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                * Princeton Discrete Math Seminar *
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Date: Thursday 1st March, 2.15 in Fine Hall 224
 
Speaker: Claudiu Raicu, Princeton

Title: Homology of clique complexes and an application to algebraic geometry

To any graph G one can associate a simplicial complex C(G), called the 
clique complex of G, whose simplices are in one-to-one correspondence 
with the complete subgraphs of G. It is thus natural to study the 
homology groups of C(G) in connection to properties of the graph G. I 
will be interested in a special class of graphs, possessing a large 
group of symmetries, and particularly in Kneser graphs. The relevance of 
these graphs to algebraic geometry (no knowledge of which will be 
assumed in the talk) is that the homology of their clique complexes 
controls the syzygies of projective embeddings of products of projective 
spaces. As one of the toy examples, I will explain how computing a 
single homology group allows one to deduce that matrices of rank 1 are 
defined by the vanishing of their 2x2 minors.

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Next week: Ankur Moitra

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