Topological combinatorics

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The project investigates the topological structures of different combinatorial objects. There are two main areas of interest within this broad theme:1. Embeddability : the project looks for characterisations of embeddability of different combinatorial objects. Along with characterisations, efficient algorithms are also desired. When no efficient algorithm is possible, a proof of NP-hardness is desired.2. Decompositionality : the project looks at ways of decomposing combinatorial structures that preserves certain properties. This second general theme includes connectivity theory and investigating width measures tied to decompositions. The methods involved in studying embeddability usually use theory from decompositionality.