|
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) |
SPEAKER :
.
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.
ABSTRACT :
Here
|
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).