Shigefumi Mori (RIMS, Kyoto, Japan)
On the classification of algebraic varieties
Abstract: In my talk I will present my personal views on the area around my research; I have been studying algebraic varieties through rational curves on them. I was first interested in a special problem called the Hartshorne Conjecture, and when I solved it I encountered a notion called an extremal ray as a biproduct, through which I got attracted to the biregular classification and the minimal model program, and furthermore to a general theory of higher dimensional birational classification. I will present them to a wider audience including algebraic geometers
Abstract: From any finite projective space, I will construct a ring that satisfies all the known properties of the cohomology ring of a smooth projective variety. I will indicate proofs of the hard Lefschetz theorem and the Hodge-Riemann relation in this context, and ask whether the ring is the cohomology ring of a geometric object.
Abstract: We generalize the classical light bulb theorem to four dimensions. I.e. a smooth 2-sphere in S2\times S 2 that intersects S 2\times 0 once and is homologous to 0\times S 2 is smoothly isotopically standard.