Ragni Piene: The problematic art of counting

Many counting problems, like

“In how many ways can a positive integer n be written as a sum of positive integers?”

“Given a polytope P, how many lattice points does the dilated polytope nP contain?”

“How many lines in a (n + 1)-dimensional space meet 2n general (n − 1)-planes?”

are solved by finding a closed form for the corresponding generating function ∑_n N_n q^n, where the N_n are the sought numbers and q is a variable. In this lecture we shall, in addition to the above questions, also address an old problem from enumerative geometry:

“How many plane curves of degree d have r singularities and pass through d(d+3)/2 - r given points in the plane?”

In this case the generating function is still unknown, but there has recently been substantial progress on the problem and its generalizations.

Program:

13.15-14.00 Precolloquium: for PhD and master students. Dan Petersen (KTH) gives a talk with the title "Algebraic curves in the projective plane".

14.30-15.30 Colloquium talk Ragni Piene, University of Oslo, "The problematic art of counting"

15.30-16.30 Coffee and SMC social get-together