65-412 Seminar on Rieman Surfaces and Integrable Systems (in English)

Course offering details
Instructors: Prof. Dr. Jörg Alexander Teschner
Event type:
Seminar
Displayed in timetable as:
M-Sem
Hours per week:
2
Language of instruction:
English
Min. | Max. participants:
5 | 14
Comments/contents: Goal of this seminar, and of the accompanying lectures 65-411 is to introduce into important aspects of the theory of classically integrable systems, many of which involve beautiful parts of the theory of Riemann surfaces. The main goal of the seminars will be to understand the main ideas of Hitchin's spectral transform, a geometric construction exhibiting the exact integrability of large classes of the known integrable models. If time permits and if there is interest we may also discuss the relation between exact integrability, Special Geometry and supersymmetry.

1. Background from Poisson-geometry, in particular the

Liouville-Arnold theorem and the notion of

algebraically completely integrable system

2. Relevant aspects from the theory of Riemann surfaces

- line bundles, sheaves and vector bundles

- branched covers and the direct image

3. Matrix polynomials and Lax pairs

(4. Integrability, Special Geometry and supersymmetry)

While it is certainly highly recommended to follow both the seminar accompanying lectures 65-411 "Riemann Surfaces und Integrable Systems", it should in principle also be possible to participate only in the seminar.
Literature: Literature:

1. V. I. Arnold. Mathematical Methods of Classical Mechanics.

Springer-Verlag, New York, 1978.

2. N. J. Hitchin, G. Segal, N. Woodhouse, and R.S. Ward.

Twistors, Loop Groups and Riemann Surfaces.

Oxford University Press, Oxford, 1997.

3. Hitchin, Nigel.

Stable bundles and integrable systems.

Duke Math. J. 54 (1987), no. 1, 91 - 114.

4. D. Freed.

Special Kahler Manifolds.

Commun. Math. Phys. 203 (1999), 31 - 52.
Class session overview
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14
 
Instructors
Prof. Dr. Jörg Alexander Teschner
Appointments
Date From To Room Instructors Appointments
1
Date Fri, 18. Oct. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
2
Date Fri, 25. Oct. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
3
Date Fri, 1. Nov. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
4
Date Fri, 8. Nov. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
5
Date Fri, 15. Nov. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
6
Date Fri, 22. Nov. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
7
Date Fri, 29. Nov. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
8
Date Fri, 6. Dec. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
9
Date Fri, 13. Dec. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
10
Date Fri, 20. Dec. 2019
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
11
Date Fri, 10. Jan. 2020
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
12
Date Fri, 17. Jan. 2020
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
13
Date Fri, 24. Jan. 2020
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
14
Date Fri, 31. Jan. 2020
To 10:15
To 11:45
Room Geom 142
Instructors Prof. Dr. Jörg Alexander Teschner
Exams in context of modules
Module(start semester)/ Course Requirement combination Exam Date Instructors Compulsory pass
Ma-M-S_1 Seminar 1 (WiSe 19/20) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 1 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_1 Seminar 1 (SuSe 19) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 2 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_1 Seminar 1 (WiSe 18/19) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 3 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_2 Seminar 2 (WiSe 19/20) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 1 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_2 Seminar 2 (SuSe 19) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 2 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_2 Seminar 2 (WiSe 18/19) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 3 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_3 Seminar 3 (WiSe 19/20) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 1 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_3 Seminar 3 (SuSe 19) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 2 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes
Ma-M-S_3 Seminar 3 (WiSe 18/19) / M-Sem Seminar on Rieman Surfaces and Integrable Systems (in English) Presentation 3 Presentation No Date Prof. Dr. Jörg Alexander Teschner Yes