In Preparation
Elana Kalashnikov. In Preparation. “A Plücker coordinate mirror for type A flag varieties”. main.pdf
Elana Kalashnikov. Submitted. “Laurent polynomial mirrors for quiver flag zero loci”. arXiv link
Alessandro Chiodo and Elana Kalashnikov. Submitted. “Mirror symmetry and automorphisms”. arXiv link
Elana Kalashnikov. Submitted. “Mirror symmetry for GIT quotients and their subvarieties”.Abstract
These notes are based on an invited mini-course delivered at the 2019 PIMS-Fields Summer School on Algebraic Geometry in High-Energy Physics at the University of Saskatchewan. They give an introduction to mirror constructions for Fano GIT quotients and their subvarieties, especially as relates to the Fano classification program. They are aimed at beginning graduate students. We begin with an introduction to GIT, then construct toric varieties via GIT, outlining some basic properties that can be read off the GIT data. We describe how to produce a Laurent polynomial mirror for a Fano toric complete intersection, and explain the proof in the case of P 2 . We then describe conjectural mirror constructions for some non-Abelian GIT quotients. There are no original results in these notes.
Wei Gu and Elana Kalashnikov. Submitted. “A rim-hook rule for quiver flag varieties”. arxiv
Alessandro Chiodo, Elana Kalashnikov, and Davide Cesare Veniani. 2020. “Semi-Calabi--Yau orbifolds and mirror pairs.” Advances in Mathematics, 363. arXiv link
Elana Kalashnikov. 5/15/2019. “Four dimensional Fano quiver flag zero loci (with an appendix by T. Coates, E. Kalashnikov, and A. Kasprzyk).” Proceedings of the Royal Society A, 475, 2225. Publisher's Version
Elana Kalashnikov. 2019. “Quiver flag varieties and mirror symmetry.” Imperial College London. kalashnikov-e-2019-phd-thesis.pdf