[Turkmath:9861] MSGSÜ Matematik Bölümü Semineri

[Ozgur Martin]

Değerli liste üyeleri,

MSGSÜ Matematik Bölümü Genel Seminerleri'nde bu hafta konuşmacımız Prof.
Ayşe Erzan. Seminerde görüşmek üzere,

Selamlar,
Özgür Martin

MSGSÜ Mathematics Seminar:

Ayşe Erzan
İstanbul Technical University


Title: Physics on networks, the graph Laplacian and discrete analysis

Abstract: The Laplace operator is perhaps the most central object in
physics - from the harmonic oscillator (the basis for "zeroth order"
modelling at least half of physical phenomena) to diffusion (the other
half!). Many phenomena of physical, biological or social interest take
place on discrete lattices (networks) which are not embedded in metric
spaces, and the graph Laplacian emerges as the apropriate operator here. I
will illustrate this with a simple example from Statistical Physics: We
normally expand fluctuations of some field in terms of the eigenfunctions
of the Laplace operator (the harmonic functions on d-dimensional Euclidean
spaces or lattices), and can systematically eliminate the "smaller
wavelegth" fluctuations in order to probe certain properties of the
physical system. The challenge is to be able to do a similar operation on
arbitrary networks.  However, obtaining the eigenvectors of the Laplace
operator on even perfectly regular networks such as Cayley trees of
arbitrarily large lattice size can be daunting. Some attempts in this
direction and many open questions will be discussed.


MSGSÜ, Bomonti Kampüsü, Matematik Bölümü Seminer Odası.

29.05.2014, saat 16:00
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