**Date:** Tuesday, 19.05, 14:15–15:00

**Place: **C115, Kronstad (OBS: Not the usual room)

**Speaker:** Jon Eivind Vatne, HiB

**Title:** Grothendieck and families of objects

**Abstract:**

Alexandre Grothendieck (1928-2014) was one of the most influential mathematician of the previous century (also known as “our century”). He led an extraordinary life, going from the center stage of mathematics in the sixties to a life in solitude later. I will give a short introduction to an important aspect of modern algebraic geometry: Mathematical objects should always be considered in families! Just as important, the spaces parametrizing families are not just sets. Grothendieck made this one of the pillars of algebraic geometry. As an example we will consider a question posed by Aasmund Kvamme for his “Adventskalender” (4/12, pasted below). Other examples we will consider (time permitting) are the family of vector subspaces of a given vector space, the family of all subsets of a vector space that can be described as solutions of sets of polynomial equations (a huge set) and state spaces appearing in physics and in computer science. Along the way, we will touch on one of the theorems cited by the committee for this year’s Abel prize, presented to Nash and Nirenberg by the king at the same time as this seminar is held.

I ein sirkel er det skrevet inn ein likesida trekant. Trekk ein tilfeldig korde gjennom sirkelen. Kor stor er sannsynligheten for at korden vert lengre enn sidekanten i trekanten (Translation: In a circle an equilateral triangle is inscribed. What is the probability that a random chord is longer than the sides of the triangle?)