Mathematisches Institut
der LMU, München
Prof. G. Kokarev, Ph.D.
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 Riemannian Geometry, Mathematical Gauge Theory, and/or Topology. We shall assume knowledge of some basic point-set topology and the definition and standard facts about smooth 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. We shall also discuss special features of Hodge Theory on compact Kähler manifolds, following the books of Wells and Huybrechts.
der LMU, München
Prof. G. Kokarev, Ph.D.
Prof. D. Kotschick, D. Phil.
Seminar - Sommersemester 2012
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 Riemannian Geometry, Mathematical Gauge Theory, and/or Topology. We shall assume knowledge of some basic point-set topology and the definition and standard facts about smooth 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. We shall also discuss special features of Hodge Theory on compact Kähler manifolds, following the books of Wells and Huybrechts.
The seminar will probably take place Thursdays, 2-4 PM, with the first seminar on May 3rd, in room B 040. 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.
D. Huybrechts: Complex Geometry, Springer-Verlag, New York-Berlin, 2005.
G. Kokarev, D. Kotschick