03-20, PSI 2017/2018 - Quantum Integrable Models (Costello & Weekes)
  • PIRSA:18030059, PSI 2017/2018 - Quantum Integrable Models - Lecture 1, 2018-03-19, PSI 2017/2018 - Quantum Integrable Models (Costello & Weekes)
  • PIRSA:18020104, Kreiman-Lakshmibai-Magyar-Weyman Ideas, 2018-02-12, Mathematical Physics
  • 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