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In grad school, I received some training in homological mirror symmetry and have begun learning about the classical Langlands program. I see that geometric Langlands at times explicitly mentions ...

A lot has been discussed on overflow regarding geometric Langlands and the physics of Kapustin and Witten's groundbreaking paper https://arxiv.org/abs/hep-th/0604151. I would like to add my two cents ...

This post is rather wordy and speculative, but I promise there is a concrete question embedded within. For experts, I'll open with a question: Question: Given a compact Riemann surface $X$, why ...

In 2002 Hausel - Thaddeus interpreted SYZ conjecture in the context of Hitchin system and Langlands duality. Let briefly explain it Let $\pi : E \to Σ$ a complex vector bundle of rank $r$ and ...

I'm not the person to understand everything in Geometric Endoscopy and Mirror Symmetry, but some parts of it are reasonably clear to me. In particular, one of the main objects, mathematically ...