Special Colloquium

Elana Kalashnikov, Harvard University

"Quiver flag varieties and mirror symmetry"

The classification of Fano varieties is one of the major open problems in algebraic geometry: to date, Fano varieties are only classified up to dimension three. Based on what is known of the classification so far, most small dimensional Fano varieties are expected to be subvarieties of either toric varieties or quiver flag varieties.  I'll discuss what is known of the four dimensional landscape, including the new Fano fourfolds found in my work with Coates and Kasprzyk.  One of the most promising tools for classifying Fano varieties in any dimension is mirror symmetry, which suggests that Fano classification is equivalent to the classification of certain Laurent polynomials, an entirely combinatorial problem. Laurent polynomial mirrors for complete intersections in toric varieties are known by work of Givental, Hori-Vafa, and Lian-Liu-Yau.  I'll discuss my work constructing Laurent polynomial mirrors for quiver flag varieties and their subvarieties, using tools ranging from toric degenerations to quantum cohomology and the Abelian/non-Abelian correspondence. 

A post-colloquium meet and greet will be held at 2:00 pm using the same Zoom meeting link.

Zoom meeting: https://zoom.us/j/99884322951?pwd=aTFMWkhLZDhZbHl5bUVTa1hBRUZhUT09