ylös hierarkiassa

Mat-1.218 Inversio-ongelmien seminaari

Vanhojen esitelmien aiheita

Syksy 2005

Syksy 2004

Kevät 2004

2003

2002

23.9. klo 14.15 - 16, sali U322 (huom. maanantai) Matti Lassas: Introduction to inverse conductivity problem

Abstract: We give a review on classical results for inverse conductivity problem started by Alberto Calderón. We pay special attention to relation of Riemannian geometry and inverse problem. Also, we discuss some recent counterexamples.

9.10. klo 12.30, sali Y307 Matti Lassas: Introduction to inverse conductivity problem: some recent counterexamples

(ks. tiivistelmä yllä)

16.10. kello 12.15, sali U358 Matias Dahl: Kontakti- ja symplektigeometria sähkömagnetiikassa

Abstract: The present work is divided into two parts. In the first part, we show that, by working in Fourier space, the Bohren decomposition and the Helmholtz's decomposition can be combined into one decomposition. This yields a completely mathematical decomposition, which decomposes an arbitrary vector field on R³ into three components. The most important properties of this decomposition is that it commutes with both the curl operator and with the time derivative. We can therefore apply this decomposition to Maxwell's equations without assuming anything about the media. When we apply this decomposition to the traditional Maxwell's equations (for E, D, B, H) on R³, we will see that Maxwell's equations split into three completely uncoupled sets of equations. Also, when a medium is introduced, the decomposed Maxwell's equations either remain uncoupled, or become coupled depending on the complexity of the medium. As a special case, the decomposed Maxwell's equations contain the Bohren decomposition.

In the second part of this work, we begin with an introduction to contact and symplectic geometry and then study their relation to electromagnetism. By studying examples, we show that the decomposed fields in the decomposed Maxwell's equations always seem to induce contact structures. For instance, for a planewave, the decomposed fields are the right and left hand circulary polarized components and each of these induce their own contact structure. Moreover, we show that each contact structure induces its own Carnot-Carathéodory metric, and the path traversed by the circularly polarized waves seem to coincide with the geodesics of these metrics.

23.10. klo 12.15, sali U358 Matti Lassas: Mikrolokaali analyysi ja inversio-ongelmat

30.10. klo 12.15, sali U358 Matti Lassas: Mikrolokaali analyysi ja inversio-ongelmat - osa 2

6.11. klo 12.15, sali U358 Nuutti Hyvönen: Impedanssitomografian elektrodimalli: approksimaatio-ominaisuudet ja inkluusioiden karakterisointi

13.11. klo 12.15, sali U358 Teemu Pennanen, HKKK: Calibrated option bounds

20.11. klo 12.15 - n. 13.30, sali U358 Teemu Pennanen, HKKK: Calibrated option bounds - osa 2

27.11. klo 12.15, sali U358 Nuutti Hyvönen: Impedanssitomografian elektrodimalli: approksimaatio-ominaisuudet ja inkluusioiden karakterisointi - osa 2

11.12. Inversiopäivät Tahkovuoressa

Kenrick Bingham 3.1.2006