Ragni Piene: The problematic art of counting

Ragni Piene, University of Oslo

Time: Wed 2011-11-16 14.30 - 15.30

Location: Oscar Kleins auditorium at Alba Nova, Roslagstullsbacken 21

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

Kollokvier 2011

Titel Datum
Wendelin Werner: Random surfaces, random geometries 2011‑12‑14
Ragni Piene: The problematic art of counting 2011‑11‑16
Günter M. Ziegler: On some partition problems and their configuration spaces 2011‑10‑12
Carles Broto: Local aspects of groups and loop spaces 2011‑05‑11
Bernd Sturmfels: Quartic Curves and their Bitangents 2011‑02‑02