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 Events
UBC
Mon 2 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Spectrum in Simplicial Complexes
ESB 4127
Mon 2 Mar 2015, 4:00pm-5:00pm

Abstract

 

Ramanujan graphs are k-regular graphs admitting optimal connectivity properties (namely, optimal expanders). Infinite families of such graphs were first constructed by Lubotzky, Phillips and Sarnak in 1988 by relating the spectrum of a graph with certain representations of GL_2(Q_p). These ideas were generalized to simplical complexes by Lubotzky, Samuels and Vishne in 2005. 
We will present a further generalization, showing that there is a natural way to relate spectral properties of simplicial complexes with certain representations of groups acting on their universal covers. Several results of this connection will be discussed. In particular, we strengthen the spectral properties of the complexes constructed by L-S-V. (Roughly speaking, we show that the complexes constructed by L-S-V have "optimal spectrum in all dimensions".)
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Colorado State University
Tue 10 Mar 2015, 4:00pm
Discrete Math Seminar
TBA
TBA
TBA
Tue 10 Mar 2015, 4:00pm-5:00pm

Abstract


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