Title of the course:  Lectures Harmonic Maps
Instructor: Associate Professor Martin Svensson
Institution: University of Southern Denmark
Dates: 6-10 January 2020
Prerequisites:  Linear Algebra, Differential Geometry, Riemannian Geometry (not a must but strongly recommended)
Level: Advanced undergraduate
Abstract: The area of harmonic maps includes a range of familiar topics from differential geometry such as harmonic functions, parametrized geodesics, holomorphic maps in Kähler geometry and minimal branched immersions. In this lecture series we will discuss harmonic maps in Riemannian geometry. After a general introduction we will focus on harmonic maps from Riemann surfaces to Lie groups and symmetric spaces. We will see a number of constructions of such maps, and along the way we will encounter twistor theory, loop groups and integrable systems in the context of harmonic maps.
Textbook, Reference or/and course webpage:
1. F.E. Burstall, Harmonic tori in spheres and complex projective spaces, J. Reine Angew. Math. 469 (1995), 149 – 177.
2. F.E. Burstall and M.A. Guest, Harmonic two-spheres in compact symmetric spaces, revisited, Math. Ann. 309 (1997), 541 – 572.
3. J. Davidov and A.G. Sergeev, Twistor spaces and harmonic maps (Russian), Uspekhi Math. Nauk 48 (1993), no. 3 (291), 3 – 96; translation in Russian Math. Surveys 48 (1993), no. 3, 1 – 91.
4. J. Dorfmeister, F. Pedit and H. Wu, Weierstrass type representations of harmonic maps into symmetric spaces, Comm. Anal. Geom. 6 (1998), no. 4, 633 – 668.
5. K. Uhlenbeck, Harmonic maps into Lie groups: classical solutions of the chiral model, J. Differential Geom. 30 (1989), no. 1, 1 – 50.
6. M. Svensson and J.C. Wood, Filtrations, factorizations and explicit formulae for harmonic maps, Comm. Math. Phys. 310 (2012), no. 1, 99 – 134. arXiv: 0909.5582
7. M. Svnesson and J.C. Wood, New constructions of twistor lifts for harmonic maps, Manuscripta Math. 144 (2014), no. 3 – 4, 457 – 502. arXiv: 1106.1832 Language: EN
Language: EN