In this course I will present some advanced topics related with gauged linear sigma models (GLSM). I will mainly focus on how to get derived equivalences and functors between triangulated categories related to CY geometries, mathematically, this  is a generalization of Orlov’s equivalence and in physics  terms this is about correspondences of B-brane categories as we move on the quantum Kahler moduli space.  I will also present extensions of these results to non-CY cases. As time allows I will also present other modern topics such as Seiberg-like dualities and the incorporation of B-type domain walls on GLSMs and their categorical interpretation.

E-mail：mromoj@tsinghua.edu.cn

Some knowledge of 2d (2,2) supersymmetric QFTs  is required as well as some basic algebraic geometry. No previous knowledge on categories will be assumed. 

For the basics:

- K. Hori et al. Mirror Symmetry vol. 1

Physics references:

-  P. Aspinwall ‘D-branes on Calabi-Yau Manifolds’ hep-th/0403166

- M. Herbst, K. Hori and D. Page ‘Phases of N=2 Theories in 1+1 Dimensions with Boundary’ hep-th/0803.2045

Math references:

- M. Ballard, D. Favero and L. Katzarkov ‘Variation of Geometric Invariant Theory quotients and derived categories’ 1203.6643 [math.AG]

- D. Halpern-Leistner ‘The Derived Category of a GIT Quotient’ 1203.0276 [math.AG]