Triangulations of Convex Polytopes
Wungkum Fong
MIT
November 5,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Let $K$ be a finite set of vectors in
$\mathbb R^n$. Let ${\operatorname{conv}^*}(K)$ be
the convex hull of $\{O\}\cup K$. Given any linear order $\prec$
on $K$, say $K= \{ v_1, v_2, v_3, \ldots, v_m\}$ with
$ v_1\prec v_2 \prec v_3 \prec \cdots \prec v_m$, we define the notion
of a \emph{$\Delta_\prec$basis}
on the linear matroid $\mathcal{M}(K)$ whose underlying set of vectors is $K$
and present a local triangulation of ${\operatorname{conv}^*}(K)$
determined by $\prec$. We will specifically look at the polytopes
${\operatorname{conv}^*}(A_n^+)$, where $A_n^+$ is the set of positive roots
of the root system $A_n$, and polytopes similarly associated to other root
systems. We will talk about their volumes, shellabilities, and Ehrhart
polynomials and, while doing so, introduce the C_n anaolog of Catalan
numbers and Narayana numbers.

Speaker's Contact Info: wungkum(atsign)math.mit.edu
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