We derive two geometric approaches to categorification of quantum invariants of links associated to an arbitrary compact simple Lie group $^L{G}$. In part I, we describe the first approach, based on an equivariant derived category of coherent sheaves on ${\cal X}$, the moduli space of singular $G$-monopoles, where $G$ is related to $^LG$ by Langlands duality. In part II, we describe the second approach, based on the derived category of a Fukaya-Seidel category of a Calabi-Yau $Y$ with potential $W$. The two approaches are related by a version of mirror symmetry, which plays a crucial role in the story. In part III, we explain the string theory origin of these results, and the relation to an approach due to Witten.

Mina Aganagic

Advances in Theoretical and Mathematical Physics

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS 是国际出版社的双月刊，发表关于理论物理和数学相互作用的所有领域的论文。

Advances in Theoretical and Mathematical Physics is a bimonthly journal published by an international publisher, focusing on research papers in all areas of the interaction between theoretical physics and mathematics.

《Advances in Theoretical and Mathematical Physics》是国际出版社出版的双月刊，专注于发表理论物理与数学交叉领域的研究论文。

Category	Quartile
物理与天体物理	4
物理与天体物理, 物理数学物理	4
物理与天体物理, 物理粒子与场物理	4

Knot categorification from mirror symmetry part I: Coherent sheaves

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Journal Info

Category	Quartile
PHYSICS, PARTICLES & FIELDS	4