In [1, 4], Fulton defines the notion of the Segre class s(X, Y) ∈ A∗X of a closed embedding of schemes X→ Y over a field k. As in Fulton, all of our schemes are finite type over a ground field k which may be of arbitrary characteristic unless stated otherwise. The Segre class allows us to measure the way in which X sits inside Y, and is functorial for sufficiently nice maps ([1, 4.2]). One impo...

These are the notes of the course given in Autumn 2007. Two good books (among many): Adams: Lectures on Lie groups (U. Chicago Press) Fulton and Harris: Representation Theory (Springer) Also various writings of Atiyah, Segal , Bott, Guillemin and Sternberg . . . .

Carlyle Jacobsen and John Fulton, at Yale in the early and mid-1930s, investigated primate frontal lobe function. Following bilateral frontal lobecotomy, monkeys and chimpanzees developed a delayedresponse deficit, being unable to perform tasks when there was a significant delay between the stimulus and the required response. There were accom panying behavioural changes, with the animals becomi...

Franklin Delano Roosevelt left us with the notion that we cannot do without Russia. But in post-war world, a tough approach to Russia has prevailed, one based on Sir Winston Churchill’s Fulton concept: there can be only total and uncompromising struggle of “countries freedom” against “tyranny.” And you need have an overwhelming superiority military power ensures “mutual understanding Russia.”1 ...

Let X be a subscheme of a reduced scheme Y. Then Y has a flat degeneration to the normal cone CXY of X, and this degeneration plays a key step in Fulton and MacPherson’s “basic construction” in intersection theory. The intersection product has a canonical refinement as a sum over the components of CXY, for X and Y depending on the given intersection problem. The cone CXY is usually not reduced,...