Elana Kalashnikov

Elana Kalashnikov is an Assistant Professor in the Department of Pure Mathematics at the University of Waterloo. Her research focuses on algebraic geometry, with particular interests in mirror symmetry, Fano varieties, quiver moduli spaces, and geometric invariant theory. Prior to joining Waterloo in 2021, she held research positions at Harvard University and the Higher School of Economics, and earned her Ph.D. in Mathematics in 2019 from Imperial College London.

I am interested in combinatorial aspects of mirror symmetry and the classification of Fano manifolds.

• 2019, Doctorate, Mathematics, Imperial College London, UK

• 2014, MSc, Mathematics and the Foundations of Computer Science, Oxford University, UK

• 2013, BA Honours in Mathematics, University of Alberta, Canada

• MATH 117 - Calculus 1 for Engineering
  • Taught in 2023
• MATH 135 - Algebra for Honours Mathematics
  • Taught in 2021
• MATH 146 - Linear Algebra 1 (Advanced Level)
  • Taught in 2022, 2026
• PMATH 965 - Topics in Geometry and Topology
  • Taught in 2023, 2026

* Only courses taught in the past 5 years are displayed.

• L. Chen and E. Kalashnikov. Littlewood–Richardson rules from quivers for two-step flag varieties (with an Appendix by Ellis Buckminster, Linda Chen and Elana Kalashnikov), arXiv:2502.15126. 47 pages

• Appendix of: E. Fatighenti, F. Tanturri, F. Tufo, On the geometry of some quiver zero loci Fano fourfolds (with an appendix by E. Kalashnikov and F. Tufo) arXiv:2406.04389.

• L. Heuberger, E. Kalashnikov. Quiver semi-invariants and SAGBI bases, arXiv:2312.17224. 37 pages. Accepted into the Journal of Algebraic Combinatorics.

• E. Kalashnikov. A toric degeneration of Kronecker moduli spaces, Journal of Algebra, Volume 686, 2026. pp 749-774.

• E. Kalashnikov, Laurent polynomial mirrors for quiver flag zero loci, Advances in Math- ematics, Volume 445. 2024.

• Gu, W., Kalashnikov, E. A rim-hook rule for quiver flag varieties. Selecta Mathemat- ica, New Series 30, 51. 2024.

• Linda Chen and E. Kalashnikov. Quantum hooks and mirror symmetry for flag vari- eties, Mathematische Zeitschrift. 305, 28. 2023.

• T. Coates, C. Doran, and E. Kalashnikov. Unwinding toric degenerations and mirror symmetry for Grassmannians, Forum of Mathematics, Sigma, 10, E111. 2022.

• L. Chen, A. Gibney, L. Heller, E. Kalashnikov, H. Larson, W. Xu. On an equivalence of divisors on M0,n from Gromov–Witten theory and conformal blocks. Transformation Groups 29, 561–590 (2024).

• E. Kalashnikov. A Plu ̈cker coordinate mirror for type A flag varieties. Bulletin of the London Mathematical Society, 54: 1308-1325. 2022.

• A. Chiodo and E. Kalashnikov. Mirror symmetry and automorphisms, Forum of Math- ematics, Sigma, 10, E52. 2022.

• A. Chiodo, E. Kalashnikov, and D. Veniani, Semi-Calabi–Yau orbifolds and mirror pairs, Advances in Mathematics 363. 2020.

• E. Kalashnikov Four dimensional Fano quiver flag zero loci, with an appendix joint with T. Coates and A. Kasprzyk. 475 Proceedings of the Royal Society A. 2019.

• E. Kalashnikov. Mirror symmetry for GIT quotients and their subvarieties, Accepted for Alberta-Saskatchewan Lectures on Algebraic Geometry in High-Energy Physics (Eds. T. Creutzig and S. Rayan), Fields Monograph Series, Springer-Nature (to ap- pear).