Coursebooks 2017-2018

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Lattice models

MATH-434

Lecturer(s) :

Hongler Clément

Language:

English

Summary

Lattice models consist of (typically random) objects living on a periodic graph. We will study some models that are mathematically interesting and representative of physical phenomena seen in the real world.

Content

We will discuss some classical lattice models, such as: random walks, percolation, Ising model, random spanning trees, gaussian free field.

We will prove non-trivial theorems for each of the models. The goal is to allow students to learn general methods and concepts from a number of detailed case studies. 

Keywords

probability, graph theory, complex analysis, lattice models, statistical mechanics

Learning Prerequisites

Required courses

Basic probability, basic analysis, linear algebra

I think that students who like to learn in the definition/theorem/proof/lemma way might be disappointed.

While the class will be completely rigorous, the emphasis is more on revealing some interesting phenomena (that somehow exists in nature) rather than on constructing some theories. The goal is to learn things that are generalizable, but I almost always prefer to work out particular cases first.

Recommended courses

None of this is mandatory, but it could help: complex analysis, basic graph theory, simulations

Assessment methods

Exam written

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12 CM1100   
12-13    
13-14     
14-15     
15-16 MAA331   
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German