Speaker: |
Nikhil Srivastava (Microsoft Research, India #9, Lavelle Road Bangalore Karnataka 560025 ) |

Organiser: |
Prahladh Harsha |

Date: |
Monday, 6 May 2013, 16:30 to 17:30 |

Venue: |
AG-80 |

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We also construct infinite families of `irregular Ramanujan' graphs, whose eigenvalues are bounded by the spectral radius of their universal cover. Such families were conjectured to exist by Linial and others. In particular, we construct infinite families of (c,d)-biregular bipartite graphs with all non-trivial eigenvalues bounded by $\sqrt{c-1}+\sqrt{d-1}$, for all $c, d \geq 3$.

Our proof exploits a new technique for demonstrating the existence of useful combinatorial objects that we call the "Method of Interlacing Polynomials" (joint work with A. Marcus and D. Spielman).