Seminar: Ricci flow
Prof. Bernd Ammann, Zimmer 119
Time and Place
Friday 8:30-10.00 in M102
Please register by email.
Please also register in G.R.I.P.S., as we send announcements
via this system.
Content of the Seminar
We will study the Ricci flow. In the first part of the seminar,
we concentrate on the Ricci flow on surfaces. The goal is to prove that the
Ricci flow yields a proof of the uniformization theorem for compact Riemann
surfaces. In the second part we will consider the flow in arbitrary dimensions.
The precise content of the second part will depend on the interests of the audience. Possible subjects are: the sphere theorem by Brendle and Schoen, or some
central ideas for the geometrization of 3-manifolds.
The seminar will probably continue in the summer term.
Program
The program of the seminar is
here as pdf-file.
Related web sites
Literature
For a list of the literature directly related to the seminar,
please have a look at the program above.
Further literature
- S. Brendle; Ricci Flow and the Sphere Theorem, AMS Graduate Studies Vol. 111, 2010
-
Böhm, Christoph; Wilking, Burkhard;
Manifolds with positive curvature operators are space forms.
Ann. of Math. (2) 167 (2008), no. 3, 1079--1097.
- M. Boileau Geometrization of 3-manifolds with symmetries
- Brendle, Simon; Schoen, Richard;
Manifolds with 1/4-pinched curvature are space forms, J. Amer. Math. Soc. 22 (2009), 287-307.
Journal, ArXiv
- Brendle, Simon; Schoen, Richard; Curvature, sphere theorems, and the Ricci flow;
Bull. AMS. 48 (2011), 1-32, ArXiv
- Brendle, Simon; Schoen, Richard;
Classification of manifolds with weakly 1/4-pinched curvatures,
Acta Math. 200, 1--13 (2008), ArXiv
- Allen Hatcher: Notes on Basic 3-Manifold Topology 2000
- John Lott's Ricci-Fluss-Seite (Strongly recommended!)
- John W. Morgan, Gang Tian; Ricci Flow and the Poincare Conjecture
- J. Milnor; Towards the Poincaré Conjecture and the Classification of 3-Manifolds
- John W. Morgan: Recent progress on the Poincaré conjecture and the classification of 3-manifolds. Bulletin Amer. Math. Soc. 42 (2005) no. 1, 57-78 (expository article explains the eight geometries and geometrization conjecture briefly, and gives an outline of Perelman's proof of the Poincaré conjecture)
- Morgan, John W.; Fong, Frederick Tsz-Ho (2010). Ricci Flow and Geometrization of 3-Manifolds. University Lecture Series. AMS
- G. Peter Scott, The geometries of 3-manifolds. (errata) Bull. London Math. Soc. 15 (1983), no. 5, 401-487.
- Peter Topping; Lectures on the Ricci flow
- Huai-Dong Cao, Xi-Ping Zhu; Hamilton-Perelman's Proof of the Poincaré
Conjecture and the Geometrization Conjecture
- Perelman's articles ArXiv 0211159,
ArXiv 0303109
and ArXiv 0307245.
Wikipedia-Page to the Ricci flow.
Formal requirements (in German)
Kriterien für benotete Leistungsnachweise
Um die üblichen Leistungsnachweise zu erhalten, sind folgende
Kriterien zu erfüllen:
- Erfolgreiches Vortragen
- Schriftliche Ausarbeitung eines Vortrages
- aktive Mitarbeit im Seminar
Unbenotete Leistungsnachweise
Wie bei benoteten Leistungsnachweisen.
Modulteilprüfung
Vortrag und Ausarbeitung bilden die Modulteilprüfung.
Bernd Ammann, 12.09.2016 oder später