Toric spaces and face enumeration on simplicial manifolds

Toric spaces and face enumeration on simplicial manifolds

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 Feifei Fan, South China Normal University

Zoom link: https://princeton.zoom.us/j/92116764865

Passcode: 114700

This talk is toward the applications of toric topology in algebraic combinatorics, especially the face enumeration problems for  triangulated spheres and further for triangulated manifolds.  A motivational problem is the celebrated g-conjecture in the theory of face enumeration. 

First, we survey how the g-conjecture came about and how it relates to the topology of a class of toric spaces, which can be viewed as a generalization of toric varieties; Using the theory of toric topology we prove some new results towards this conjecture. Finally, we give a topological interpretation for several fundamental results in algebraic combinatorics.