Towards a Mathematical Theory of 3D Mirror Symmetry

Explore the mathematical implications of 3D mirror symmetry in this 59-minute mathematics colloquium talk by Justin Hilburn from Perimeter Institute. Delve into the world of supersymmetric quantum field theory dualities and their connections to various areas of mathematics. Discover how 3D mirror symmetry, a duality of 3D N=4 QFTs, leads to a conjectured equivalence between two 2-categories associated with mirror hyperkähler manifolds. Examine the algebro-geometric category studied by Kapustin-Rozansky-Saulina and the more enigmatic category related to 3D generalized Seiberg-Witten equations. Learn about the role of this conjecture in mathematics and its connection to symplectic duality in geometric representation theory. Gain insights into the mathematical consequences of quantum field theory dualities and their potential to bridge different mathematical disciplines.