Teaching

Finance Décentralisée (ISFA, M2, 2024 / 2025)

• Articles pour les présentations : 

  1. Efficiency and Security in DeFi Lending. 

  2. Liquid Staking: When Does it Help ? 

  3. Axioms for Constant Function Market Makers. 

  4. Miner Collusion and the Bitcoin Protocol. 

  5. Bitcoin: A Natural Oligopoly. [v1 & v2]

  6. Anatomy of a Run: The Terra Luna Crash. 

  7. Contagion in Decentralized Lending Protocols: A Case Study of Compound.

  8. DeFi-ying the Fed? Monetary Policy Transmission to Stablecoin Rates. 

  9. Attacks on Dynamic DeFi Interest Rate Curves. 

  10. Robust Restaking Networks [Pour comprendre le contexte : EigenLayer: The Restaking Collective.]

Deep Learning (ISFA, M2, 2023 / 2024)

• Page du cours

Mesures de Risque (ISFA, M2, 2022-)

• Notes de cours

• Partiel 2023

Modèles Aléatoires Discrets (ISFA, M1, 2022-)

• Notes de cours

• TD [ Voir avec le chargé de TDs ]

Théorie de l'intégration de Lebesgue (ISFA, L3, 2022-)

• Notes de cours

• TD [ Voir avec le chargé de TDs ]

Statistical Field Theory and 2d Conformal Field Theory (EPFL, PhD course, 2020)

• Videos of the lesson.

• Live Notes

• Exercises

Link for the Zoom lesson:  https://epfl.zoom.us/j/67596518104

Lecture Notes: 

• Part 1: The simple random walk. 

• Part 2: Discrete Partial Differential Equations and Random Walks. 

• Part 3: Uniform Spanning Tree.

• Part 4: Percolation.

• Part 5: Ising Model. 

• Part 6: Dimers. 

Videos: PlayList 

• Week 1: Introduction & Simple Random Walk.  

• Week 2: Detailed proof of Polya's theorem (audio only). 

• Week 3: Expectation of the return time (the reflection principle),
    Discrete Partial Differential Equations and Random Walks (Part 1)

• Week 4: DPDEs and Random Walks: Laplace, Poisson, and Heat Equations.

• Week 5:  DPDEs and Random Walks; the Uniform Spanning Trees. 

• Week 6: Wilson algorithm; Percolation.

• Week 7:  Percolation: Definition, Phase transition & RSW estimates.

• Week 8: Percolation: RSW estimates, Equicontinuity, and boundary conditions.  

• Week 9: Percolation: Cauchy-Riemann Equations, Holomorphicity of the limit. 

• Week 10: Ising Model: Definition, Boundary Conditions, Markov Property and Sampling via Dynamics. 

• Week 11: Ising Model: Sampling and Graphical Expansions. 

• Week 12: Ising Model: Graphical Expansions and Consequences. 

• Week 13: Ising Model: Magnetisation and Phase Transition 

• Week 14: Counting Dimers.

Previous Exams: 2019, 2018, 2017.