El seminario de doctorantes se presenta como un aporte a la vida doctoral a través de la comunicación, tanto matemática como de convivencia, entre las y los doctorantes del departamento. Para esto, se incentiva a las y los doctorantes a presentar parte de sus investigaciones o bien, parte de los conocimientos adquiridos en sus estudios. Además, dejamos la puerta abierta a los estudiantes de magister que quieran participar de nuestras actividades. Por último, doctorantes de otras universidades que quieren participar como oyentes y/o expositores, no duden en contactarnos a: seminario.doctorantes@dim.uchile.cl

El seminario está pensado con una frecuencia bimensual (Martes de 14:30 a 15:30, on-line al menos por este semestre), comenzando el Martes 23 de Marzo del 2021.

Contacto para consultas.

Seminario del 6 de abril de 2021: Jorge Aguayo

Estimadas/os compañeras y compañeros.

Tenemos el agrado de invitarles a la exposición de Álvaro Bustos (DIM)
en el seminario de doctorantes.
Esta se llevará a cabo el día martes 6 de Abril a las 14:30 hrs vía
Zoom.

Expositor: Jorge Aguayo
Título:    An inverse problem in Fluid Mechanics applied in Biomedicine

Resumen:
One of the main causes of problems in the human cardiovascular system is malformations in the aortic valve. There exists exploratory techniques to verify the status of an aortic valve, but these procedures are invasive or are not able to detect valve geometry. The aim is to define and study an inverse problem such that, based on measurements of the velocity field of the blood passing through a valve, an estimate of the valve geometry is given in response. Although it is possible to consider this problem as one of obstacle shape optimization, the disadvantage of this technique would be the need of modifying the discretization of the domain at every iteration of the identification procedure. In contrast, the proposed distributed resistance term here allows us to work in a fixed domain to solve the valve shape identification problem adding a penalization term.
This research includes a justification for using fictitious domains to study obstacles immersed in incompressible viscous fluids through a simplified version of Brinkham’s law in porous media applied in Navier-Stokes equations, the formulation and analysis of an identification of parameters problem associated to this inverse problem and numerical experiments in FEniCS and dolfin-adjoint illustrating the applicability of this method.

Link zoom: https://uchile.zoom.us/j/82919875247?pwd=eWNhU0t2WFhrSnIyNmtrdWo3RUJxdz09
Código de acceso: 206782

Seminario del 23 de marzo de 2021: Álvaro Bustos

Estimadas/os compañeras y compañeros.

Tenemos el agrado de invitarles a la exposición de Álvaro Bustos (DIM)
en el seminario de doctorantes.
Esta se llevará a cabo el día martes 23 de Marzo a las 14:30 hrs vía
Zoom.

La charla se titula: Automorphisms and extended symmetries of
number-theoretic positive
entropy subshifts.

Resumen: We will discuss one- and multidimensional subshifts
constructed via number-theoretically defined subsets of the integers
(e.g. the visible lattice points in the plane, k-free integers, etc.),
focusing our interest on their groups of automorphisms and extended
symmetries, which are naturally defined conjugacy invariants. This type
of shift space exhibits symmetry rigidity (that is, its group of
automorphisms is essentially trivial), but is compatible with positive
entropy and shows interesting variations on their extended symmetry
groups, which may be small (finite) or large extensions of the
corresponding automorphism group; we show examples of each of these
behaviors, which come from real and imaginary quadratic number fields.

Link:
https://uchile.zoom.us/j/82919875247?pwd=eWNhU0t2WFhrSnIyNmtrdWo3RUJxdz09
Código de acceso: 206782

Esperando que seamos numerosos,
Seminario de doctorantes.