Keywords
Awards & distinctions
- 2023 SMAI-GAMNI PhD award for the best thesis defended in applied mathematics for engineering sciences.
- 2023 Prix solennel de thèse - Chancellerie des universités de Paris
- 2023 PGMO PhD award for the best thesis in optimization and operational research.
Team
QUANTIC
Biography
Remi Robin is a researcher whose work lies at the intersection of applied mathematics, quantum physics, and shape optimization. His research focuses in particular on the modeling and control of open quantum systems, with applications in quantum reservoir engineering and the stabilization of quantum states, such as GKP qubits or cat states. He also explores problems in geometric optimization, studying the existence and regularity of solutions for hypersurfaces that minimize shape functionals under constraints, as well as issues related to magnetohydrodynamics and the design of nuclear fusion devices, such as stellarators. His approach combines rigorous theoretical tools (partial differential equations, control theory, geometric analysis) with advanced numerical methods, particularly exterior finite element methods. His recent contributions include the analysis of optimal control phenomena in quantum physics, such as the *chattering* phenomenon, and the study of the controllability of nonlinear dynamical systems, such as the generalized Burgers equations.
Publication(s)
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2025
Convergence of Bipartite Open Quantum Systems Stabilized by Reservoir Engineering DOI : 10.1007/s00023-024-01481-8
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2025
Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint DOI : 10.4171/IFB/523
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2025
Shape Optimization of Harmonic Helicity in Toroidal Domains DOI : 10.1007/s10957-024-02588-y
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2023
Stability and decoherence rates of a GKP qubit protected by dissipation DOI : 10.1016/j.ifacol.2023.10.1776
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2023
Small-time global null controllability of generalized Burgers'equations DOI : 10.1051/cocv/2023021
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2022
Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations DOI : 10.1016/j.jde.2022.02.042
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2022
Minimization of magnetic forces on stellarator coils DOI : 10.1088/1741-4326/ac7658
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2022
Chattering phenomenon in quantum optimal control DOI : 10.1088/1367-2630/acab24
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2022
Optimal shape of stellarators for magnetic confinement fusion DOI : 10.1016/j.matpur.2022.05.005
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2021
A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment DOI : 10.1007/s11538-020-00829-5
Teaching
Differential, Integral, and Stochastic Calculus I (Math1)
This first module of UE11 will begin with an introduction to the topology of metric spaces: open sets, closed sets, density, completeness, compactness, and the space of continuous maps between metric spaces. We will then cover the essential elements of measure theory (without doing all the proofs in lecture), which allows us to define the Lebesgue integral; we will clarify how it differs from the Riemann integral covered in preparatory classes. This integral will allow us to define the main functional spaces used in the mathematical study of equations in physics—the Lp spaces—and in particular the L2 space. We will then study Hilbert spaces (of which L2 is an archetypal example), which are generalizations of Euclidean spaces to infinite dimensions, and we will examine their main properties, in particular the existence of so-called Hilbert bases. The final part of the course will be devoted to differential calculus for mappings from Rn to Rm: the concept of a partial derivative, the differential of a mapping, the finite increase theorem in Rd, the implicit function theorem, and the local inversion theorem. Advanced tutorial sessions will allow motivated students to go beyond the concepts required for the exam: more in-depth analysis of measure and integration theory, functional analysis, Banach spaces, the Hahn-Banach theorem, operators in infinite-dimensional spaces, Sobolev spaces… This theoretical course aims to provide the foundations that will enable students to tackle the major challenges of applied mathematics, in particular the study and numerical solution of differential equations, partial differential equations, and optimization.
Optimization
This optimization course covers finite-dimensional convex nonlinear optimization. It begins by presenting the fundamentals of convex analysis and the sufficient and necessary conditions for optimality. Next, optimization algorithms—first for unconstrained problems and then for constrained problems—are discussed in detail, along with detailed proofs of convergence guarantees. Finally, elements of advanced convex analysis are covered to provide an introduction to non-smooth optimization methods. This course includes lectures (10 hours), tutorials (8 hours), and practical sessions conducted in Python (6 hours). Detailed ContentChapter 1: Optimality Conditions and Convex Analysis (3 hours)Definitions, optimality conditions, convex analysis (convex function, subdifferential, optimality conditions, strong convexity)Chapter 2: Numerical Methods for Differentiable Optimization (15 hours)2.1 Unconstrained Optimization: Gradient Methods (optimal step size, linear search, stochastic gradient)Newton and quasi-Newton (BFGS)2.2 Constrained OptimizationLagrange multipliers, stationarity conditionsKKT conditions, active constraint algorithmsDuality and saddle points, Uzawa’s algorithmChapter 3: Introduction to Non-Smooth Optimization (6 hours) Advanced convex analysis: Fechner transform, proximal operator; subgradient methods, proximal gradient method, bundle methods