papers

(Feel free to contact me for published versions.)

1. Transformers in the guise of many-particle systems
   forthcoming
   2024
   
   
2. On the number of modes of Gaussian kernel density estimators
   with Philippe Rigollet and Yihang Sun
   forthcoming
   2024
   [github]
   
   
3. Constructive approximate transport maps with normalizing flows
   with Antonio Alvarez-Lopez and Domènec Ruiz-Balet
   forthcoming
   2024
   
   
4. Measure-to-measure interpolation using Transformers
   with Philippe Rigollet and Domènec Ruiz-Balet
   preprint
   2024
   
   
5. Dynamic metastability in the self-attention model
   with Hugo Koubbi, Yury Polyanskiy and Philippe Rigollet
   preprint
   2024
   [github]
   
   
6. A mathematical perspective on Transformers
   with Cyril Letrouit, Yury Polyanskiy and Philippe Rigollet
   Bulletin of the AMS
   2024
   [github]
   
   
7. The emergence of clusters in self-attention dynamics
   with Cyril Letrouit, Yury Polyanskiy and Philippe Rigollet
   NeurIPS
   2024
   [github]
   
   
8. Control of the Stefan problem in a periodic box
   with Debayan Maity
   Mathematical Models and Methods in Applied Sciences
   2023
   [github]
   
   
9. Optimal controller design via Brunovsky's normal form
   with Enrique Zuazua
   IEEE Transactions on Automatic Control
   2023
   [github]
   
   
10. Sparsity in long-time control of neural ODEs
    with Carlos Esteve-Yagüe
    Systems & Control Letters
    2023
    [github]
    
    
11. Turnpike in optimal control of PDEs, ResNets, and beyond
    with Enrique Zuazua
    Acta Numerica
    2022
    [github]
    
    
12. Turnpike in Lipschitz-nonlinear optimal control
    with Carlos Esteve-Yagüe, Dario Pighin and Enrique Zuazua
    Nonlinearity
    2022
    [github]
    
    
13. Large-time asymptotics in deep learning
    with Carlos Esteve-Yagüe, Dario Pighin and Enrique Zuazua
    preprint
    2021
    [github]
    
    
14. Controllability of one-dimensional viscous free boundary flows
    with Enrique Zuazua
    SIAM Journal on Control and Optimization
    2021
    
    
15. Null-controllability of perturbed porous medium gas flow
    ESAIM Control, Optimisation and Calculus of Variations
    2020
    
    

Theses

T1. Control in moving interfaces and deep learning
PhD Thesis
Universidad Autónoma de Madrid
2021
(The version published on the UAM library webpage contains formatting errors not caused by me.)

T2. Obstacle problems: theory and applications
MSc Thesis
Université de Bordeaux
2018