I think the 3-manifolds mentioned at 14:12 as part of arithmetic Chern-Simons theory are Calabi-Yau 3-folds. Calabi-Yau manifolds satisfy mirror symmetry (A-model, B-model). Calabi-Yau manifolds are also have the symplectic geometry of Higgs bundles as moduli spaces of Higgs bundles which are equivalent to hyperkähler manifolds. Note Kähler manifolds have a symplectic structure, complex structure, and Riemannian structure. This mirror symmetry gives them the duality mentioned throughout and as this matches the A-model side with the symplectic topology of Higgs bundles and hyperkähler manifolds mentioned at 30:15.
Everytime I hear about Langlands and QFT being mentioned together, I just get excited! What a wonderful and deep connection in between the world of numbers and the realm that we inhabit!
I think the 3-manifolds mentioned at 14:12 as part of arithmetic Chern-Simons theory are Calabi-Yau 3-folds. Calabi-Yau manifolds satisfy mirror symmetry (A-model, B-model). Calabi-Yau manifolds are also have the symplectic geometry of Higgs bundles as moduli spaces of Higgs bundles which are equivalent to hyperkähler manifolds. Note Kähler manifolds have a symplectic structure, complex structure, and Riemannian structure.
This mirror symmetry gives them the duality mentioned throughout and as this matches the A-model side with the symplectic topology of Higgs bundles and hyperkähler manifolds mentioned at 30:15.
Everytime I hear about Langlands and QFT being mentioned together, I just get excited! What a wonderful and deep connection in between the world of numbers and the realm that we inhabit!
The proof of the GLC isn't exactly the KW route but the physical intuition deeply informs it
Great bear in the sky 27:35