1. B. Colbois and A. Girouard
    Metric upper bounds for Steklov and Laplace eigenvalues

Book Chapters
  1. A. Girouard and I. Polterovich
    Spectral geometry of the Steklov problem. Shape optimization and spectral theory,
    120-148. De Gruyter Open Ltd, Warsaw/Berlin. 2017.
Published and accepted papers
  1. A. Girouard, M. Karpukhin, M. Levitin, I. Polterovich
    The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript,
    Journal of Spectral Theory, Volume 12 (2022), no. 1, Pages 195-225.

  2. A. Girouard, M. Karpukhin, J. Lagacé
    Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems,
    Geometric and Functional Analysis: Volume 31 (2021), Issue 3, Pages 513-561.

  3. A. Girouard, J. Lagacé
    Large Steklov eigenvalues via homogenisation on manifolds,
    Inventiones mathematicae: Volume 226 (2021), Issue 3, Pages 1011-1056.

  4. A. Girouard, A. Henrot, J. Lagacé
    From Steklov to Neumann via homogenisation,
    Archive for Rational Mechanics and Analysis: Volume 239 (2021), Issue 2, Pages 981-1023.

  5. A. Girouard, R. Laugesen
    Robin spectrum: two disks maximize the third eigenvalue.
    Indiana University Mathematics Journal: Volume 70 (2021), Issue 6, Pages 2711-2742.

  6. B. Colbois, A. Girouard, A. Hassannezhad
    The Steklov and Laplacian spectra of Riemannian manifolds with boundary.
    Journal of Functional Analysis: Volume 278 (2020), Issue 6.

  7. B. Colbois, A. Girouard, A. Métras
    Hypersurfaces with prescribed boundary and small Steklov eigenvalues
    Canadian Mathematical Bulletin: Volume 63 (2020), Issue 1.

  8. B. Colbois, A. El Soufi, A. Girouard
    Compact manifolds with fixed boundary and large Steklov eigenvalues.
    Proceedings of the American Mathematical Society: Volume 147 (2019), Issue 9, Pages 3813–3827.

  9. B. Colbois, A. Girouard, K. Gittins
    Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space.
    The Journal of Geometric Analysis: Volume 29 (2019), Issue 2, Pages 1811–1834.

  10. A. Girouard, J. Lagacé, I. Polterovich, A. Savo
    The Steklov spectrum of cuboids.
    Mathematika, Volume 65 (2019), Issue 2, Pages 272-310.

  11. B. Colbois, A. Girouard, Binoy Raveendran
    The Steklov spectrum and coarse discretizations of manifolds with boundary.
    Pure and Applied Mathematics Quarterly: Volume 14 (2018), Issue 2, Pages 357-392.

  12. D. Cianci, A. Girouard
    Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations.
    Annals of Global Analysis and Geometry: Volume 54 (2018), Issue 4, Pages 529–539.

  13. A. Girouard and I. Polterovich
    Spectral geometry of the Steklov problem.
    Journal of spectral theory, Volume 7 (2017), Issue 2, Pages 321–359.

  14. A. Girouard, R. Laugesen, B. Siudeja
    Steklov eigenvalues and quasiconformal maps of simply connected planar domains.
    Archive for Rational Mechanics and Analysis
    Volume 219 (2016), Issue 2, Pages 903-936.

  15. A. Girouard, L. Parnovski, I. Polterovich, D. Sher
    The Steklov spectrum of surfaces: asymptotics and invariants.
    Mathematical Proceedings of the Cambridge Philosophical Society.
    Volume 157 (2014), Issue 3, Pages 379-389.)

  16. B. Colbois and A. Girouard,
    The spectral gap of graphs and Steklov eigenvalues on surfaces.
    Electronic Research Announcements in Mathematical Sciences ,
    Volume 21 (2014), Pages 19–27.

  17. B. Colbois, A. Girouard, M. Iversen,
    Uniform stability of the Dirichlet spectrum for rough outer perturbations,
    Journal of Spectral Theory
    Volume 3 (2013), Issue 4, Pages 575–599.

  18. B. Colbois, A. El Soufi, A. Girouard,
    Isoperimetric control of the spectrum of a compact hypersurface,
    Journal für die reine und angewandte Mathematik
    Issue 683 (2013), Pages 49-65.

  19. A. Girouard, I. Polterovich
    Upper bounds for Steklov eigenvalues on surfaces.
    Electronic Research Announcements in Mathematical Sciences ,
    Volume 19 (2012), Pages 77–85.

  20. B. Colbois, A. El Soufi, A. Girouard,
    Isoperimetric control of the Steklov spectrum,
    Journal of Functional Analysis
    Volume 261 (2011), Issue 5, Pages 1384-1399.

  21. A. Girouard and I. Polterovich,
    On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues,
    Functional Analysis and its Applications
    Volume 44 (2010), Issue 2, Pages 106-117.

  22. A. Girouard and I. Polterovich,
    Shape optimization for low Neumann and Steklov eigenvalues,
    Mathematical Methods in the Applied Sciences
    Volume 33 (2010), Issue 4, Pages 501-516.

  23. A. Girouard, N. Nadirashvili, I. Polterovich,
    Maximization of the second positive Neumann eigenvalue for planar domains,
    Journal of Differential Geometry
    Volume 83 (2009), no. 3, Pages 637-662.

  24. A. Girouard,
    Fundamental tone, concentration of density to points and conformal degeneration on surfaces,
    Canadian Journal of Mathematics
    Volume 61 (2009), Issue 3, Pages 548-565.

  25. A. Girouard,
    Relative homological linking,
    Topological methods in nonlinear analysis
    Volume 30 (2007), Issue 2, Pages 211-222.
  1. A. Girouard, Dégénérescence et problèmes extrémaux pour les valeurs propres du laplacien sur les surfaces,
    PhD, Université de Montréal, 2008.

  2. A. Girouard, Enlacement homologique relatif,
    MSc, Université de Montréal, 2002.
Course notes
  1. A. Girouard and Y. Saint-Aubin, Mathématiques assistées par ordinateur, Université de Montréal, 2010.