MISANU

Seminar for Combinatorics, Geometry, Algebra and Topology

PROGRAM

Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)

PLAN RADA ZA OKTOBAR 2024:

Petak, 25.10.2024. u 14:15, Kneza Mihaila 36, sala 301f i Online
Margaret Bayer, University of Kansas
GRAPHS AND RECONSTRUCTION OF POLYTOPES
How much combinatorial information is needed to determine the face lattice of a convex polytope? The talk will survey results on this question. An old result by Blind and Mani, and Kalai, shows that the graph of a simple d-polytope determines the combinatorial type of the d-polytope. More recent work of Doolittle, et al., extends the result on simple polytopes to polytopes with few nonsimple vertices. The d/2-skeleton of a simplicial d-polytope determines the combinatorial type of the polytope (Perles), and this has been extended (by Dancis) to simplicial manifolds. Also considered will be the question of dimensional ambiguity: when is a k-complex the k-skeleton of polytope of different dimensions. In particular, results by Espenschied on the graphs of crosspolytopes will be discussed.
Zajednički sastanak sa Odeljenjem za matematiku.

Ponedeljak, 28.10.2024. u 11:30, Kneza Mihaila 36, sala 301f
Joana-Claudia Lazar, Politehnica University of Timisoara, Romania
MINIMAL DISPLACEMENT SET FOR 8-LOCATED SIMPLICIAL COMPLEXES WITH SD'-PROPERTY
We investigate the structure of the minimal displacement set in an 8-located simplicial complex with the SD'-property. We show that such set embeds isometrically into the complex. A simplicial complex is 8-located if it is flag and every full homotopically trivial loop of length at most 8, is contained in a 1-ball. We show that the minimal displacement set in a weakly systolic simplicial complex embeds isometrically into the complex and that it is systolic. As corollaries, we prove that any isometry of a weakly systolic complex either fixes the barycentre of some simplex (elliptic case) or it stabilizes a thick geodesic (hyperbolic case).

Utorak, 29.10.2024. u 14:15, Matematički fakultet, sala 840
Margaret Bayer, University of Kansas
COUNTING FACES AND FLAGS IN POLYTOPES
This is a survey talk about the numbers of faces and the numbers of chains of faces in convex polytopes, and, more generally, the rank numbers and chain numbers in Eulerian posets. It starts with Euler, goes through the g-theorem on face vectors of simplicial polytopes, and continues with the cd-index. It includes recent work by a variety of authors. Mentioned briefly will be connections to toric varieties, Bruhat order and Hopf algebras.

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