Spring 2004 schedule

Mathematics Department Colloquium : Autumn 2004 schedule


   Monday, September 27, 1600-1700

Speaker : Alexander Stolin, Göteborg.

Title : Fermat's Last Theorem and the Kervaire-Murthy conjectures

Abstract :In my talk I will explain how one and the same method from algebraic number theory can be used in the proofs both of some cases of Fermat's Last Theorem and of the Kervaire-Murthy conjecture in algebraic K-theory

Lecture notes


   Monday, October 11, 1600-1700

Speaker : Iurii Drozd, Kiev (currently at Uppsala).

Title : Vector bundles over singular projective curves.

Abstract (preliminary 06/10/04) :I present the results on the classification of vector bundles over singular projective curves, mostly obtained by Greuel and me. In particular, the tame-wild dichotomy for this problem is established and all vector bundles are classified in the tame case. I also present a classification of stable vector bundles over a cuspidal cubic (a wild curve with respect to the classification of all vector bundles). .


   Monday, November 1, 1600-1700

Speaker : Natan Kruglyak, Luleå.

Title : Calderon-Zygmund type Decompositions, Covering Theorems and Applications.

Abstract : In 1952 A. Calderon and A. Zygmund, in their fundamental paper 'On the Existence of Certain Singular Integrals' used a geometric construction (which goes back to F. Riesz "rising sun" lemma) to define a family of decompositions of a given function into "good" and "bad" parts. This construction happens to be a cornerstone of modern harmonic analysis and is used in such fundamental results as the John-Nirenberg characterisation of BMO, the Fefferman-Stein maximal theorem, characterisation of A_p weights and others.

It is possible to see that Calderon-Zygmund decompositions correspond to a special couple of functional spaces, namely the couple (L_1, L_{\infty}). In the talk I plan to discuss

(a) possibilities and difficulties of an extension of this construction to other couples

(b) a covering theorem which appears in connection with this extension

(c) applications to the theory of interpolation and singular integrals.


   Monday, November 22, 1600-1700

Speaker : Alan Rendall, Albert-Einstein Institut, Golm (Deutschland).

Title : Mathematics of cosmic acceleration.

Abstract :Recent astronomical observations show that the expansion of the universe is accelerating. I will explain how attempts to understand this theoretically lead to the concepts of the cosmological constant and dark energy. Mathematical problems which arise naturally in this context involve the study of the global dynamics of certain classes of solutions of the Einstein equations. It appears that a particular solution (the de Sitter solution) acts as an attractor for the dynamics. That this is so can be proved by using a combination of tools from the theory of partial differential equations (symmetric hyperbolic systems) and differential geometry (conformal invariants).