LECTURE 1. INVARIANTS AND DISCRIMINANTS OF PLANE CURVES
Preface to Lecture 1
CHAPTER 1. Plane Curves
1. The three basic invariants
2. Properties of the basic invariants
3. Computation of basic invariants
4. Extremal curves and tree-like curves
5. The numerology
6. Cobordisms
7. Long curves
CHAPTER 2. Legendrian Knots
8. From plane curves to Legendrian knots
9. The space of Legendrian curves
10. The basic invariant J+
11. The Legendrian linking numbers
12. Calculation of linking numbers
LECTURE 2. SYMPLECTIC AND CONTACT TOPOLOGY OF CAUSTICS AND WAVE
FRONTS, AND STURM THEORY
CHAPTER 3. Singularities of Caustics and Sturm Theory
13. The Lagrangian collapse and the last geometrical theorem of
Jacobi
14. The four cusp theorem
15. Sturm theory and Morse theory
16. Proof of the four cusps theorem
CHAPTER 4. Singularities of Wave Fronts and the Tennis Ball Theorem
17. The wave fronts reversal
18. The front reversal four cusps theorem
19. The proof of the existence of four cusps on a front
20. The tennis ball theorem
References
