TOPICS IN RANDOM MATRIX THEORY

Jacobus Verbaarschot
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Department of Physics and Astronomy, Stony Brook
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Announcements

Syllabus

Overview of lecture and list of topics to be discussed.

Lecture 1. Spectra of complex systems and statistical analysis of spectra.

Lecture 2. Random matrix theories and their classification in terms of symmetric spaces.

Lecture 3. The Orhtogonal Polynomial Method.

Lecture 4. Universality of the Microscopic Spectral Density.

Lecture 5. Analyticity and the average Spectral Density for an arbitrary potential.

Lecture 6. Universality in RMT: Orthogonal Polynomials.

Lecture 7. Grassmann Integration.

Lecture 8. Integration theorems for superintegrations.

Lecture 9. The Supersymmetric Method of Random Matrix Theory: The One-Point Function.

Lecture 10. The Supersymmetric Method of Random Matrix Theory: The Two-Point Function.

Lecture 11. Itzykson-Zuber Integrals and the Duistermaat-Heckman Theorem.

Lecture 12. Itzykson-Zuber Integrals for Rectangular Matrices.

Lecture 13. The Calogero-Sutherland-Moser Model.

Lecture 14. Hilbert Space Quantization of a Random Hopping Model.

Lecture 16. On the Calculation of Some Integrals (Lecture given by Madan Lal Mehta).

Lecture 17. Symmetries of the QCD Partition Function.

Lecture 18. Symmetries of the QCD Partition Function for two colors and fundamental fermions.

Lecture 19. Infrared Limit of the QCD Partition Function and Leutwyler-Smilga Sum-Rules.

Lecture 20. Partial Quenching and the Valence Quark Mass Dependence of the Chiral Condensate.

Lecture 21. Hirota Equations for 2d Quantum Gravity Models. (Lecture and lecture notes by Olindo Corradini).

Lecture 22. The Color Flavor Transformation. (Lecture and lecture notes by Achim Schwenk).

Lecture 23. Spectral Correlations of the QCD Dirac Operator at Finite Temperature. (Lecture and lecture notes by Bertram Klein).

Summer/Winter School Lectures.

Lectures on applications of RMT to QCD given at Osaka and Kyoto in 1998.

Lectures on applications of RMT to QCD given at Cambridge in 1997.

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