Introduction to random geometry

MATH-531 / 5 crédits

Enseignant: Aru Juhan

Langue: Anglais

Summary

We will discuss and study several models of random geometry - these are probabilistic models of random curves, surfaces, metrics often stemming from statistical physics and or field theories.

Content

We will consider different models of random geometry, both continuous and discrete. Some possible models include: 
- random walk / Brownian motion
- loop soups
- Schramm-Loewner evolution
- Gaussian free field
- planar maps / Gaussian multiplicative chaos
- gauge theories
- etc...
The exact models will be chosen organically during the course.

Keywords

Random Geometry, Brownian motion, Schramm Loewner Evolution, Gaussian free field, Gaussian multiplicative chaos

Learning Prerequisites

Required courses

Measure-theory based probability theory
Good basic understanding of complex analysis

Assessment methods

Oral exam / oral presentation (to be seen)

Resources

Moodle Link

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Introduction to random geometry
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel
  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Introduction to random geometry
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel
  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Introduction to random geometry
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel

Semaine de référence

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