Seminar on geometry, symmetry, and physics, Fall 2018

(aka mirror symmetry/related topics)

Thursdays (usually) 1:30-2:30 pm in Serin Lab E372

Organized by Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward

September 11 Laura Starkston, UCSD. Symplectic Isotopy Problems.

Abstract: We will discuss some problems and results about symplectic surfaces in 4-manifolds, particularly in the complex projective plane. The main question is to classify symplectic surfaces up to symplectic isotopy. If the surface has singularities, we restrict the isotopies to the class of surfaces with the same model singularities.

September 20 No talk

September 27 Homological mirror symmetry for Grassmannians: rectangles

Marsh-Rietsch proposed Landau-Ginzburg mirrors for the complex Grassmannians Gr(k,n), building on Peterson's work on the quantum cohomology of flag varieties. We confirm that they satisfy homological mirror symmetry when n=p prime. The proof describes an explicit correspondence between Lagrangian branes generating the Fukaya category of Gr(k,p) and sheaves generating the category of singularities of the mirror potential. The assumption n=p forces the singularities to lie in a special cluster chart of the mirror, that we call rectangular, by an argument that combines arithmetic properties of sums of roots of unity and Stanley's hook-content formula for the number of semi-standard tableaux on a Young diagram.

October 4 Yoel Groman, Columbia (?)

October 11

October 18

October 25

November 1

November 8

November 14 (SPECIAL DAY: Wednesday) Dmitry Tonkonog, Berkeley.

November 29