Tuesday 08 November, 11-12, IM PAN, room 321 - Discussion group

Wednesday 09 November, 11:00-12:00, IM PAN, room 321 - **Nick Dewaele**: A condition number for underdetermined systems

Wednesday 09 November, 14:30-15:30, IM PAN, room 321 - **Maciej Gałązka**: 14th cactus variety

Please note that November 11th is a national holiday in Poland. On this day there are usually demonstrations in Warsaw: some of the main streets will be closed to traffic and several bus and tram lines will suspend or modify their activity.

Abstracts

*Nick Dewaele - A condition number for underdetermined systems*

For parametric systems of equations of the form F(x,p) = 0, the condition number provides a way of measuring the sensitivity of the solution x with respect to small perturbations of p. However, many systems found in applications admit infinitely many solutions x for each value of p. Multiplicative tensor decompositions, such as Tucker or tensor train decompositions, are examples of such systems. I will discuss one way of generalising the concept of the condition number to these systems.

*Maciej Gałązka - 14th cactus variety*

Cactus varieties are obstructions in the problem of getting equations of secant varieties. We investigate the simplest case when the cactus variety can be different from the corresponding secant variety, the 14th cactus variety of the Segre-Veronese embedding, Veronese embedding, and the Segre embedding.