Abstract: 

To any Borel function f defined on [0,T] with values in R^d we can associate the push-forward measure μ_f. If A is a Borel subset of R^d then μ_f(A) measures the time spent by f in A. μ_f is called the occupation measure. If this measure is absolutely continuous with respect to Lebesgue measure then the density is called the local time. In this talk I will try to discuss :

1. The connection between the local time, the regularity of f and the dimension d
2. The connection with stochastic processes
3. A second definition of local time
4. The definition of intersection local time and the link with the points of self-intersection (or multiple points)
5. Multiple points of the Brownian motion
6. The connection with polymers
7. What if intersection local time fails to exist?