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Mathematics Department Colloquium : Autumn 2007 schedule


   Monday, September 17, 1530-1630

SPEAKER : Petter Bränden, KTH.

TITLE : Negative dependence and the geometry of polynomials.

ABSTRACT : Pemantle recently pointed out that there is, as yet, no useful theory of negatively dependent "repelling" events. We develop a theory of negative dependence for the class of strongly Rayleigh probability measures. This class is defined by means of geometric properties of the generating polynomials of the measures and contains uniform random spanning tree measures, determinantal measures (for contractions), balls-and-bins measures and distributions for symmetric exclusion processes. In the process we settle several conjectures of Liggett, Pemantle and Wagner, respectively, and extend Lyons' recent results on determinantal measures.

This is joint work with Julius Borcea (SU) and Thomas M. Liggett (UCLA), ArXiv: 0707.2340


   Wednesday, October 10, 1530-1630 (OBS!! Unusual day)


TITLE : The invariant subspace problem : an overview.

ABSTRACT : Let $X$ be a real or complex separable Banach space, and $T$ a bounded linear operator on $X$. A closed subspace $M$ of $X$ is said to be non-trivial if it is different from $\{0\}$ and $X$, and invariant by $T$ if $T(M)\subseteq M$. When $X$ is infinite-dimensional, the Invariant Subspace Problem is to know whether for any $T$ there exists a non-trivial subspace of $X$ which is invariant by $T$. This question has been answered in the negative by Enflo and Read, but it is still open when $X$ is supposed to be a Hilbert space. I will give an overview of this problem and discuss some methods for constructing non-trivial invariant subspaces.


   Monday, October 15, 1530-1630

SPEAKER : Johannes Brasche, Clausthal, Germany.

TITLE : Weyl functions and spectra.



   Monday, November 26, 1530-1630

SPEAKER : Mats Andersson, Chalmers.

TITLE : Ideals of holomorphic functions and residue currents.

ABSTRACT : Any analytic variety in $\C^n$, or more generally any ideal of holomorphic functions, can be represented as the annihilator of an analytic object, a so-called residue current. This was proved independently by Dickenstein-Sessa and Passare some 20 years ago for the case when the ideal is given as a so-called complete intersection. The general case was recently obtained in a joint work with E Wulcan. We will indicate the construction of such residue currents, and discuss some applications; for instance we obtain (in a joint work with H Samuelsson) new existence results for the $\dbar$-equation on analytic varieties.


   Monday, December 10, 1530-1630

SPEAKER : Bengt Johansson, NCM.

TITLE : Den negativa trenden ännu inte bruten. Vem bryr sig om matematiken ?

ABSTRACT : Jag föreslår en kort sammanfattning av pågående och planerade nationella insatser, utredningar och reformer som direkt eller indirekt berör matematiken i vårt utbildningssystem - och något om bakgrund och motiv till de satsningar som görs och planeras. Tänker också nämna något om det arbete som pågår och planeras på europeisk nivå inom EU och bland multinationella industriföretag kopplade till European Round Table Industrialists, ERT. Därefter diskussion.

(OBS! Föredraget är på svenska).