| Speaker: | konstantin aleshkin (Kavli IPMU) |
|---|---|
| Title: | Mirror Symmetry via Coherent-Constructible Correspondence for abelian GLSM. |
| Date (JST): | Fri, Nov 08, 2024, 15:30 - 17:00 |
| Place: | Seminar Room B |
| Abstract: |
Homological mirror symmetry (HMS) relates B-model branes (derived category of coherent sheaves) on one variety with A-model branes (a version of the Fukaya category) for its mirror. HMS for toric varieties is well-studied. In particular, it has a concrete description in terms of an "intermediate" category—the category of constructible sheaves on the mirror torus. This construction is known as the Coherent-Constructible Correspondence, developed by Bondal, Fang, Liu, Treumann, Zaslow, Kuwagaki, and others. This construction is explicit; in particular, in the Fano case, it was shown that the central charge of a B-brane (generating series of Gromov-Witten invariants) is equal to the central charge of the mirror A-brane (oscillatory integral). Data of a 2d N=2 supersymmetric Gauged Linear Sigma Model (GLSM) can be represented by a toric orbifold together with a superpotential (homogeneous holomorphic function). GLSM has been studied in physics for over 30 years, and recently general mathematical theories have been developing as well with many interesting questions remaining. I plan to explain how Coherent-Constructible Correspondence of the underlying toric variety can be used to study mirror symmetry for the GLSM, discuss the relation of central charges and examples. |
