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                * Princeton Discrete Math Seminar *
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Speaker: Varun Sivashankar (Princeton)

Thursday 23rd April, 3:00 in Fine Hall 224.

Title: Upper bound on the k-th eigenvalue of a graph

It is a well-known fact that the first eigenvalue of an n-vertex graph is 
at most n-1 while the second eigenvalue is at most n/2-1. Up until 
recently, even the question of bounding the third eigenvalue was open. In 
this talk, we will prove a general upper bound on the k-th eigenvalue of a 
graph, which is tight for k = 2,3,4,8 and 24. We will discuss the close 
relation of the graph eigenvalue problem with projection constants and 
equiangular lines.

Joint work with Quanyu Tang and Tanay Wakhare

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