Prof. Dr. Matthias Lesch
Mathematisches Institut

The idea of this seminar is to pick some very influential papers in global analysis and present each of them in a couple of sessions. A list will be put together according to the prerequisites and interests of the participants. We might include for example some of the following articles:

• Atiyah M.F., Patodi, V.K. and Singer, I.M.: Spectral asymmetry and Riemannian geometry I--III. Math. Proc. Cambridge Philos. Soc.
• Atiyah M.F.: Elliptic operators, discrete groups and von Neumann algebras. Asterisque, No. 32-33, (1976), 43--72.
• Atiyah M.F. and Bott R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523--615.
• Boutet de Monvel, L.: Boundary problems for pseudo-differential operators. Acta Math. 126 (1971), no. 1-2, 11--51.
• Cheeger J.: Analytic torsion and the heat equation. Ann. of Math. (2) 109 (1979), no. 2, 259--322.
• Cheeger J. and Simons J.: Differential characters and geometric invariants. Lecture Notes in Math., 1167 (1985), 50--80.
• Chern S.S. and Simons J.: Characteristic forms and geometric invariants. Ann. of Math. (2) 99 (1974), 48--69.
• Hörmander, L.: The spectral function of an elliptic operator. Acta Math. 121
• Hörmander, L.: Fourier integral operators I and II. Acta Math. 127 und 128
• Mathai, V. and Quillen, D.: Superconnections, Thom classes, and equivariant differential forms. Topology 25 (1986), no. 1, 85--110.
• Melrose, R.B.: Transformation of boundary problems. Acta Math. 147 (1981), no. 3-4, 149--236.
• Müller, W. : Analytic torsion and $R$-torsion of Riemannian manifolds. Adv. in Math. 28 (1978), no. 3, 233--305.

Module: S2B3 / S4B3

Prerequisites: Reading scientific articles in global analysis requires knowledge of the topics covered in the Bachelor's courses "Globale Analysis I" and "Partielle Differentialgleichungen und Funktionalanalysis". It is not necessary to have attended to my course on Atiyah-Singer index theory.

Preliminary Discussion: Wed. Sept. 19, 10am, SR B, Beringstr. 4.
Interested students who are unable to attend to this are encouraged to contact Matthias Lesch or Michael Bohn before the beginning of the semester.

When and Where: Wednesdays 10-12, SR G (next to Wolfgang Paul lecture hall, Kreuzbergweg)

Contact: If you are interested you should informally contact Matthias Lesch (lesch@math.uni-bonn.de) or Michael Bohn (mbohn@math.uni-bonn.de)

Schedule of Talks:

17.10.2007	Boris Vertman	Cheeger J.: Analytic torsion and the heat equation. (I)
24.10.2007	Boris Vertman	Cheeger J.: Analytic torsion and the heat equation. (II)
31.10.2007	Jonathan Pfaff	Müller, W. : Analytic torsion and $R$-torsion of Riemannian manifolds.
07.11.2007	Stefan Behrens	Chern S.S. and Simons J.: Characteristic forms and geometric invariants. (I)
14.11.2007	Stefan Behrens	Chern S.S. and Simons J.: Characteristic forms and geometric invariants. (II)
21.11.2007	Benjamin Himpel	Cheeger J. and Simons J.: Differential characters and geometric invariants.
28.11.2007	Bram Mesland	Atiyah M.F. and Bott R.: The Yang-Mills equations over Riemann surfaces. (I)
05.12.2007		Dies Academicus
12.12.2007	Konstantina Panagiotidou	Atiyah M.F. and Bott R.: The Yang-Mills equations over Riemann surfaces. (II)
19.12.2007	Michael Bohn	Atiyah M.F. and Bott R.: The Yang-Mills equations over Riemann surfaces. (III)
09.01.2007	Daniel Lyons	Atiyah M.F.: Elliptic operators, discrete groups and von Neumann algebras. (I)
16.01.12.2007	Matthias Lesch	Atiyah M.F.: Elliptic operators, discrete groups and von Neumann algebras. (II)
23.01.2008	Amru Hussein	Melrose, R.B.: Transformation of boundary problems. (I)
30.01.2008	Maurice de Gosson	Melrose, R.B.: Transformation of boundary problems. (II)
06.02.2008	Leonardo Cano Amru Hussein Maurice de Gosson	Melrose, R.B.: Transformation of boundary problems. (III)