Ongoing Projects (n=4)

• Study of the Inverse Eigenvalue problem for the set of doubly stochastic matrices. Specifically, the study of specific and general cases of the Perfect and Mirsky conjecture. See the introduction of this paper for a brief overview of the problem.

• Study of questions related to entrywise Loewner positivity preservers on matrices. Specifically, the study of entrywise functions preserving a generalization of Loewner positivity on sets of matrices.

• Study of a vast generalization of Hardy's inequality on function spaces. In collaboration with Pierre-Olivier Parisé.

• Study of a characterization of infinite doubly stochastic matrices with unit operator ℓp-norms. In collaboration with Raphaël Arler (Cégep student) and Javad Mashreghi.

• Study of the Ingleton minimization problem (which is connected to matroid theory, information theory, determinantal inequalities). In collaboration with Pierre-Olivier Parisé.

 Research Papers (n=19)

1. Random vector norms and the energies of square and triangle-free graphs   ⟨arXiv - PDF⟩
   Ludovick Bouthat, Ángel Chávez, Sam Sheng. Submitted.

2. Number of orbits of k-subsets of permutations   ⟨arXiv - ResearchGate - PDF⟩
   Ludovick Bouthat, Raghavendra Tripathi, Journal of algebraic combinatorics, Submitted.

3. On the convergence of doubly stochastic Markov Chains
   Ludovick Bouthat, Nicolas Doyon, Javad Mashreghi, Frédéric Morneau-Guérin. Publicacions Matematiques, Accepted.

4. Hunter’s positivity theorem and random vector norms   ⟨arXiv - ResearchGate - PDF⟩
   Ludovick Bouthat, Ángel Chávez, Stephan Ramon Garcia. In: Operator Theory, Related Fields, and Applications. Operator Theory: Advances and Applications, vol 307. Birkhäuser, Cham, 149–215, 2025.

5. On the Geometry of the Birkhoff Polytope. I. The operator ℓp-norms   ⟨arXiv - ResearchGate - PDF⟩
   Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. Acta Sci. Math. (Szeged), 91, 227–245, 2025. 

6. On the Geometry of the Birkhoff Polytope. II. The Schatten p-norms   ⟨arXiv - ResearchGate - PDF⟩
   Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. Acta Sci. Math. (Szeged), 2024.

7. La théorie de la sommabilité : une généralisation quasi-arithmétique   ⟨ResearchGate - PDF⟩
   Julien April, Ludovick Bouthat. Bulletin AMQ, 64(2), 28–50, 2024.

8. On the monotonicity of left and right Riemann sums   ⟨arXiv - ResearchGate - PDF⟩
   Ludovick Bouthat. Sampling Theory, Signal Processing, and Data Analysis, 22(14), 2024. 

9. On the Submultiplicativity of Matrix Norms Induced by Random Vectors   ⟨arXiv - ResearchGate - PDF⟩
   Ludovick Bouthat. Complex Anal. Oper. Theory, 73(18), 2024. 

10. The diameter of the Birkhoff Polytope   ⟨ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. Special matrices, 12(1), 2024. 

11. On a question of Erdős on doubly stochastic matrices   ⟨arXiv - ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. Linear and Multilinear Algebra, 72(17) : 2823–2844, 2024.

12. Hardy-type inequalities for ℓp sequences   ⟨arXiv - ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. Journal of Mathematical Inequalities, 17(3) : 1165–1178, 2023. 

13. La représentation des matrices bistochastiques en produits de T-transformations   ⟨ResearchGate - PDF⟩
    Ludovick Bouthat. Bulletin AMQ, 63(1) :11–20, 2023. 

14. On the norm of normal matrices   ⟨ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. RIMS Kôkyûroku Bessatsu, B93, 2023. 

15. Monotonicity of left and right Riemann sums   ⟨ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin. Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis. Operator Theory : Advances and Applications, Birkhäuser/Springer, Cham, 290 : 89–113, 2023. 

16. The p-norm of circulant matrices   ⟨arXiv - ResearchGate - PDF⟩
    Ludovick Bouthat, Apoorva Khare, Javad Mashreghi, Frédéric Morneau-Guérin. Linear and Multilinear Algebra, 70(21) : 7176–7188, 2022. 

17. The critical point and the p-norm of the Hilbert L-matrix   ⟨arXiv - ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi. Linear Algebra Appl., 634 :1–14, 2022. 

18. L-matrices with lacunary coefficients   ⟨ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi. Oper. Matrices, 15(3) :1045–1053, 2021. 

19. The norm of an infinite L-matrix   ⟨ResearchGate - PDF⟩
    Ludovick Bouthat, Javad Mashreghi. Oper. Matrices, 15(1) :47–58, 2021.

 Thesis and Dissertations (n=2)

1. Les matrices doublement stochastiques : une étude géométrique   ⟨PDF⟩
   Ludovick Bouthat. Université Laval, Master, 2022. 

2. Conjecture de Sendov et produits de Blaschke finis   ⟨PDF⟩
   Ludovick Bouthat. Université Laval, Bachelor, 2020.

 Vulgarization Papers (n=1)

1. L’enveloppe spectrale des matrices bistochastiques : Une étude de cas du comportement étrange des petits nombres   ⟨PDF⟩
   Ludovick Bouthat. Notes from the Margin, 14 : 3–4, 2023.