microlocal analysis

suggested by jnwang
1. A. Grigis and J. Sjöstrand, Microlocal Analysis for Differential Operators: An Introduction (London Mathematical Society Lecture Note Series).

2. G. Folland, Introduction to Partial Differential Equations (Chapter 8).

3. L. Hormander, Fourier integral operators I, Acta Math., 127, 79-183 (1971).

4. J.J. Duistermaat and L. Hormander, Fourier integral operators II, Acta Math., 128, 183-269 (1972).

5. L. Hormander, The Analysis of Linear Partial Differential Operators, Vol I-IV.

6. F. Treves, Introduction to pseudodifferential and Fourier integral operators, Vol I, II.

7. J.J. Duistermaat, Fourier Integral Operators.

suggested by y. safarov
1. M. Dimassi and J. Sj¨ostrand, Spectral asymptotics in the semi-classical Limit, LMS Lecture
Notes Series, vol. 268, Cambridge University Press, Cambridge, 1999.

2. L. H¨ormander, The analysis of linear partial differential operators. I-IV, Springer-Verlag,
New York, 1984.

3.M. Shubin, Pseudodifferential operators and spectral theory, “Nauka”, Moscow, 1978; English
transl., Springer-Verlag, 1987.

4.M. Taylor, Pseudodifferential operators, Princeton Univ. Press, Princeton, New Jersey, 1981.

5.Yu. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential
operators, American Mathematical Society, Providence, Rhode Island, 1996.

6.http://math.mit.edu/~rbm/18.157-F07.html Richard Melrose
Warning: the stationary phase formula in [Treves] is wrong.

wave eqns

wave eqns

msri video

http://www.msri.org/calendar/workshops/WorkshopInfo/300/show_workshop

http://www.msri.org/calendar/workshops/WorkshopInfo/424/show_workshop

lectures on nonlinear wave equations, sogge

lectures on nonlinear hyperbolic differential equations, hormander

Algebraic geometry

[SOFTWARES]

• Macaulay 2: Computational Algebraic Geometry
  http://www.commalg.org/m2win/
• Singular:A Singular Introduction to Commutative Albegra
• CoCoA:Computational Commutative Algebra I

[BOOKS]
Elementary

• Ideals, Varieties and Algorithms by Cox, Little and O’Shea
• Introduction to Algebraic Geometry by Hassett
• Elementary Algebraic Geometry by Hulek
• Undergraduate Algebraic Geometry by Reid
• Computational Algebraic Geometry by Schenck
• An Invitation to Algebraic Geometry by Smith, Kahanp¨a¨a, Kek¨al¨ainen andTraves

Advanced

• Harris
• Hartshorne
• Shafarevich

Narasimhan cpt riemann surface