I am strongly committed to teaching and pedagogical innovation, and I bring extensive experience in this area. I am particularly interested in positions with a strong teaching focus.

I study the well-posedness (existence and unicity of local and global solutions, continuity of the flow) in low regularity functional spaces. I have studied the Quasilinear Wave Equation (QLW) and the Half-Wave maps equation (HWM). In the rational case, (HWM) reduces to a Calogero-Moser system of ODE describing the dynamics of a system of interacting solitons. Most notably, I have shown that (QLW) is ill-posed in H^(7/4) ln(H)^(-b) and found and proved an explicit formula for (HWM) that I later used to show well-posedness.

In parallel, I conduct research in Artificial Intelligence and in safe Reinforcement Learning. I work at the intersection of deep learning and formal methods to create learning algorithms that are provably safe, even during training, and to synthesize controller satisfying complex and global specifications expressed in probabilistic and temporal logic (PCTL). 

Interests

Teaching of Mathematics, Pedagoy, Teaching at Bachelor level. Research in: Neuro-symbolic AI, ResNets, PDE and Analysis in ML, Reinforcement Learning (RL) and Dynamic Programming (Q-Learning, Value Iteration), Shielding and Safe RL, Controller Synthesis, Probabilistic and/or Temporal Specifications, Continuous Control, Stability of Learning Algorithms, Regularity Theory and Generalization Bounds, Asymptotic Analysis of Learning Dynamics.

Teaching

EPFL 09.2016-02.2020

Analysis 1 - Fall 2016 - Bachelor

Keywords: Series of numbers, real analysis, limits, continuity, power series, topology, Riemann integral, series of functions.

Advanced analysis 2 - Spring 2017 - Bachelor

Keywords: Functions of several variables, differentiability, gradient, Hessian, integrals, ordinary differential equations, Banach and metric spaces, Lagrange multipliers.

Analysis 1 - Fall 2017 - Bachelor

Keywords: Series of numbers, real analysis, limits, continuity, power series, topology, Riemann integral, series of functions.

Advanced analysis 2 - Spring 2018 - Bachelor

Keywords:  Functions of several variables, differentiability, gradient, Hessian, integrals, ordinary differential equations, Banach and metric spaces, Lagrange multipliers.

Sobolev spaces and elliptic PDEs - Fall 2018 - Master

Keywords: Partial differential equations, Heat equation, wave equation, Duhamel’s principle, heat kernel, Sobolev spaces, weak solutions.

Functional Analysis 2 - Spring 2019 - Master

Keywords:  Locally convex spaces, topological dual, inductive limits, continuity, spectral family, Stieltjes integrals.

Evolutional partial differential equations - Fall 2019 - Master

Keywords: Non-linear and quasi-linear PDEs, envelopes, Cauchy-Kowalevski, characteristic varieties, hyperbolic PDEs, parabolic PDEs, kernel, contraction semigroups, Hille-Yosida.

Dynamics and bifurcation - Spring 2020 - Bachelor

Keywords: Local and global behavior of nonlinear dynamical systems arising from maps and ODEs. Theoretical and computational aspects studied. Lyapunov stability.

Algebraic Structures - Fall 2020 - Bachelor

Keywords: Fermat theorem (RSA), Euclide algorithm, groups and morphisms, Lagrange, quotient group, semi-direct product, usual groups (dihedral, quaternions …) 

University of Basel 03.2021-02.2025

Selected topics from analysis - Spring 2021 - Bachelor

Keywords: Student seminar, each student prepares a specific subject and is evaluated. Focuses and advanced analysis and mathematical physics.

Analysis and PDEs - Fall 2021 - Master

Keywords: Sobolev spaces, weak solutions, heat propagator, convolutions, energy methods, wave equation, harmonic functions, Green’s functions.

Proof from the book - Spring 2022 - Bachelor

Keywords: Student seminar, each student prepares a specific subject and is evaluated.

Measure and integration theory - Fall 2022 - Bachelor

Keywords: Sigma algebras, measures, Borelians, Lebesgue measure and integration, theorems on limits of integrals, density.

Fourier analysis - Spring 2023 - Master

Keywords: Lorentz spaces, Fourier Series, Fourier transform on L1 and L2, convolutions, inversion, Plancherel and Parseval theorems.

Mathematics and computers - Fall 2023 - Bachelor

Keywords: Matlab, Maple, introduction to programming and algorithmics, RSA, linear algebra.

Numerics - Spring 2024 - Bachelor

Keywords: Matlab, algorithmics for mathematics, error propagation, linear algebra, complexity analysis.

Numerics for Differential Equation- Fall 2024 - Bachelor

Keywords: Matlab, error propagation, stability, convergence, Runge-Kutta, Adams-Bashforth, BDF-k.

Publications

Artificial Intelligence

[11] PROSH: Probabilistic Shielding for Model-free Reinforcement Learning 

2025, arXiv, Link

Submitted to NeurIPS (A*) 2026

[10] SC$^2$: Safe Control via Shielding for CPCTL Specifications 

Accepted to KR (A*) 2026

[9] Synthesis of Safety Specifications for Probabilistic Systems 

2025, arXiv, Link

Accepted to AAMAS (A*) 2026

[8] PROSH: Probabilistic Shielding for Model-free Reinforcement Learning 

2025, arXiv, Link

Accepted to AAMAS (A*) 2026 as extended abstract

Analysis and PDE

[7] Scattering of Rational Solutions to the Half-Wave Maps Equation 

2025, arXiv, Link

Submitted to PURE and APPLIED ANALYSIS

[6] Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles 

2024, arXiv, Link

Submitted to Analysis and PDEs

 [5] On the stability of the ill-posedness of a quasi-linear wave equation in two dimensions with initial data in  $H^{7/4} (\ln H)^{-\beta}$ 

2024, arXiv, Link

[4] A Study on the Well-Posedness of 1D Energy-Critical Half-Wave Maps Equations 

2023, arXiv, Link

Submitted to Communications in PDEs

[3] Ill-posedness of a quasilinear wave equation in two dimensions for data in $H^{7/4} (\ln H)^{-\beta}$ 

2023, Pure and Applied Analysis, Link

[2] Ill-Posedness of the quasilinear wave equation in the space $H^{7/4}(\ln H)^{-\beta}$ in $\mathbb{R}^{2+1}$ (Ph.D thesis)

2021 - Ph.D thesis at EPFL, Link

Combinatorics

[1] Computation of Al-Salam Carlitz and Askey-Wilson Moments using Motzkin Paths 

2021 - The Electronic Journal of Combinatorics, Link