# Tuyen Trung Truong: Can we intersect a line in the plane with itself?

Date: 16. 2. 2018

Source: Complex analysis seminar

Source: Complex analysis seminar

Četrtek, 22.02.2018 ob 12:30, Plemljev seminar na Jadranski 19

V ČETRTEK, 22. februarja ob 12. uri in 15 minut, bo v okviru seminarja za kompleksno analizo predaval prof. Tuyen Trung Truong z Univerze v Oslu, Norveska. Naslov predavanja bo

Title: Can we intersect a line in the plane with itself?

Abstract: Bezout's theorem says that two distinct irreducible curves C_1 and C_2 in the projective plane intersect at deg(C_1)deg(C_2) when multiplicities are counted. This can be reinterpreted in complex analysis as follows: the wedge intersection [C_1]\wedge [C_2] of the currents of integration [C_1] and [C_2] is a positive measure with mass deg(C_1)deg(C_2). What happens if C_1=C_2=C? No answer had yet been given in the literature about what should [C]\wedge [C] be. In this talk, I will show that if we allow a certain generalisation of measures, the so-called strong submeasures, then we can define [C]\wedge [C] for all curves C in such a way to preserve Bezout's theorem. The result applies more general to intersection of positive closed currents on compact Kahler manifolds and to dynamics.

Seminar bo v Plemljevem seminarju na Jadranski 19. Vljudno vabljeni!

Vodji seminarja

Josip Globevnik in Franc Forstnerič

Title: Can we intersect a line in the plane with itself?

Abstract: Bezout's theorem says that two distinct irreducible curves C_1 and C_2 in the projective plane intersect at deg(C_1)deg(C_2) when multiplicities are counted. This can be reinterpreted in complex analysis as follows: the wedge intersection [C_1]\wedge [C_2] of the currents of integration [C_1] and [C_2] is a positive measure with mass deg(C_1)deg(C_2). What happens if C_1=C_2=C? No answer had yet been given in the literature about what should [C]\wedge [C] be. In this talk, I will show that if we allow a certain generalisation of measures, the so-called strong submeasures, then we can define [C]\wedge [C] for all curves C in such a way to preserve Bezout's theorem. The result applies more general to intersection of positive closed currents on compact Kahler manifolds and to dynamics.

Seminar bo v Plemljevem seminarju na Jadranski 19. Vljudno vabljeni!

Vodji seminarja

Josip Globevnik in Franc Forstnerič