- Lecturer
- Jørgen Ellegaard Andersen (Aarhus) and Ib Madsen (Aarhus).
- Contents
- Understanding the geometry and topology of the moduli space of Riemann surfaces has been a goal of central importance in mathematics for a century. A little later the moduli space of holomorphic bundles over Riemann Surfaces has emerged as an important mathematical theme. - The term
*moduli space*of structures of a given kind refers to the set of*all*such structures, suitably topologized. Moduli spaces of geometric structures, such as Riemann surfaces and bundles over Riemann Surfaces also carry beautiful geometric structures them self. - These moduli spaces were primarily studied using techniques of algebraic geometry and Teichmuller theory but during the last 2 decades also by using techniques from quantum field theory from mathematical physics. Most recently algebraic topology and the theory of Toeplitz-operators has been applied to the moduli spaces, and that with great success. There have been three major breakthroughs within the last couple of years:- The Madsen-Weiss solution of the Mumford conjecture.
- The Chas-Sullivan discovery of new structures on loop spaces of manifolds.
- The Andersen proof of Turaev's asymptotic faithfulness conjecture.

- Literature
- Course lecture notes.
- Schedule
- All lectures are in Koll G Wednesdays 12 - 14.
- 31/8. IM: Introduction I.
- 7/9. No lecture.
- 14/9. IM: Introduction II.
- 21/9. JEA: Introduction I.
- 28/9. JEA: Introduction II.
- 5/10. JEA: Introduction III.
- 12/10. JEA: Introduction IV.
- 2/11. JEA: Introduction V.
- 9/11. JEA: Modular functors I.
- 15/11. JEA: Modular functors II.
- 30/11. JEA: Modular functors III.
- 7/12. JEA: Modular functors IV.
- 14/12. IM: Introduction III.

Revised 19.12.2006

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