(org by M. Alim, A. Balasubramanian, F. Beck, A. Brochier, J. Teschner)
## Schedule

## References

This is a collection of some basic references for the seminar.
## First Half

### Introductory Lectures/Notes

### Papers

## Second Half

### Introductory Lectures/Notes

### Papers

Apart from the GMN paper ([11] above), we will also use :

This is a webpage for the ZMP Seminar (Summer’ 17) on Hitchin Systems, Non Abelian Hodge and Wall Crossing

The Seminar is divided into two halves. The **first half** (Apr13-May 11) will be an introduction to various mathematical foundations regarding Hitchin Systems. In the **second half** (Jun 01 - Jul 06), we will study the problem of Wall crossing in four dimensional N=2 theories. The solution to this problem in specific theories turns out to intimately involve the Hitchin System. Some of the foundational material that is discussed in the first half will be useful for the second half.

** Note** : On Apr 13 and Jun 01, there will be two talks as part of the ZMP Seminar

Dates | Potential Topic | References | Speakers | Notes/Summary |
---|---|---|---|---|

Apr 13-I | Intro to Hitchin (Self-duality Eqns, Hyperkahler structure) | [1,6a,2] | Áron Szabó | Speaker's Notes |

Apr 13-II | Harmonic Metric and Nonabelian Hodge | [6a,4] and Sec 2 of [7] | Arpan Saha | Speaker's Notes |

Apr 27 | More NAH, Twistor Space Construction | [8,10] for NAH ; [6c], Sec 3 of [11] for Twistor Space ; | Florian Beck (NAH) , Troy Figiel (Twistor) | Speaker's Notes (for Twistors, updated on May 11) |

May 11 | Twistor Space Construction (contd) | [6c], Sec 3 of [11], [5] | Troy Figiel | (see updated link above) |

Jun 01-I | The Hitchin Integrable System | [6b, 3], Chapter 1 of [18] | Adrien Brochier | Speaker's notes |

Jun 01-II | Introduction to wall crossing in N=2 theories | Murad Alim | ||

Jun 22 | Special Geometry of Integrable Systems | Florian Beck | ||

Cancelled(G20) | BPS Spectrum and the Hitchin System | Aswin Balasubramanian | - |

- What is a Higgs Bundle ? (AMS Notices) Bradlow, Garcia-Prada, Gothen.
- Moduli of Higgs Bundles , A. Neitzke’s notes
- JT's notes
- Higgs bundles and local systems on Riemann surfaces, R. Wentworth

- Hyperkahler Metrics and Supersymmetry , Hitchin-Karlhede-Lindstrom-Rocek
- Hitchin’s Papers :
- Opers vs Non-Abelian Hodge , Dumitrescu et al
- Non-abelian Hodge Theory (
**pdf**), C. Simpson - Higgs Bundles and Local Systems, C. Simpson
- Non-abelian Hodge Theory, K. Corlette
- Four-dimensional wall-crossing via three-dimensional field theory, Gaiotto-Moore-Neitzke

- N=2 Supersymmetric dynamics for pedestrians , Y. Tachikawa
- Introduction to Seiberg-Witten Integrable Systems, R. Donagi
- Hitchin Systems in N=2 Field Theory, A. Neitzke

- Seiberg-Witten’s papers :
- Special Kahler Manifolds, D. Freed
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, M. Kontsevich and Y. Soibelman
- More On Gauge Theory and Geometric Langlands, E. Witten