In these lecture notes I consider one remarkable system of differential equations that
appeared in the papers of physicists on two-dimensional topological field theory (TFT) in the …

We review recent progress in 2D gravity coupled to d< 1 conformal matter, based on a
representation of discrete gravity in terms of random matrices. We discuss the saddle point …

These are notes based on two lectures given at the Conference on Geometry and Topology
(Harvard University, April 1990). The first was mainly devoted to explaining a conjecture …

6.1. 3. Evaluation of the partition function 252 A. 2. Supersymmetric quantum mechanics 319
6.1. 4. Evaluation ofthe observables: knot A. 3. Topological sigma models 320 invariants 255 …

Following the discovery of spacetime anomaly cancellation in 1984 [1], string theory has
undergone rapid development in several directions. The early hope of making direct contact …

We review the status of Liouville field theory and discuss the identification of states and
operators. The quantum theory has two kinds of states (and operators). Local operators …

We calculate correlation functions in minimal topological field theories. These twisted
versions of N= 2 minimal models have recently been proposed to describe d< 1 matrix …

We consider the double-scaling limit in the hermitian matrix model for 2D quantum gravity
associated with the measure exp ∑ j= 1^ N t_ j^ Z^ 2j, N\geqq 3. We show that after the …

We give a derivation of the loop equation for two-dimensional gravity from the KdV
equations and the string equation of the one-matrix model. We find that the loop equation is …

We consider the topological B-model on local Calabi-Yau geometries. We show how one
can solve for the amplitudes by using-algebra symmetries which encode the symmetries of …