James B. Kennedy

I am a mathematician, currently an assistant professor ("professor auxiliar com agregação") at the Department of Mathematics in the Faculty of Sciences of the University of Lisbon, and a member of the research centre Grupo de Física Matemática (Group of Mathematical Physics, GFM), currently as vice-director. I am also (as of 2024) a collaborator of the research centre CIDMA.

I was previously (in reverse chronological order) a research fellow in Lisbon within in the scope of the program Investigador FCT 2015 of the Fundação para a Ciência e a Tecnologia, Portugal (reference IF/01461/2015) from 2017 to 2020, a postdoc ("wissenschaftlicher Mitarbeiter") at the Institut für Analysis, Dynamik und Modellierung of the University of Stuttgart, Germany, from 2013 to 2017, a Humboldt Fellow at the Institut für Angewandte Analysis of Ulm University, Germany, from 2011 to 2013, and a postdoc at the Grupo de Física Matemática at the University of Lisbon, Portugal, from 2010 to 2011, after completing my PhD at the School of Mathematics and Statistics of the University of Sydney, Australia, in 2010.

Here you can find my profiles on MathSciNet (subscription required), zbMATH Open, Google Scholar and ORCID, as well as my entry in the Mathematics Genealogy Project.

Contact Details

Recent Courses

• Análise Matemática III (Semester 1, 2024/25)
• Métodos Matemáticos nas Ciências (Semester 2, 2023/24)
• Operator Semigroups and Evolution Equations (Semester 2, 2023/24)
• Análise Matemática III (Semester 1, 2023/24)
• Applied Functional Analysis (Semester 1, 2023/24)
• Métodos Matemáticos nas Ciências (Semester 2, 2022/23)
• Análise Matemática III (Semester 1, 2022/23)
• Tópicos de Matemática (Semester 1, 2022/23)

Research Interests

• Elliptic and parabolic partial differential equations
• Applications of operator theory to partial differential equations
• Spectral theory of differential equations
• Isoperimetric and similar inequalities for eigenvalues of differential operators
• Variational methods
• Quantum graphs

Publications and Preprints

1. (with J. Rohleder) On the hot spots conjecture in higher dimensions, preprint arXiv:2410.00816
2. (with J. P. Ribeiro) Cheeger cuts and Robin spectral minimal partitions of metric graphs, to appear in J. Anal. Math., preprint arXiv:2310.02701
3. (with M. Ahrami, Z. El Allali and E. M. Harrell II), Optimizing the fundamental eigenvalue gap of quantum graphs, J. Phys. A: Math. Theor. 57 (2024), 385205, preprint arXiv:2401.04344
4. Geometric spectral theory of quantum graphs, Commun. Math. 32 (2024), 393-439, preprint arXiv:2310.02707
5. (with L. N. Baptista and D. Mugnolo) Mean distance on metric graphs, J. Geom. Anal. 34 (2024), 137, MR4719985, preprint arXiv:2312.04952
6. (with P. Freitas) On domain monotonicity of Neumann eigenvalues of convex domains, 2023, preprint arXiv:2307.06593
7. (with M. Hofmann and A. Serio) Spectral minimal partitions of unbounded metric graphs, J. Spectr. Theory 13 (2023), 593-622, MR4651734, preprint arXiv:2209.03658
8. Translation from the German, W. Arendt and K. Urban, Partial Differential Equations: An Introduction to Analytical and Numerical Methods, Graduate Texts in Mathematics 294, Springer, Cham, 2023, MR4628013
9. (with G. Berkolaiko, P. Kurasov and D. Mugnolo) Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap, Proc. Amer. Math. Soc. 151 (2023), 3439-3455, MR4591778, preprint arXiv:2206.10046
10. (with M. Düfel, D. Mugnolo, M. Plümer and M. Täufer) Boundary conditions matter: on the spectrum of infinite quantum graphs, 2022, preprint arXiv:2207.04024
11. (with S. Bögli and R. Lang) On the eigenvalues of the Robin Laplacian with a complex parameter, Anal. Math. Phys. 12 (2022), 39, MR4376240, preprint arXiv:1908.06041
12. (with D. Buoso) The Bilaplacian with Robin boundary conditions, SIAM J. Math. Anal. 54 (2022), 36-78, MR4358025, preprint arXiv:2105.11249
13. (with W. Arendt) Disjointness-preserving operators and isospectral Laplacians, J. Spectr. Theory 11 (2021), 1471-1510, MR4349669, preprint arXiv:2002.09207
14. (with M. Hofmann, D. Mugnolo and M. Plümer) On Pleijel's nodal domain theorem for quantum graphs, Ann. Henri Poincaré 22 (2021), 3841-3870, MR4325879, preprint arXiv:2012.05808
15. (with P. Freitas) Extremal domains and Pólya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles, Int. Math. Res. Not. IMRN (2021), 13730-13782, MR4320795
16. (with J. Rohleder) On the hot spots of quantum graphs, Comm. Pure Appl. Anal. 20 (2021), 3029-3063, MR4315494, preprint arXiv:2003.14335
17. (with M. Hofmann) Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs, Lett. Math. Phys. 111 (2021), 96, MR4289271, preprint arXiv:2102.07585
18. (with M. Hofmann, D. Mugnolo and M. Plümer) Asymptotics and estimates for spectral minimal partitions of metric graphs, Int. Equ. Oper. Theory 93 (2021), 26, MR4260660, preprint arXiv:2007.01412
19. (with P. Kurasov, C. Léna and D. Mugnolo) A theory of spectral partitions of metric graphs, Calc. Var. PDE 60 (2021), 61, MR4239815, preprint arXiv:2005.01126
20. A family of diameter-based eigenvalue bounds for quantum graphs, pp. 213-239 in F. M. Atay et al, eds., Discrete and continuous models in the theory of networks, Oper. Theory Adv. Appl. 281, Springer, Cham, 2020, MR4181348, preprint arXiv:1807.08185
21. (with R. Lang) On the eigenvalues of quantum graph Laplacians with large complex δ couplings, Port. Math. 77 (2020), 133-161, MR4163973, preprint arXiv:2001.10244
22. (with G. Berkolaiko, P. Kurasov and D. Mugnolo) Surgery principles for the spectral analysis of quantum graphs, Trans. Amer. Math. Soc. 372 (2019), 5153-5197, MR4009401, preprint arXiv:1807.08183
23. (with J. Rohleder) On the hot spots of quantum trees, Conference proceedings of the joint 89th annual meeting of the International Association of Applied Mathematicians and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung, PAMM 18 (2018), e201800122, preprint arXiv:1808.02274
24. A toy Neumann analogue of the nodal line conjecture, Arch. Math. (Basel) 110 (2018), 261-271, MR3761137, preprint arXiv:1706.10037
25. (with G. Berkolaiko, P. Kurasov and D. Mugnolo) Edge connectivity and the spectral gap of combinatorial and quantum graphs, J. Phys. A: Math. Theor. 50 (2017), 365201, MR3688110, preprint arXiv:1702.05264
26. (with D. Bucur and P. Freitas) The Robin Problem, Chapter 4 in A. Henrot (ed.), Shape optimization and spectral theory, de Gruyter Open, Warsaw-Berlin, 2017, MR3681148
27. (with D. Mugnolo) The Cheeger constant of a quantum graph, Conference proceedings of the joint 87th annual meeting of the International Association of Applied Mathematicians and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung, PAMM 16 (2016), 875-876, preprint arXiv:1604.07453
28. (with P. Freitas) Summation formula inequalities for eigenvalues of Schrödinger operators, J. Spectr. Theory 6 (2016), 483-503, MR3551175, preprint arXiv:1605.01925
29. (with P. Kurasov, D. Mugnolo and G. Malenová) On the spectral gap of a quantum graph, Ann. Henri Poincaré 17 (2016), 2439-2473, MR3535868, preprint arXiv:1504.01962
30. (with D. Daners and J. Glück) Eventually and asymptotically positive semigroups on Banach lattices, J. Differential Equations 261 (2016), 2607-2649, MR3507982, preprint arXiv:1511.05294
31. (with P. Freitas) Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator, Osaka J. Math. 53 (2016), MR3492805, preprint arXiv:1605.01928
32. (with R. Chill and D. Hauer) Nonlinear semigroups generated by j-elliptic functionals, J. Math. Pures Appl. (9) 105 (2016), 415-450, MR3465809, preprint arXiv:1412.4151
33. (with D. Daners and J. Glück) Eventually positive semigroups of linear operators, J. Math. Anal. Appl. 433 (2016), 1561-1593, MR3398779, preprint arXiv:1511.09020
34. (with W. Arendt and A.F.M. ter Elst) Analytical aspects of isospectral drums, Oper. Matrices 8 (2014), 255-277, MR3202939, preprint arXiv:1305.1775
35. (with W. Arendt, A.F.M. ter Elst and M. Sauter) The Dirichlet-to-Neumann operator via hidden compactness, J. Funct. Anal. 266 (2014), 1757-1786, MR3146835, preprint arXiv:1305.0720
36. Closed nodal surfaces for simply connected domains in higher dimensions, Indiana Univ. Math. J. 62 (2013), 785-798, MR3164844, preprint arXiv:1009.1502
37. (with P.R.S. Antunes and P. Freitas) Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian, ESAIM: Control Optim. Calc. Var. 19 (2013), 438-459, MR3049718, preprint arXiv:1204.0648
38. The nodal line of the second eigenfunction of the Robin Laplacian in R² can be closed, J. Differential Equations 251 (2011), 3606-3624, MR2837697, preprint arXiv:1009.4768
39. On the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians, Z. Angew. Math. Phys. 61 (2010), 781-792, MR2726626, preprint arXiv:0910.3966
40. (with D. Daners) On the asymptotic behaviour of the eigenvalues of a Robin problem, Differential Integral Equations 23 (2010), 659-669, MR2654263, preprint arXiv:0912.0318
41. An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions, Proc. Amer. Math. Soc. 139 (2009), 627-633, MR2448584
42. A Faber-Krahn inequality for the Laplacian with generalised Wentzell boundary conditions, J. Evol. Equ. 8 (2008), 557-582, MR2438387
43. (with D. Daners) Uniqueness in the Faber-Krahn inequality for Robin problems, SIAM J. Math. Anal. 39 (2007/08), 1191-1207, MR2368899
44. PhD thesis: On the isoperimetric problem for the Laplacian with Robin and Wentzell boundary conditions, The University of Sydney, 2010. Summary in Bull. Aust. Math. Soc. 82 (2010), 348-350, MR2685158