This is a past event.

Speaker: Professor Juan Migliore,  University of Notre Dame

Abstract:

The so-called “Lefschetz Properties” have attracted a great deal of attention in recent years. Informally, they have the following form. Given a fixed set of dimensions of some objects, you make a “general choice” of something (to be explained in the talk) that produces a new dimension. There is an expected value for this dimension, and the game is to understand under what circumstances this expected value fails to be achieved. There is a striking variety of situations where this kind of behavior has been studied. In this talk we give two very different examples, both having to do with projective planes. After recalling the necessary facts about projective planes, we describe a very geometric setting and a much more algebraic setting.