Emilio Lauret

I am a mathematician working in Córdoba, Argentina. I was an Oberwolfach Leibniz Fellow at the Oberwolfach Mathematical Institute in 2013-2014 and an Alexander von Humboldt Postdoctoral Fellow at Humboldt-Universität zu Berlin in 2017-2018.

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 homogeneous spaces or locally homogeneous spaces, so the tools come from Lie theory.

emiliolauret at gmail.com.

Curriculum vitae.

Positions:

Research interests:

  • Spectral geometry: isospectrality, spectral rigidity, spectra of homogeneous manifolds.
  • Lie theory: weight multiplicity formulas, branching rules.
  • Number theory: lattice point theorems, quadratic forms.

Preprints:

  1. On the SO(n+3) to SO(n) branching multiplicity space. Emilio Lauret and Fiorela Rossi Bertone. May 2018, arxiv:1805.03109.
  2. Strong multiplicity one theorems for locally homogeneous spaces of compact type. Emilio Lauret and Roberto Miatello. April 2018, arxiv:1804.08288.
  3. The smallest Laplace eigenvalue of homogeneous 3-spheres. Emilio Lauret. January 2018, arXiv:1801.04259.
  4. A computational study on lens spaces isospectral on forms. Emilio Lauret. March 2017, arXiv:1703.03077. Appendix with computational results.

Publications:

  1. Weight multiplicity formulas for bivariate representations of classical Lie algebras. Emilio Lauret and Fiorela Rossi Bertone. J. Math. Phys., in press since August 2018. arXiv:1708.07905.
  2. Spectral uniqueness of bi-invariant metrics on symplectic groups. Emilio Lauret. Transform. Groups, in press since June 2018. arXiv:1706.09012. doi: 10.1007/s00031-018-9486-5 . See the published version for free.
  3. The spectrum on p-forms of a lens space. Emilio Lauret. Geom. Dedicata, in press since February 2018. arXiv:1604.02471, doi:10.1007/s10711-018-0322-9. See the published version for free.
  4. Multiplicity formulas for fundamental strings of representations of classical Lie algebras. Emilio Lauret and Fiorela Rossi Bertone. J. Math. Phys. 58 (2017), 111703. arXiv:1706.07839, doi: 10.1063/1.4993851.
  5. 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. See the published version for free.
  6. 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. See the published version for free.
  7. 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.
  8. Non-strongly isospectral spherical space forms. Emilio Lauret, Roberto Miatello and Juan Pablo Rossetti. In "Mathematical Congress of the Americas", Contemporary Mathematics 656 (2016), 95-118. arXiv:1505.02554, doi: 10.1090/conm/656/13104.
  9. 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. See the published version for free.
  10. 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.
  11. 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. See the published version for free.
  12. 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.
  13. 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.
  14. 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.

Other monographs:

  • Read my reviews in Zentralblatt and MathSciNet.
  • Introducción a grupos aritméticos. Notas de curso junto a Roberto Miatello y Benjamin Linowitz, para la escuela AGRA III Aritmética, Grupos y Análisis, Córdoba, Argentina, 9 al 20 de Julio 2018. PDF.
  • Anillos de enteros de cuerpos cuadráticos. Notas de curso, elENA VI. Julio 2012. PDF.
  • Representaciones de formas cuadráticas y hermíticas. Algunos aspectos geométricos y topológicos. PhD Thesis. Advisor: Roberto Miatello. Marzo 2011. PDF.
  • (with Agustín García Iglesias) Exámenes de Doctorado 1996-2009 (download) and Exámenes de Doctorado 2009-2016 (download).
  • Series de Dirichlet. Revista de Educación Matemática (REM). Volumen 23 - N° 3 (2008). PDF.
  • Lattices en grupos de Lie. Trabajo final de la Licenciatura en Matemática. Director: Roberto Miatello. Marzo 2006. PDF.

Teaching:

  • 2018 2do cuatrimestre. Teoría Algebraica de Números (especialidad/curso de posgrado).
  • 2017, 1er cuatrimestre. Análisis Matemático 1.
  • 2016, 1er cuatrimestre. Teoría Algebraica de Números (especialidad/curso de posgrado).
  • 2016, 1er cuatrimestre. Análisis Matemático 1.
  • 2015, 2do cuatrimestre. Análisis Matemático 2.
  • 2015, 1er cuatrimestre. Análisis Matemático 1.
  • 2014, 1er cuatrimestre. Análisis Matemático 3.
  • 2013, 1er cuatrimestre. Análisis Matemático 1.
  • 2012, 2do cuatrimestre. Álgebra 2.
  • 2012, 1er cuatrimestre. Análisis Matemático 3.
  • 2011, 2do cuatrimestre. Geometría 1.
  • 2011, 1er cuatrimestre. Análisis Matemático 1.
  • 2010, 1er cuatrimestre. Análisis Matemático 1.
  • 2009, 2do cuatrimestre. Análisis Matemático 2.
  • 2009, 1er cuatrimestre. Análisis Matemático 1.
  • 2008, 2do cuatrimestre. Funciones Analíticas.