Presentation Date:
One of the central topics of the interaction between QFT and math is mirror symmetry for 2d theories. This theory has a more mysterious and exotic friend one dimension higher, sometimes called 3d mirror symmetry, which relates two 3-dimensional theories with N=4 supersymmetry. For roughly a decade, I struggled to understand this phenomenon without understanding what most of the words in the previous sentence meant. Eventually, I wised up and based on work of Braverman, Finkelberg, Nakajima, Dimofte, Gaiotto, Hilburn and others, I actually did learn a little bit, and will now try to explain to you what I learned. This knowledge has some interesting payoffs in the mathematics related to 3d theories, such as an understanding of Bezrukavnikov and Kaledin's noncommutative resolutions of the Coulomb branch, and explaining a lot of interesting Koszul dualities between category O's.
