1-2-3 Seminar: Measuring singularities in char 0 and p via "thresholds"

Attach a real number to a mathematical object. If we are careful, we can get an "if and only if" statement of a property of the object in terms of whether a certain threshold value is reached. e.g. attach a number representing the effort spent and find a threshold value for completion of the PhD. The thresholds vary for different p (person/ characteristic). We will investigate two thresholds for singularities, log canonical threshold in characteristic 0 and F-pure threshold in prime characteristic p. We will use them to rate the badness of the singularities of a polynomial or an ideal, and compute some examples.