Mathematisches Institut
der LMU, München
Prof. D. Kotschick, D. Phil.
We shall discuss Hodge - de Rham theory on compact smooth manifolds, following the book of Warner. This is an ideal supplement to the courses on Geometry of Manifolds and/or Topology. We shall assume knowledge of some basic point-set topology and the definition and easiest properties of manifolds.
We shall treat the basics of sheaf theory, which are very important in complex analysis and algebraic geometry as well. Some of the lectures on the Hodge theorem have an analytic flavour, and will introduce basic tools for studying elliptic differential operators on manifolds. Students with an interest in partial differential equations could sign up for such a talk and learn the required geometry in the course of the seminar. Time permitting, we shall also discuss special features of Hodge Theory on compact Kähler manifolds, following the books of Wells and Griffiths-Harris.
der LMU, München
Prof. D. Kotschick, D. Phil.
Seminar - Wintersemester 2002/03
Seminar on Hodge Theory
We shall discuss Hodge - de Rham theory on compact smooth manifolds, following the book of Warner. This is an ideal supplement to the courses on Geometry of Manifolds and/or Topology. We shall assume knowledge of some basic point-set topology and the definition and easiest properties of manifolds.
We shall treat the basics of sheaf theory, which are very important in complex analysis and algebraic geometry as well. Some of the lectures on the Hodge theorem have an analytic flavour, and will introduce basic tools for studying elliptic differential operators on manifolds. Students with an interest in partial differential equations could sign up for such a talk and learn the required geometry in the course of the seminar. Time permitting, we shall also discuss special features of Hodge Theory on compact Kähler manifolds, following the books of Wells and Griffiths-Harris.
Participants should contact Prof. Kotschick, preferably during his office hours, or by email. The seminar will probably take place Thursdays, 11-13, with the first seminar on October 31st, in room 251. There are still some talks left for additional participants.
Plan of lectures
References:
F. W. Warner: Foundations of Differentiable Manifolds and Lie Groups, Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin, 1983.
R. Wells: Differential Analysis on Complex Manifolds, Second edition. Graduate Texts in Mathematics, 65. Springer-Verlag, New York-Berlin, 1980.
P. Griffiths and J. Harris: Principals of Algebraic Geometry, Wiley Classics Library. John Wiley & Sons, Inc., New York, 1994.
D. Kotschick