##
TOPICS IN RANDOM MATRIX THEORY

*
Jacobus Verbaarschot
*
.

*
Department of Physics and Astronomy, Stony Brook
*
.

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.