>>81
>Ngo は Fundamental Lemma を 証 明 した [ Cha ] ことで ICM 2010 で Fields Medal を 授 与 されたが , その 主 要 な 道 具 Hitchin ?bration も 数 理 物 理 に 起 源 を 持 つもの である 。

Edward Witten Mirror Symmetry, Hitchin's Equations, And Langlands Duality
"2. Mirror Symmetry And Hitchin’s Equations"
"3. The Hitchin Fibration"
"3.1. A Few Hints."・・・か
これがどれだけNgo は Fundamental Lemmaに寄与したか不明だが
Langlands DualityもMirror Symmetryに呑み込まれようとしている・・

http://arxiv.org/abs/0802.0999
Mirror Symmetry, Hitchin's Equations, And Langlands Duality　Edward Witten　(Submitted on 7 Feb 2008)
Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$.
But understanding these statements is extremely difficult without picking a complex structure on $C$ and using Hitchin's equations.
We sketch the essential statements both for the ``unramified'' case that $C$ is a compact oriented two-manifold without boundary, and the ``ramified'' case that one allows punctures.
We also give a few indications of why a more precise description requires a starting point in four-dimensional gauge theory.

Comments: 15 pp
Subjects:
Representation Theory (math.RT); Mathematical Physics (math-ph)
Cite as:
arXiv:0802.0999v1 [math.RT]
Submission history
From: Edward Witten [view email]
[v1] Thu, 7 Feb 2008 16:11:53 GMT (18kb)