Sesión número 114 del Seminario Iberoamericano de Matemáticas (SIM114)
Lugar: Casas del Tratado en Tordesillas, sede del Centro Tordesillas de Relaciones con Iberoamérica y Portugal.
Las conferencias se podrán seguir vía Cisco WebEx Meeting en el siguiente link:
Fecha: Miércoles 23 de Junio de 2021
PROGRAMA (hora GMT+2):
16:30-17:30 Javier Jiménez-Garrido (Universidad de Cantabria)
Título: "Equality of ultradifferentiable classes by means of indices of mixed O-regular variation". (Joint work with Gerhard Schindl and Javier Sanz)
Resumen: In the theory of ultradifferentiable function spaces there exist two classical approaches in order to control the growth of the derivatives of the functions belonging to such classes: either one uses a weight sequence or a weight function. Motivated by the comparison of both methods, that in general are mutually distinct, ultradifferentiable classes defined in terms of weight matrices have been introduced. In this general framework, one is able to treat both classical settings in a uniform and convenient way but also more classes. In this talk, we characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These indices, defined by means of weight sequences and (associated) weight functions, are extending the notion of O-regular variation to a mixed setting. Hence we are extending the known comparison results concerning classes defined in terms of a single weight sequence and of a single weight function and give also these statements an interpretation expressed in O-regular variation.
17:45-18:45 Pedro Fortuny Ayuso (Universidad de Oviedo)
Título: "C^\infty Equisingularity of germs of plane and space branches".
Resumen: Using C-infinity vector fields, we obtain the classical topological classification of plane branches over C and R, and also of branches in space (any dimension). The latter provides hints to answering the question "what is equisingularity of branches/curve in space?".