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Finite Field Grassmannian:�Algebra & Combinatorics

Ran Tessler, Elad Tzalik

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Weizmann Institute of Science

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Simplicial Complexes

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Plan for Today

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Simplicial Complexes – Connectivity

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Simplicial Complexes – Homological Connectivity

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Simplicial Complexes – Homological Connectivity

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Simplicial Complexes – Homological Connectivity

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Simplicial Complexes – Expansion

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Simplicial Complexes – Expansion

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The Linial-Meshulam-Wallach Theorem

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Grassmann Complexes

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Grassmann Complexes

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Grassmann Complexes

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The Linial-Meshulam-Wallach Theorem - Sketch

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Questions and conjectures

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Natural minimal fillings are optimal.

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Colorful boundary operator?

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If time permits

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Thank You!