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The problematic art of counting
  SMC Colloquium

Wednesday 16 November 2011
from 14:30 to 15:30
at Oscar Kleins auditorium
Speaker : Ragni Piene (University of Oslo)
Abstract :

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.


AlbaNova  | Last modified 02 June 2015 09:08  |  HELP