[Turkmath:9811] MSGSU Matematik semineri, Ayşe Erzan, 15.05.2014, 16:00

[AYHAN GÜNAYDIN]

Değerli liste üyeleri
MSGSÜ Matematik Bölümü Genel Seminerleri'nde bu hafta konuşmacımız Ayşe
Erzan. Konuşmanın detayları aşağıda.

Selamlar,
Ayhan Günaydın



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MSGSÜ Mathematics Seminar


Speaker: Ayşe Erzan (Istanbul 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 appropriate 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 wavelength  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.

15.05.2014, saat 16:00

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