The speaker continued his talk of relative trace formula. The relative trace formula in itself consists of two ways of expressing a period integral of a kernel function. On the spectral side, one computes the contribution from each representation. On the geometric side, one computes the contribution of orbits of group elements. The fun thing happens when one has two relative trace formulae for two groups that somehow there is a match between orbits in the two groups and there is a way to match up the test functions on the two sides. Then one gets certain interesting identities such as a relation of periods and L-values. Of course, it is easier said than done.

There was no respite. We tried to outrun the all-devouring shadow...