Realization spaces of combinatorial structures
Ponente: Baptiste Gros
Institución: Universidad de Montpellier
Tipo de Evento: Investigación
Institución: Universidad de Montpellier
Tipo de Evento: Investigación
| Cuándo |
26/02/2025 de 13:00 a 14:00 |
|---|---|
| Dónde | ZOOM ID 882 9372 3602 |
| Agregar evento al calendario |
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A classical theorem due to Steinitz states that any dimension 3-polytope can be continuously deformed into any equivalent polytope (or its mirror image) through equivalent polytopes. In other words, the realization space of a 3-polytope up to mirror image is connected. In fact, Steinitz’s theorem even says that the realization space (modulo affine transforms) is a topological ball.
Since then, a lot of progress has been made in the study of realization spaces of combinatorial structures. In particular, I will present a surprising theorem due to Mnëv that concerns objects closely related to polytopes, called chirotopes, but that reaches conclusions radically different from Steinitz’s theorem. After explaining how Mnëv’s « universality » theorem lead us to introduce a new combinatorial structure, called Strong Geometry, I present a universality result on the realization space of strong matroids.
