2 dimensional mirror symmetry has given a great effect both on mathematics and physics. The mirror symmetry has been extended to dimension three, giving more diversified results on geometry, physics and arithmetic.
More recently, it is extended even to dimension four.
So, this semester, we begin by briefly reviewing the three dimensional mirror symmetry on SYZ type(by Chan and Leung) symmetry and BFM(Berzukavnikov, Finkelberg, Mirkovic), BFN(Braverman, Finkelberg, Nakajima). And then we cover more on three dimensional mirror symmetry following the paper by Kapustin, Rozansky and Saulina and another papers by Teleman.
For four dimensional mirror symmetry, we study vertex operator algebra describing the Schur sector containing Higgs branch of 4d theory and the Coulomb branch of the effective 3d theory following the papers by Pang Shan, Dan Xie, Wenbin Yan, Yiwen Pan and Peihe Yang.
These lectures are self contained and what we cover this semester is connected to the "Relative Langlands Duality" of next semester.
