The Faculty of Mathematical Science, in collaboration with the Journal Revista Matemática Complutense, established in 2002 the Santaló Lecturer figure. Such a position is occupied each year by a distinguished invited professor (proposed by the Editorial Board and ratified by the Faculty Council) who is asked to submit an article to the Journal and give a colloquium about it.

Santaló Conference 2021

Speaker: Carolyn S. Gordon, Dartmouth College (USA)

Title: Detecting (or not!) geometry and topology from spectral data

Abstract: Inverse spectral geometry asks the extent to which geometric and topological information is encoded in spectral data. The geometric objects we will consider are bounded Euclidean domains and also more general compact Riemannian manifolds. We will look at two types of spectral data: the spectrum of the Laplacian (with Dirichlet or Neumann boundary conditions) and the Steklov spectrum. The inverse spectral problem for the Laplacian is sometimes phrased as “Can one hear the shape of a drum?'' since the eigenvalues of a plane domain correspond to the characteristic frequencies of vibration of the domain viewed as a vibrating membrane. The Steklov spectrum of a bounded domain or of a Riemannian manifold M with boundary is the eigenvalue spectrum of the so-called Dirichlet-to-Neumann operator, which inputs smooth functions u on the boundary of M and outputs the normal derivative across the boundary of the unique harmonic extension of u to M. While Steklov introduced the Steklov spectrum in 1902, it remained largely dormant for many years. Motivated in part by striking applications, the study of the Steklov spectrum has dramatically accelerated in recent years. After introducing the Laplace and Steklov spectra, we will give a partial survey, comparing and contrasting some of the inverse spectral results and techniques for the Laplace spectrum and the Steklov spectrum.

Day: Thursday, September 30, 13:00.

Place: Room Miguel de Guzmán, Faculty of Mathematical Science. Follow the sesion through Youtube

Past conferences:

• June 25, 2020, María Dolores Ugarte (Universidad Pública de Navarra, Spain) On spatio-temporal confounding in areal models with a data analysis on gender-based violence.
• October 3, 2019, Noel Cressie (National Institute for Applied Statistics Research Australia, University of Wollongong, Australia) Atmospheric carbon and the statistical science of measuring, mapping, and uncertainty quantification
• October 4, 2018, Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences, Germany) Learning algebraic varieties from samples
• October 26, 2017, Ignacio Cirac (Max Planck Institute of Quantum Optics): Quantum Information technologies
  
• October 20, 2016, Luigi Ambrosio (Scuola Normale Sup Pisa): Well posednessof ODE's and continuity equations with nonsmooth vector fields and applications
• October 8, 2015, Hélène Esnault (Freie Unversität Berlin): Fundamental Groups in Algebraic Geometry
• October 16, 2014, Lajos Horváth (University of Utah): Statisitcal Inference from Curves
• October 10, 2013, Nigel Hitchin (Oxford University): Complex and Quaternionic Differential Geometry.
• October 18, 2012, Eduard Feireisl (Academy of Sciences of the Czech Republic): Mathematics of fluids in motion.
• October 6, 2011, Juan Luis Vázquez (Universidad Autónoma de Madrid): Mathematical Theories of Heat and Diffusion
• October 7, 2010,  Giuseppe Buttazzo (Università di Pisa): Spectral Optimization Problems
• October 8, 2009, David E. Edmunds (University of Sussex): Embeddings, Hardy operators and nonlinear problems.
• October 16, 2008, Alfio Quarteroni  (Ecole Polytechnique Federale de Lausanne): Mathematical models for technology, medicine, and sport.
• October 4, 2007, Nigel Kalton (University of Missouri, Columbia): The nonlinear geometry of Banach spaces.
• October 3, 2006, Narayanaswamy Balakrishnan (McMaster University, Ontario): Permanents, order statistics, outliers, and robustness.
• October 7, 2005, Marcelo Viana (Instituto de Matematica Pura e Aplicada, Rio de Janeiro): Dinámica en el espacio de diferenciales abelianas.
• October 6, 2004, Hans Triebel (Friedrich-Schiller-Universität): The recent theory of function spaces on Euclidian spaces, fractals, and quasi-metric spaces.
• October 7, 2003, Jack K. Hale (Georgia Institute of Technology): Stability in gradient systems.
• October 7, 2002, Charles T. C. Wall (University of Liverpool): The geometry of abstract groups and their splittings.