A set of permutations on $n$ points is intersecting if, for
any two of its elements, there is some point which is sent to the same
point by both of them. How large can such a set be? Similarly, a set
of partial permutations (meaning injections defined on some $r$ points
of the $n$-set, for some fixed $r$) is intersecting if, for any two of its
elements, there is some point on which they are both defined and is
sent to the same point by both of them. Again, how large can such a
set be?

We shall survey and discuss some results on these problems. We will
also mention some fascinating conjectures in this area.

This talk includes joint work with Peter Cameron and Imre Leader.

New probability models are proposed for the analysis of marked point
processes. These models deal with the type of data that arrive
or are observed in possibly unequal time intervals such as
financial transactions, earthquakes among others. The models
treat both the time between event arrivals and the observed marks
as stochastic processes. We adopt a class of bivariate
distributions to form the bivariate mixture transition
distribution(BMTD). In these models the
conditional bivariate distribution of the next
observation given the past is a mixture of conditional
distributions given each one of the last p observations or a
selection of past p events. The identifiability of the model is
investigated, and EM algorithm is developed to obtain estimates
of the model parameters. Simulation and real data examples are
used to demonstrate the utility of these models.

Last time I described the (na\"ive) algebraic geometry way to define

For K a C.M. abelian extension of a totally real base-field k with
Galois group G, Solomon has recently constructed for each prime p a Z p[G] ideal of Q p[G] related to values of Dirichlet L-functions at s=1 and conjectured that this ideal is contained within Z p[G]. Jones has subsequently shown that for each odd p the Equivariant Tamagawa Number Conjecture (or ETNC) implies that Solomon's ideal should actually be contained within the Fitting ideal of the class-group of O K. I shall explain how to define analogous ideals related to values of Dirichlet L-functions at integers r strictly greater than 1 and provide a sketch of the techniques used to show that the ETNC relates these `higher Solomon ideals' to the Fitting ideals of certain natural cohomology groups (and thus, when the Quillen-Lichtenbaum conjecture is valid, to Fitting ideals of Quillen K-groups of O K). In particular, for certain choices of K/k and r these results are
unconditional as the relevant cases of the ETNC and Quillen-Lichtenbaum conjecture are known to be valid.