You are cordially invited to our next Monday Lecture &
Colloquium on July 2nd at 14:15 h & 16:00 h at FU Berlin. Location: Freie Universität Berlin Takustr. 9 14195 Berlin Time: Monday, July 2nd - 14:15 h Lecture: Benjamin Burton (University of Queensland, Australia) Title: From parameterised to non-parameterised algorithms in knot theory Abstract:We describe some recent developments in treewidth-based algorithms for knots, which exploit the structure of the underlying 4-valent planar graph. In particular, we show how these led to the first general sub-exponential-time algorithm for the HOMFLY-PT polynomial, and we describe some recent progress on parameterised algorithms for unknot recognition. Coffee & Tea Break Time: Monday, July 2nd - 16:00 h Colloquium: Laith Rastanawi (Freie Universität Berlin) Title: On the Dimension of the Realization Spaces of
Polytopes The study of
realization spaces of convex polytopes is one of the oldest
subjects in Polytope Theory. Most likely, it goes back to Legendre
(1794). A lot of progress took place since that time. However,
many questions remained open. In general, computing the dimension
of the realization space $\mathcal{R}(P)$ of a d-polytope $P$ is
hard, even for $d = 4$, as shown by Mnëv (1988) and
Richter-Gebert (1996).In this presentation, we will discuss two
criteria to determine the dimension of the realization space, and
use them to show that $\dim \mathcal{R}(P) = f_1(P) + 6$ for a
3-polytope $P$, and $\dim \mathcal{R}(P) = df_{d-1}(P)$ (resp.
$\dim \mathcal{R}(P) = df_0(P)$ ) for a simple (resp. simplicial)
$d$-polytope $P$. We will also discuss the realization spaces of
some interesting 2-simple 2-simplicial 4-polytopes. Namely, we
will consider the realization space of the 24-cell and of a 2s2s
polytope with 12 vertices which was found by Miyata (2011), and
give a better bound for/determine its dimension.
-- Graduiertenkolleg 'Facets of Complexity' www.facetsofcomplexity.de/monday |