KAWA lecture notes on complex hyperbolic geometry

Junior Seminar: Hyperbolic Geometry Lecture Notes

Our first construction is very similar in spirit to an analogous one in Euclidean space. The group of isometries of Euclidean R is given by O(n) ⊕ R or SO(n) ⊕ R if we want to preserve orientation; the first factor is made up of rotations and reflections (in the non-orientation-preserving case) about the origin, while the second factor gives translations. Now, it turns out that O(n) is generate...

Hyperbolic Groups Lecture Notes

Lecture Notes on Hyperbolic Conservation Laws

These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: 1. Meaning of the conservation equations and definition of weak solutions. 2. Shocks, Rankine-Hugoniot equations and admissibility conditions. 3. Genuinely nonlinear and linearly degenerate characteristic fields. Solution to the Ri...

Projective Geometry Lecture Notes

2 Vector Spaces and Projective Spaces 3 2.1 Vector spaces and their duals . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Projective spaces and homogeneous coordinates . . . . . . . . . . . . . . . 5 2.2.1 Visualizing projective space . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Homogeneous coordinates . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Linear subspaces . . . . ....

Lecture Notes on Local Analytic Geometry

The aim of the CIMPA-ICTP-UNESCO-MESR-MICINN-PAKISTAN Research School on Local Analytic Geometry at Abdus Salam School of Mathematical Sciences, GC University Lahore, Pakistan (organized by A. D. Choudary, Alexandru Dimca and Gerhard Pfister) was to introduce the participants to local analytic geometry and related topics. A basis of the course was the book entitled Local Analytic Geometry (cf. ...