## Colloquium YORDANOV, Borislav “On the Global Behavior of Solutions to a Non-autonomous Nonlinear Wave Equation in 3D”, TORIELLI, Michele “Sectional matrices and geometrical consequences of their extremal behaviour”

2016-07-27

Date

2016-7-27

Place

Room 501, Faculty of Science Bld. #4, Hokkaido University

15:00–16:00 YORDANOV, Borislav

16:00–16:30 Tea time

16:30–17:30 TORIELLI, Michele

18:30– Banquet

YORDANOV, Borislav

Title：On the Global Behavior of Solutions to a Non-autonomous Nonlinear Wave Equation in 3D

Abstract：We study the 3D wave equation with a non-autonomous nonlinearity which is effective only on a given space-time surface (line). Such equations are closely related to the equations arising in equivariant wave maps. For some non-characteristic surfaces (lines), we establish the global existence of unbounded solutions in the energy space using the Hardy inequality. We also show the finite time blow up of solutions when the nonlinearity is effective on a characteristic surface and the initial data are non-negative.

TORIELLI, Michele

Title：Sectional matrices and geometrical consequences of their extremal behaviour

Abstract：In this talk I will recall the definition of the sectional matrix of an homogenous ideal as given by Bigatti and Robbiano. I will describe the main properties of the sectional matrix and give some geometrical consequences of this properties, especially in the case of ideals of points in projective space. This is part of a work in progress with Bigatti and Palezzato.