Journal articles and preprints
97. On the (growing) gap between Dirichlet and Neumann eigenvalues. Indiana Univ. Math. J., to appear (with Miguel Gama).
96. Extremal problems for clamped plates under tension. J. Math. Pures Appl. 208:103867 (2026), 36pp (with Roméo Leylekian).
95. On domain monotonicity of Neumann eigenvalues of convex domains. Proc. Amer. Math. Soc. 153 (2025), 5315-5328 (with James B. Kennedy).
94. Sharp inequalities and asymptotics for polyharmonic eigenvalues. Calc. Var. Partial Differential Equations 64:295 (2025), 37pp (with Davide Buoso).
93. Pólya-type inequalities on spheres and hemispheres. Ann. Inst. Fourier (Grenoble) 75 (2025), 979–1051 (with Jing Mao and Isabel Salavessa).
92. Recurrence formulae for spectral determinants. J. Number Theory 267 (2025), 134–175 (with José Cunha).
91. The spectral determinant for second order elliptic operators on the real line. Lett. Math. Phys. 114:65 (2024), 17pp (with Jiří Lipovský).
90. Optimisation of functional determinants on the circle. In Ivan Kupka Legacy, A Tour Through Controlled Dynamics, AIMS on Applied Mathematics 12 (2024), 155–171 (with Jean-Baptiste Caillau, Yacine Chitour and Yannick Privat).
89. Families of non-tiling domains satisfying Pólya's conjecture. J. Math. Phys. 64 (2023), 121503, 7pp (with Isabel Salavessa).
88. Two balls maximize the third Neumann eigenvalue in hyperbolic space. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXIII (2022), 1325–1355 (with Richard S. Laugesen).
87. Bessel quotients and Robin eigenvalues. Pacific J. Math. 315 (2021), 75–87.
86. Extremal domains and Pólya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles. Int. Math. Res. Not. IMRN (2021), no. 18, 13730–13782 (with James B. Kennedy).
85. From Neumann to Steklov and beyond, via Robin: the Weinberger way. Amer. J. Math. 143 (2021), 969–994 (with Richard S. Laugesen).
84. Optimal unions of scaled copies of domains and Pólya's conjecture. Ark. Math. 59 (2021), 11–51 (with Jean Lagacé and Jordan Payette).
83. A Gelfand–Levitan trace formula for generic quantum graphs. Anal. Math. Phys. 11:56 (2021), 19pp (with Jiří Lipovský).
82. The determinant of one-dimensional polyharmonic operators of arbitrary order. J. Funct. Anal. 279 (2020), 108783, 30pp (with Jiří Lipovský).
81. The damped wave equation with singular damping. Proc. Amer. Math. Soc. 148 (2020), 4273–4284 (with Nicolas Hefti and Petr Siegl).
80. From Steklov to Neumann and beyond, via Robin: the Szegö way. Canadian J. Math. 72 (2020), 1024–1043 (with Richard S. Laugesen).
79. Maximal determinants of Schrödinger operators on bounded intervals. J. Éc. polytech. Math. 7 (2020), 803–829 (with Clara Aldana and Jean-Baptiste Caillau).
78. Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles. Proc. Amer. Math. Soc. 148 (2020), 1109–1120 (with Davide Buoso).
77. On the behaviour of clamped plates under large compression. SIAM J. Appl. Math. 79 (2019), 1872–1891 (with Pedro R. S. Antunes and Davide Buoso).
76. Spectral determinant for the damped wave equation on an interval. Acta Phys. Polon. A 136 (2019), 817–823 (with Jiří Lipovský).
75. A remark on Pólya's conjecture at low frequencies. Arch. Math. (Basel) 112 (2019), 305–311.
74. The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions. Math. Ann. 372 (2018), 1081–1101.
73. The damped wave equation with unbounded damping. J. Differential Equations 264 (2018), 7023–7054 (with Petr Siegl and C. Tretter).
72. Decay of solutions for a class of nonlinear Schrödinger equations in ℝ and the stability of shock profiles for a quasilinear Benney system. Nonlinearity 31 (2018), 1110–1119 (with João-Paulo Dias).
71. Sharp bounds for the modulus and phase of Hankel functions with applications to Jaeger integrals. Math. Comp. 87 (2018), 289–308.
70. A free boundary approach to the Faber–Krahn inequality. Contemp. Math. 700 (2017), 73–86 (with Dorin Bucur).
69. Bounds and extremal domains for Robin eigenvalues with negative boundary parameter. Adv. Calc. Var. 10 (2017), 357–379 (with Pedro R. S. Antunes and David Krejčiřík).
68. The spectrum of geodesic balls on spherically symmetric manifolds. Comm. Anal. Geom. 25 (2017), 507–544 (with Denis Borisov).
67. Eigenvalue asymptotics for the damped wave equation on metric graphs. J. Differential Equations 263 (2017), 2780–2811 (with Jiří Lipovský).
66. Asymptotic behaviour of extremal averages of Laplacian eigenvalues. J. Stat. Phys. 167 (2017), 1511–1518.
65. Summation formula inequalities for eigenvalues of Schrödinger operators. J. Spectral Theory 6 (2016), 483–503 (with James B. Kennedy).
64. Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction. Appl. Math. Optim. 73 (2016), 313–328 (with Pedro R. S. Antunes).
63. Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator. Osaka J. Math. 53 (2016), 397–416 (with James B. Kennedy).
62. Alexandrov's isodiametric conjecture and the cut locus of a surface. Tohoku Math. J. 67 (2015), 405–417 (with David Krejčiřík).
61. The first Robin eigenvalue with negative boundary parameter. Adv. Math. 280 (2015), 322–339 (with David Krejčiřík).
60. Spectra of graphene nanoribbons with armchair and zigzag boundary conditions. Rev. Math. Phys. 26 (2014), 1450018 (32 pages) (with Petr Siegl).
59. Optimal ball placement in rugby conversions. SIAM Rev. 56 (2014), 673–690.
58. Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds. Calc. Var. Partial Differential Equations 51 (2014), 701–724 (with Jing Mao and Isabel Salavessa).
57. On the spectrum of deformations of compact double-sided flat hypersurfaces. Anal. PDE 6 (2013), 1051–1088 (with Denis Borisov).
56. Asymptotic behaviour of optimal spectral planar domains with fixed perimeter. J. Math. Phys. 54 (2013), 053504 (with Dorin Bucur).
55. Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian. ESAIM: Control, Optimisation and Calculus of Variations 19 (2013), 438–459 (with Pedro R. S. Antunes and James B. Kennedy).
54. Asymptotics for the expected lifetime of Brownian motion on thin domains in ℝn. J. Theoret. Probab. 26 (2013), 284–309 (with Denis Borisov).
53. Optimal spectral rectangles and lattice ellipses. Proc. Royal Soc. A Math. Phys. Eng. Sci. 469 (2013), 20120492 (with Pedro R. S. Antunes).
52. On the role of spectral markers and stability in spine models. J. Mech. Behavior Biomed. Materials 14 (2012), 19–28 (with Pedro R. S. Antunes).
51. Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians. J. Opt. Theory Appl. 154 (2012), 235–257 (with Pedro R. S. Antunes).
50. Eigenvalue asymptotics for almost flat compact hypersurfaces. Dokl. Akad. Nauk. 442 (2012), 151–155; translation in Dokl. Math. 85 (2012), 18–22 (with Denis Borisov).
49. Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem. Adv. Math. 228 (2011), 2352–2365 (with Barbara Brandolini, Carlo Nitsch and Cristina Trombetti).
48. On the inverse spectral problem for Euclidean triangles. Proc. Royal Soc. A Math. Phys. Eng. Sci. 467 (2011), 1546–1562 (with Pedro R. S. Antunes).
47. A spectral Bernstein theorem. Ann. Mat. Pura Appl. 190 (2011), 77–90 (with Isabel Salavessa).
46. Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. ESAIM: Control, Optimisation and Calculus of Variations 16 (2010), 646–676 (with Bartłomiej Siudeja).
45. On the characterization of harmonic and subharmonic functions via mean-value properties. Potential Anal. 32 (2010), 189–200 (with João Palhoto Matos).
44. Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in ℝd. J. Funct. Anal. 258 (2010), 893–912 (with Denis Borisov).
43. On the effect of sharp rises in blood pressure in the Shah-Humphrey model for intracranial saccular aneurysms. Biomech. Model. Mechanobiology 8 (2009), 457–471.
42. Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. J. Differential Equations 247 (2009), 3028–3039 (with Denis Borisov).
41. Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions on thin planar domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 547–560 (with Denis Borisov).
40. Hearing the weights of weighted projective planes. Ann. Global Anal. Geom. 33 (2008), 373–395 (with Miguel Abreu, Emily B. Dryden and Leonor Godinho).
39. A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains. Proc. Amer. Math. Soc. 136 (2008), 2997–3006 (with David Krejčiřík).
38. Location of the nodal set for thin curved tubes. Indiana Univ. Math. J. 57 (2008), 343–376 (with David Krejčiřík).
37. A numerical study of the spectral gap. J. Phys. A 41 (2008), 055201 (with Pedro R. S. Antunes).
36. On convex surfaces with minimal moment of inertia. J. Math. Phys. 48 (2007), 122902 (with Richard S. Laugesen and Gerrard F. Liddell).
35. Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi. J. Funct. Anal. 251 (2007), 376–398.
34. Unbounded planar domains whose second nodal line does not touch the boundary. Math. Res. Lett. 14 (2007), 107–111 (with David Krejčiřík).
33. Waveguides with combined Dirichlet and Robin boundary conditions. Math. Phys. Anal. Geom. 9 (2006), 335–352 (with David Krejčiřík).
32. New bounds for the principal Dirichlet eigenvalue of planar regions. Experiment. Math. 15 (2006), 333–342 (with Pedro R. S. Antunes).
31. A Li-type criterion for zero-free half-planes of Riemann's zeta function. J. London Math. Soc. 73 (2006), 399–414.
30. Upper and lower bounds for the first Dirichlet eigenvalue of a triangle. Proc. Amer. Math. Soc. 134 (2006), 2083–2089.
29. Extension of Abel's Lemma with q-series implications. Ramanujan J. 10 (2005), 137–152 (with George E. Andrews).
28. Geometrically induced discrete spectrum in curved tubes. Differential Geom. Appl. 23 (2005), 95–105 (with Pierre Duclos and David Krejčiřík).
27. Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums. Math. Comp. 74 (2005), 1425–1440.
26. Instability results for the damped wave equation in unbounded domains. J. Differential Equations 211 (2005), 168–186 (with David Krejčiřík).
25. On the first twisted Dirichlet eigenvalue. Comm. Anal. Geom. 12 (2004), 1083–1103 (with Antoine Henrot).
24. A lower bound to the spectral threshold in curved tubes. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004), 3457–3467 (with Pavel Exner and David Krejčiřík).
23. Closed nodal lines and interior hot spots of the second eigenfunction of the Laplacian on surfaces. Indiana Univ. Math. J. 51 (2002), 305–316.
22. Memory driven instability in a diffusion process. SIAM J. Math. Anal. 33 (2002), 1090–1106 (with Brian R. Duffy and Michael Grinfeld).
21. On the invariant spectrum of S1-invariant metrics on S2. Proc. London Math. Soc. 84 (2002), 213–230 (with Miguel Abreu).
20. On minimal eigenvalues of Schrödinger operators on manifolds. Commun. Math. Phys. 217 (2001), 375–382.
19. Lyapunov functionals and stability for FitzHugh–Nagumo systems. J. Differential Equations 169 (2001), 208–227 (with Carlos Rocha).
18. Delay induced instabilities in gyroscopic systems. SIAM J. Control Optimization 39 (2000), 196–207.
17. Stability of stationary solutions of nonlocal reaction–diffusion equations in n-dimensional space. Differential and Integral Equations 13 (2000), 265–288 (with Mikhail Vishnevskii).
16. Spectral sequences for quadratic pencils and the inverse spectral problem for the damped wave equation. J. Math. Pures Appl. 78 (1999), 965–980.
15. On the optimal value of the spectral abscissa for a system of linear oscillators. SIAM J. Matrix Anal. Appl. 21 (1999), 195–208 (with Peter Lancaster).
14. Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: a counterexample to the constant damping conjecture. SIAM J. Control Optimization 37 (1999), 376–387.
13. Quadratic matrix polynomials with Hamiltonian spectrum and oscillatory damped systems. Z. Angew. Math. Phys. 50 (1999), 64–81.
12. Nonlocal reaction–diffusion equations. In Differential Equations with Applications to Biology, Fields Inst. Commun. 21, AMS (1999), 187–204.
11. Positivity results for a nonlocal elliptic equation. Proc. Roy. Soc. Edinburgh 128 (1998), 697–715 (with Guido Sweers).
10. The linear wave equation, Hamiltonian symmetry, and the importance of being odd. Disc. Cont. Dyn. Syst. 4 (1998), 635–640.
9. Eigenvalue problems for the wave equation with strong damping. Proc. Roy. Soc. Edinburgh A 127 (1997), 755–771.
8. Stability of finite-dimensional systems with indefinite damping. Adv. Math. Sci. Appl. 7 (1997), 435–446 (with Michael Grinfeld and Philip Knight).
7. Some results on the stability and bifurcation of stationary solutions of delay–diffusion equations. J. Math. Anal. Appl. 206 (1997), 59–82.
6. Stability results for the wave equation with indefinite damping. J. Differential Equations 132 (1996), 338–352 (with Enrique Zuazua).
5. On some eigenvalue problems related to the wave equation with indefinite damping. J. Differential Equations 127 (1996), 320–335.
4. Stability of stationary solutions of a nonlocal reaction–diffusion equation. Quart. J. Mech. Appl. Math. 48 (1995), 557–582.
3. Stationary solutions of an equation modelling ohmic heating. Appl. Math. Lett. 7 (1994), 1–6 (with Michael Grinfeld).
2. Bifurcation and stability of stationary solutions of nonlocal scalar reaction–diffusion equations. J. Dynam. Differential Equations 6 (1994), 613–629.
1. A nonlocal Sturm-Liouville eigenvalue problem. Proc. Roy. Soc. Edinburgh A 124 (1994), 169–188.
Books (as editor, book chapters)
2. The Robin problem. In Shape optimization and spectral theory, 2017, 78–119. Antoine Henrot (ed.), De Gruyter. (with Dorin Bucur and James B. Kennedy).
1. Topics in functional differential and difference equations, Fields Inst. Commun. 29, AMS, Providence, RI, 2001 (co-editor: Teresa Faria).
Proceedings
4. A lower bound to the spectral threshold in curved quantum layers. In Functional Analysis and Operator Theory for Quantum Physics (2017), 261–269. Volume dedicated to Pavel Exner on the occasion of his 70th birthday. J. Dittrich, H. Kovařík, and A. Laptev (eds.), EMS Publishing House (with David Krejčiřík).
3. Characterization and parameterization of the singular manifold of a simple 6–6 Stewart platform. In Nonlinear Science and Complexity (2011), 255–262, J. A. T. Machado et al. eds. (with Tiago Charters).
2. (In)stability results for the wave equation with indefinite damping. In Proceedings of Equadiff 95 (1998), 350–355.
1. Bogdanov singularity in the FitzHugh–Nagumo equations. In Proceedings of Equadiff 91 (1993), 496–500 (with Carlos Rocha).
Reports
12. Modelling percolation and fractal structure in aerogels. 92nd European Study Group with Industry (2013) (with Adérito Araújo, Joaquim Correia, Michael Grinfeld, Jevgenija Pavlova and Diogo Pinheiro).
11. Modelling fiber flow in fiberboard manufacturing. 86th European Study Group with Industry (2012) (with Diogo Pinheiro, João Penedones and José Matos).
10. Asymptotic behaviour of some eigenvalue optimisation problems. Oberwolfach report no. 33/2012.
9. Balanced Scorecard. 81st European Study Group with Industry (2011) (with Elisete Correia and Irene Oliveira).
8. Detecting singularities of Stewart platforms. Mathematics-in-Industry Case Studies 1 (2009), 66–80, Fields Institute Publications (with Tiago Charters and Ricardo Enguiça).
7. Fraud detection in plastic card operations. 69th European Study Group with Industry (2009) (with Paulo C. Aguiar and António J. Rodrigues).
6. Approximating low eigenvalues of the Laplacian: analysis, geometry and numerics. Oberwolfach report no. 06/2009.
5. Scheduling in a factory. 65th European Study Group with Industry (2008) (with Jorge Orestes Cerdeira, Tiago Charters, Manuel Cruz and Paulo Vasconcelos).
4. Electrostatic separation of rubber and textiles. 65th European Study Group with Industry (2008).
3. Cooling of a rotor. 65th European Study Group with Industry (2008) (with Nuno Lopes).
2. Stewart platform. 60th European Study Group with Industry (2007) (with Tiago Charters and Ricardo Enguiça).
1. Sharp dynamic bounds for eigenvalues of the Laplacian. Oberwolfach report no. 18/2007.
Other
2. European Study Groups with Industry at 40 years. SIAM News, March 2009.
1. European Study Groups with Industry in Portugal: importing a forty year old concept. CIM Bulletin, December 2008.