Conferencia Santaló
La Facultad de Matemáticas, en colaboración con la Revista Matemática Complutense, creó en 2002 la figura del Conferenciante Santaló. Cada año un profesor distinguido es invitado (propuesto por el Consejo Editorial de RMC y ratificado por la Junta de la Facultad), y se le pide enviar un artículo a la Revista y dar una conferencia-coloquio al respecto. Esta conferencia marca el inicio de la actividad docente e investigadora de la Facultad en cada año académico.
Conferencia Santaló 2023
Conferenciante: Philippe Souplet, Université de la Sorbonne, Paris Nord (Francia)
Título: The role of Liouville-type theorems in partial differential equations
Abstract: The Cauchy-Liouville theorem (1844) states that any bounded entire function of a complex variable is necessarily constant. Another related and very classical fact is that this remains true for any harmonic function over the whole Euclidean space (in arbitrary dimensions). In the realm of PDE’s, by a Liouville-type theorem, one usually means a statement asserting the nonexistence of solutions in the wholespace (or a suitable unbounded domain), the solutions being sometimes subjected to certain restrictions (e.g., nonconstant, or with some sign or growth conditions). Numerous results of this kind have appeared over the years and many far-reaching applications have arisen, conferring Liouville-type theorems an important role in the theory of PDE’s. In this lecture, we will survey some aspects of historical and current developments on the topic, and underline some connections with other mathematical areas, such as the calculus of variations, geometry, fluid dynamics or optimal stochastic control. Starting with the problem of minimal surfaces (Lagrange, Bernstein, de Giorgi,Bombieri,...) and with the connections of Liouville-type theorems with regularity theory for linear elliptic systems (Giaquinta, Nečas,...), we will then turn to semilinear elliptic equations (where strong initial motivation came from the Yamabe problem), eventually leading to the development (1980-2000’s) of powerful tools to show existence and a priori estimates for nonlinear Dirichlet problems. In connection with Liouville-type theorems, we will encounter such key concepts as scaling, zooming and doubling techniques, Alexandrov-Serrin moving planes methods and topological degree.
In the more recent period, this line of research has also led to much progress in the study of singularities of solutions, both for stationary (elliptic) and evolution PDEs. In the latter category, especially for the description of finite time blow-up singularities, Liouville-type theorems turn out to play an important role in numerous problems (nonlinear reaction-diffusion, Hamilton-Jacobi and Navier-Stokes equations, harmonic maps and Ricci flows, KdV, nonlinear wave and Schrödinger equations,...). In view of such diversity, we will thus of course giveonly a partial overview.
Fecha y hora: viernes 29 de septiembre de 2022, 13:00.
Lugar: Aula Miguel de Guzmán, Facultad de Ciencias Matemáticas y Canal de Youtube de la Facultad.
Conferencias
- (2022) Convergence of Fourier Series and modern developments. Christoph Thiele (Hausdorff Center for Mathematics, Alemania)
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(2021) Detecting (or not!) geometry and topology from spectral data. Carolyn S. Gordon (Dartmouth College, EE.UU.)
- (2020) On spatio-temporal confounding in areal models with a data analysis on gender-based violence. María Dolores Ugarte (Universidad Pública de Navarra, España)
- (2019) Atmospheric carbon and the statistical science of measuring, mapping, and uncertainty quantification. Noel Cressie (National Institute for Applied Statistics Research Australia, University of Wollongong, Australia)
- (2018) Learning algebraic varieties from samples. Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences, Alemania)
- (2017) Tecnologías cuánticas de la información: Conferencia Santaló. Ignacio Cirac (Instituto Max-Planck de Óptica Cuántica, Alemania)
- (2016) Well posedness of ODE’s and continuity equations with nonsmooth vector fields and applications. Luigi Ambrosio (Scuola Normale Superiore di Pisa, Italia)
- (2015) Fundamental Groups in Algebraic Geometry.Hélène Esnault (Freie Universität Berlin)
- (2014) Statistical Inference from Curves. Lajos Horváth (University of Utah)
- (2013) Complex and Quaternionic Differential Geometry. Nigel Hitchin (Oxford University)
- (2012) Mathematics of fluids in motion. Eduard Feireisl (Academy of Sciences of the Czech Republic)
- (2011) Mathematical Theories of Heat and Diffusion. Juan Luis Vázquez (Universidad Autónoma de Madrid)
- (2010) Spectral Optimization Problems. Giuseppe Buttazzo (Università di Pisa)
- (2009) Embeddings, Hardy operators and nonlinear problems. David E. Edmunds (University of Sussex)
- (2008) Mathematical models for technology, medicine, and sport. Alfio Quarteroni (Ecole Polytechnique Federale de Lausanne)
- (2007) The nonlinear geometry of Banach spaces. Nigel Kalton (University of Missouri, Columbia)
- (2006) Permanents, order statistics, outliers, and robustness. Narayanaswamy Balakrishnan (McMaster University, Ontario)
- (2005) Dinámica en el espacio de diferenciales abelianas. Marcelo Viana (Istituto de Matematica Pura e Aplicada, Rio de Janeiro)
- (2004) The recent theory of function spaces on Euclidian spaces, fractals, and quasi-metric spaces. Hans Triebel (Friedrich-Schiller-Universität)
- (2003) Stability in gradient systems.Jack K. Hale (Georgia Institute of Technology)
- (2002) The geometry of abstract groups and their splittings. Charles T. C. Wall (University of Liverpool)
Más información sobre los artículos publicados en la Revista Matemática Complutense por cada uno de ellos en:
Luis Santaló
Luis Antonio Santaló Sors (Gerona, España , 9 de octubre de 1911 – Buenos Aires, Argentina, 23 de noviembre de 2001), más conocido por Luis Santaló, fue un matemático español de fama internacional que se exilió en Argentina en 1939 al iniciarse la Segunda Guerra Mundial y ser partidario del derrotado bando republicano en España. Desarrolló una fecunda labor en la Argentina donde se le otorgó el título de profesor emérito de la Universidad de Buenos Aires. Publicó más de cien trabajos de investigación fundamental y de divulgación; y varios libros, en especial sobre Geometría integral, tema en el que se le considera uno de sus fundadores.