-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathHitchinSystems.toc
54 lines (54 loc) · 4.31 KB
/
HitchinSystems.toc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
\select@language {english}
\contentsline {chapter}{\tocchapter {Chapter}{1}{Introduction}}{5}
\contentsline {section}{\tocsection {}{1.1}{Local Case}}{5}
\contentsline {section}{\tocsection {}{1.2}{Teichm\"uller theory}}{6}
\contentsline {section}{\tocsection {}{1.3}{Link to Knots}}{6}
\contentsline {section}{\tocsection {}{1.4}{Mirror Symmetry}}{6}
\contentsline {chapter}{\tocchapter {Chapter}{2}{Overview and Definitions}}{8}
\contentsline {chapter}{\tocchapter {Chapter}{3}{Symplectic Quotients in Finite and Infinite Dimensions}}{9}
\contentsline {chapter}{\tocchapter {Chapter}{4}{Hyperk\"ahler Quotients and Integrable Systems}}{10}
\contentsline {section}{\tocsection {}{}{Introduction}}{10}
\contentsline {section}{\tocsection {}{4.1}{Symplectic Reduction and K\"ahler Quotients}}{10}
\contentsline {subsection}{\tocsubsection {}{4.1.1}{Rapid Review of Symplectic Reduction}}{10}
\contentsline {subsection}{\tocsubsection {}{4.1.2}{Quotients and K\"ahler Structure}}{11}
\contentsline {section}{\tocsection {}{4.2}{Hyperk\"ahler Quotients}}{12}
\contentsline {subsection}{\tocsubsection {}{4.2.1}{Rapid Review of Hyperk\"ahler Manifolds}}{12}
\contentsline {subsection}{\tocsubsection {}{4.2.2}{Quotients and Hyperk\"ahler Structure}}{13}
\contentsline {subsection}{\tocsubsection {}{4.2.3}{Main Example}}{13}
\contentsline {chapter}{\tocchapter {Chapter}{5}{Stability and the Narasimhan-Seshadri Theorem}}{16}
\contentsline {chapter}{\tocchapter {Chapter}{6}{Teichmueller Theory}}{17}
\contentsline {chapter}{\tocchapter {Chapter}{7}{Construction of the Hitchin Moduli Space}}{18}
\contentsline {section}{\tocsection {}{7.1}{Definitions}}{18}
\contentsline {section}{\tocsection {}{7.2}{Summary of results}}{18}
\contentsline {section}{\tocsection {}{7.3}{$\mathcal {M}_{H}$ is a dimension $12\left (g-1\right )$ smooth manifold}}{19}
\contentsline {subsection}{\tocsubsection {}{7.3.1}{Idea of Proof}}{19}
\contentsline {subsection}{\tocsubsection {}{7.3.2}{Linearization of $(\star )$}}{19}
\contentsline {subsection}{\tocsubsection {}{7.3.3}{Elliptic Complexes}}{19}
\contentsline {subsection}{\tocsubsection {}{7.3.4}{$\mathcal {M}_{H}$ is a smooth manifold}}{20}
\contentsline {section}{\tocsection {}{7.4}{The tangent space}}{21}
\contentsline {section}{\tocsection {}{7.5}{$\mathcal {M}_{H}$ has a complete hyperkahler metric}}{21}
\contentsline {subsection}{\tocsubsection {}{7.5.1}{Idea of Proof}}{21}
\contentsline {subsection}{\tocsubsection {}{7.5.2}{Hyperkahler structure}}{22}
\contentsline {section}{\tocsection {}{7.6}{Summary of topological results}}{22}
\contentsline {chapter}{\tocchapter {Chapter}{8}{Integrable Systems and Spectral Curves}}{23}
\contentsline {chapter}{\tocchapter {Chapter}{9}{Meromorphic Connections and Stokes Data}}{24}
\contentsline {chapter}{\tocchapter {Chapter}{10}{The Langlands Program and Relations to Geometric Langlands}}{28}
\contentsline {chapter}{\tocchapter {Chapter}{11}{Spectral Curves and Irregular Singularities}}{29}
\contentsline {chapter}{\tocchapter {Chapter}{12}{The Stokes Groupoid}}{30}
\contentsline {chapter}{\tocchapter {Chapter}{13}{Cluster Varieties}}{31}
\contentsline {chapter}{\tocchapter {Chapter}{14}{The Hitchin System and Teichmueller Theory II}}{32}
\contentsline {chapter}{\tocchapter {Chapter}{15}{Geometric Langlands and Mirror Symmetry}}{33}
\contentsline {chapter}{\tocchapter {Chapter}{16}{Hitchin Systems and Supersymmetric Field Theories}}{34}
\contentsline {section}{\tocsection {}{16.1}{Introduction and definitions}}{34}
\contentsline {subsection}{\tocsubsection {}{16.1.1}{Supersymmetry}}{34}
\contentsline {subsection}{\tocsubsection {}{16.1.2}{BPS States}}{35}
\contentsline {subsection}{\tocsubsection {}{16.1.3}{Moduli of Vacua}}{35}
\contentsline {section}{\tocsection {}{16.2}{Compactification and Dimensional Reduction}}{36}
\contentsline {section}{\tocsection {}{16.3}{5D Super Yang-Mills Theory}}{37}
\contentsline {subsection}{\tocsubsection {}{}{Compactification on $C$}}{38}
\contentsline {section}{\tocsection {}{16.4}{Compactification from (2,0) 6D Theory}}{38}
\contentsline {chapter}{\tocchapter {Chapter}{17}{Pyongwon's II}}{40}
\contentsline {chapter}{\tocchapter {Chapter}{18}{Phil's II}}{41}
\contentsline {chapter}{\tocchapter {Chapter}{19}{Lei's II}}{42}
\contentsline {chapter}{\tocchapter {Chapter}{20}{Honghao's II}}{43}
\contentsline {chapter}{\tocchapter {Chapter}{}{Bibliography}}{44}