LiU / Matematiska Institutionen

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Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Bodil Stavklint litemat@mai.liu.se senast torsdagar kl 08.00.

Vi har dessutom ett arkiv av gamla nummer.

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***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v40 2004

Matematiska kollokviet

Onsdagen den 6 oktober, kl. 13.00-14.00 talar Professor Natan Krugljak, Luleå,

On one new covering theorem and its applications.

Sammanfattning: Classical covering theorems (Vitali, Whitney, Besicovitch) are not only beautiful but they also have important applications in analysis, harmonic analysis, theory of approximations, ergodic theory and PDEs. Some years ago in connection with real interpolation of Sobolev spaces appeared theorems which have simultaniously features of Whitney and Besicovitch covering theorems. I plan to discuss these new theorems and their applications to interpolation and possible applications to singular integrals.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.

Välkomna!
Anders Björn,
Vladimir Kozlov,
Svante Linusson och
Stefan Rauch-Wojciechowski

Licentiatseminarium

Fredagen den 24 september kl 10.15 försvarar Jonas Bergman sin licentiatavhandling med titeln

Conformal Einstein spaces and Bach tensor generalizations in $ n$ dimensions.

Platsen är Glashuset och opponent är docent Mattias Marklund, Institutionen för fysik, Umeå Universitet.

Abstract: In this thesis we investigate necessary and sufficient conditions for an $ n$-dimensional space, $ n \geq 4$, to be locally conformal to an Einstein space. After reviewing the classical results derived in tensors we consider the four-dimensional spinor result of Kozameh, Newman and Tod. The involvement of the four-dimensional Bach tensor (which is divergence-free and conformally well-behaved) in their result motivates a search for an $ n$-dimensional generalization of the Bach tensor $ B{}_{ab}$ with the same properties. We strengthen a theorem due to Belfagón and Jaén and give a basis ($ U{}_{ab}$, $ V{}_{ab}$ and $ W{}_{ab}$) for all $ n$-dimensional symmetric, divergence-free 2-index tensors quadratic in the Riemann curvature tensor. We discover the simple relationship $ B{}_{ab} = \frac{1}{2} U{}_{ab} + \frac{1}{6}V{}_{ab}$ and show that the Bach tensor is the unique tensor with these properties in four dimensions. Unfortunately we have to conclude, in general that there is no direct analogue in higher dimension with all these properties.

Nevertheless, we are able to generalize the four-dimensional results due to Kozameh, Newman and Tod to $ n$ dimensions. We show that a generic space is conformal to an Einstein space if and only if there exists a vector field satisfying two conditions. The explicit use of dimensionally dependent identities (some of which are newly derived in this thesis) is also exploited in order to make the two conditions as simple as possible; explicit examples are given in five and six dimensions using these tensor identities.

For $ n$ dimensions, we define the tensors $ \mathfrak{b}_{abc}$ and $ \mathfrak{B}_{ab}$, and we show that their vanishing is a conformal invariant property which guarantees that the space with non-degenerate Weyl tensor is a conformal Einstein space.

Välkomna!

Jämställdhetsseminarium

Onsdag 13 oktober kl 15-17 arrangerar MAI:s jämställdhetsgrupp ett seminarium med Christer Knuthammar, ordförande i universitetets jämställdhetsråd, på temat

"LiU och jämställdhet - visioner och verklighet."

Christer Knuthammar bidrar med reflektioner som grund för diskussion och eftertanke. Därefter följer gemensam fika och diskussion. Ingen föranmälan krävs.

Plats: Glashuset.

Varmt välkommen!
MAI:s jämställdhetsgrupp

Arbetsmiljöombud

Nytt arbetsmiljöombud för MAI är Theresia Roth, throt@mai.liu.se.



Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Bodil Stavklint senast torsdagar kl 08.00.
Linköpings universitet, 581 83 Linköping
Tel 013-281000, Fax 013-149403
E-mail: litemat@mai.liu.se


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Sidan underhålls av: LiteMat litemat@mai.liu.se
Senast ändrad: Wed 2012-08-29; 15:43 CEST