Research interests
Spectral geometry: isospectrality and spectral uniqueness problems, estimates of Laplace eigenvalues.
Differential geometry: homogeneous Riemannian manifolds, Einstein manifolds of positive scalar curvature.
Lie theory: weight multiplicity formulas, branching rules.
Number theory: lattice point theorems, quadratic forms.
I am interested in the interaction between the spectrum of the Laplace operator and the geometry of a compact Riemannian manifold. I usually work with (locally and globally) homogeneous spaces, so the tools come from Lie theory.
[Spanish]: Puedes encontrar un video panorámico de mis intereses en geometría espectral en mi stand virtual Geometría espectral inversa en Bahía Blanca de la Muestra de líneas de investigación en geometría en Argentina del Congreso Monteiro 2021 (26 de mayo al 4 de junio de 2021).
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Recorded talks
In English
Isospectrality among homogeneous Riemannian manifolds, TYAN Virtual Workshop on Differential Geometry, February 21, 2022.
Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups, MCA 2021, July 23, 2021.
Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups (asynchronous talk), 3rd Geometric Analysis Festival. July 2021. (Download the slides.)
Diameter and Laplace eigenvalue estimates for homogeneous Riemannian manifolds, Geometry Webinar AmSur/AmSul. July 9, 2020.
In Spanish (en castellano)
Sobre multiplicidades de pesos de representaciones de álgebras de Lie semisimple, ERAG, Universidad Nacional de la Plata. Del 1 al 3 de diciembre de 2021.
Curso en la VirtUMA 2021 "¿Se puede oír la forma de un tambor?". 20 al 24 de septiembre de 2021.
Clase 1 (tambores isospectrales): grabación y filminas,
Clase 2 (toros planos isospectrales): grabación y filminas,
Clase 3 (espacios lentes isospectrales): grabación y filminas.
Geometría espectral inversa en Bahía Blanca, stand virtual de la Muestra de líneas de investigación en geometría en Argentina del Congreso Monteiro 2021, Universidad Nacional del Sur. Del 26 de mayo al 4 de junio de 2021.
Sobre el primer autovalor del Laplaciano en esferas homogéneas (comunicación asincrónica), Congreso Monteiro 2021, Universidad Nacional del Sur. Del 26 de mayo al 4 de junio de 2021.
Sobre subgrupos discretos equivalentes en representaciones, Seminario de Álgebra, Combinatoria y Teoría de Lie, Universidad Nacional del Sur, Bahía Blanca, Argentina. 27 de marzo de 2020.
Estimaciones del menor autovalor positivo del Laplaciano, Seminario del Grupo de Geometría Diferencial, FaMAF, Universidad Nacional de Córdoba, Argentina. 25 de julio de 2019.
Articles
Preprints
The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems. Benjamin Linowitz and Emilio Lauret. May 2023, arXiv:2305.10950.
Spectrally distinguishing symmetric spaces I. Emilio Lauret and Juan Sebastián Rodríguez. Nov 2023, arXiv:2311.09719.
Isospectral CR manifolds with respect to the Kohn Laplacian. Gerson Gutierrez, Emilio Lauret, and Juan Pablo Rossetti. Dic 2023, arXiv:2312.15214.
Published and accepted articles
Diameter and displacement of sphere involutions. Renato Bettiol and Emilio Lauret. Matemática Contemporânea 57 (2023), 23-31. arXiv:2205.05186, doi: 10.21711/231766362023/rmc573.
The stability of standard homogeneous Einstein manifolds. Emilio Lauret and Jorge Lauret. Math. Z. 303 (2023), 16. arXiv:2112.08469, doi: 10.1007/s00209-022-03174-6. Read the published version for free.
Full Laplace spectrum of distance spheres in symmetric spaces of rank one. Renato Bettiol, Emilio Lauret, and Paolo Piccione. Bull. Lond. Math. Soc. 54:5 (2022), 1683-1704. arXiv:2012.02349, doi: 10.1112/blms.12650.
The first eigenvalue of a homogeneous CROSS. Renato Bettiol, Emilio Lauret, and Paolo Piccione. J. Geom. Anal. 32 (2022), 76. arXiv:2001.08471, doi: 10.1007/s12220-021-00826-7. Read the published version for free.
Strong representation equivalence for compact symmetric spaces of real rank one. Emilio Lauret and Roberto Miatello. Pacific J. Math. 314:2 (2021), 333-373. arxiv:1812.09606, doi: 10.2140/pjm.2021.314.333.
Diameter and Laplace eigenvalue estimates for compact homogeneous Riemannian manifolds. Emilio Lauret. Transform. Groups 28:4 (2023), 1629–1650. arXiv:2007.07199, doi: 10.1007/s00031-022-09693-0. Read the published version for free.
Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups. Emilio Lauret. Potential Analysis 58 (2023), 37-70. arXiv:2004.00350. doi: 10.1007/s11118-021-09932-1. Read the published version for free.
Strong multiplicity one theorems for locally homogeneous spaces of compact type. Emilio Lauret and Roberto Miatello. Proc. Amer. Math. Soc. 148 (2020), 3163-3173. arxiv:1804.08288, doi: 10.1090/proc/14980.
On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups. Emilio Lauret. Proc. Amer. Math. Soc. 148 (2020), 3375-3380. arxiv:1906.03325, doi: 10.1090/proc/14969.
Non-solvable Lie groups with negative Ricci curvature. Emilio Lauret and Cynthia Will. Transform. Groups 27:1 (2022), 163-179. arxiv:1905.12572, doi: 10.1007/s00031-020-09582-4. Read the published version for free.
The smallest Laplace eigenvalue of homogeneous 3-spheres. Emilio Lauret. Bull. Lond. Math. Soc. 51:1 (2019), 49-69. arXiv:1801.04259, doi: 10.1112/blms.12213.
A computational study on lens spaces isospectral on forms. Emilio Lauret. Exp. Math. 30:2 (2021), 268-282. arXiv:1703.03077, doi: 10.1080/10586458.2018.1538908. Appendix with computational results.
On the SO(n+3) to SO(n) branching multiplicity space. Emilio Lauret and Fiorela Rossi Bertone. Comptes Rendus Acad. Sci. Paris, Ser. I Math. 356 (2018), 1112-1124. arxiv:1805.03109, doi: 10.1016/j.crma.2018.09.004.
Weight multiplicity formulas for bivariate representations of classical Lie algebras. Emilio Lauret and Fiorela Rossi Bertone. J. Math. Phys. 59:8 (2018), 081705. arXiv:1708.07905, doi: 10.1063/1.5043305.
Spectral uniqueness of bi-invariant metrics on symplectic groups. Emilio Lauret. Transform. Groups 24:4 (2019), 1157-1164. arXiv:1706.09012, doi: 10.1007/s00031-018-9486-5. Read the published version for free.
The spectrum on p-forms of a lens space. Emilio Lauret. Geom. Dedicata 197 (2018), 107-122. arXiv:1604.02471, doi:10.1007/s10711-018-0322-9. Read the published version for free.
Multiplicity formulas for fundamental strings of representations of classical Lie algebras. Emilio Lauret and Fiorela Rossi Bertone. J. Math. Phys. 58:11 (2017), 111703. arXiv:1706.07839, doi: 10.1063/1.4993851.
An explicit formula for the Dirac multiplicities on lens spaces. Sebastian Boldt and Emilio Lauret. J. Geom. Anal. 27 (2017), 689-725. arXiv:1412.2599, doi:10.1007/s12220-016-9695-x. Read the published version for free.
Spectra of orbifolds with cyclic fundamental groups. Emilio Lauret. Ann. Global. Anal. Geom. 50 (2016), 1-28. arXiv:1510.05948, doi: 10.1007/s10455-016--9498-0. Read the published version for free.
Spectra of lens spaces from 1-norm spectra of congruence lattices. Emilio Lauret, Roberto Miatello and Juan Pablo Rossetti. Int. Math. Res. Not. IMRN 2016 (2016), 1054-1089. arXiv:1311.7167, doi: 10.1093/imrn/rnv159.
Representation equivalence and p-spectrum of constant curvature space forms. Emilio Lauret, Roberto Miatello and Juan Pablo Rossetti. J. Geom. Anal. 25 (2015), 564-591. arXiv:1209.4916. doi: 10.1007/s12220-013-9439-0. Read the published version for free.
A generalized Hermite constant for imaginary quadratic fields. Wai Kiu Chan, Maria Ines Icaza and Emilio Lauret. Math. Comp. 84 (2015), 1883-1900. arXiv:1307.3714. doi: 10.1090/S0025-5718-2015-02903-2.
A numerical study on exceptional eigenvalues of certain congruence subgroups of SO(n,1) and SU(n,1). Emilio Lauret. Ramanujan J. 35 (2014), 179-204. arXiv:1212.0674. doi: 10.1007/s11139-014-9590-7. Read the published version for free.
Representation equivalent Bieberbach groups and strongly isospectral flat manifolds. Emilio Lauret. Canad. Math. Bull. 57 (2014), 357-363. arXiv:1210.0894. doi: 10.4153/CMB-2013-013-2.
An asymptotic formula for representations of integers by indefinite hermitian forms. Emilio Lauret. Proc. Amer. Math. Soc. 142 (2014) 1-14. arXiv:11096697. doi: 10.1090/S0002-9939-2013-11726-0.
Strongly isospectral manifolds with nonisomorphic cohomology rings. Emilio Lauret, Roberto Miatello and Juan Pablo Rossetti. Rev. Mat. Iberoam. 29 (2013) 611-634. arXiv:1103.0249. doi: 10.4171/RMI/732.
Survey articles
Recent results on the spectra of lens spaces. Emilio Lauret, Roberto Miatello, and Juan Pablo Rossetti. In "Special Section: An Homage to Manfredo P. do Carmo", Sao Paulo J. Math. Sci. 15:1 (2021), 240-267. arxiv:1904.01146, doi: 10.1007/s40863-019-00154-3.
Non-strongly isospectral spherical space forms. Emilio Lauret, Roberto Miatello and Juan Pablo Rossetti. In "Mathematical Congress of the Americas", Contemp. Math. 656 (2016), 95-118. arXiv:1505.02554, doi: 10.1090/conm/656/13104.