Around the theory of f-vectors

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ABSTRACTPrincipal Investigator: Novik, Isabella Proposal Number: DMS - 0801152Institution: University of WashingtonTitle: Around the theory of f-vectorsThe PI will continue studying the face numbers of various classes of cell complexes. Specifically, she proposes to work on centrally symmetric polytopes, simplicial complexes and posets whose geometric realization is a manifold, and cubical complexes. As previous works suggest, this will require applying existing and developing new combinatorial, algebraic, topological, and possibly analytical techniques, thus strengthening connections between different parts of Mathematics.Cell complexes provide a convenient way to build various shapes from smaller and simpler blocks, such as for example pyramids or cubes. A natural question then is what restrictions on the number of building blocks are imposed by specific shapes. Variations of this question (e.g., what is the minimal number of blocks required) have practical importance when one wants to represent/store such a structure in a computer.