Moduli Space of Planar Polygons

par Mohamed Boukholkhal

lundi 27 avr. 2026, 16:30 → 17:30 Europe/Paris

S435 (UMPA)

Studying spaces of geometric objects is a very natural idea in mathematics. A famous example is the real projective space (i.e., the space of vectorial lines in R^n). In this talk, we will focus on the configuration space of planar polygons: given an n-tuple of positive real numbers, one can ask what the space of planar polygons with edge lengths prescribed by this n-tuple looks like. Using Morse theory, we will show that the space of equilateral pentagons is a closed orientable surface of genus 4 (a torus with four holes).