**CSE Seminar**

**Speaker:** Leonid Bunimovich, Regents' Professor of Mathematics, Georgia Tech

**Title:**

How to compress networks while keeping their important characteristics**Abstract:**

One of the fundamental concerns in the study of networks is

understanding the relation between a network's structure ("topology") and

its dynamics (evolution in time). However, the networks we often encounter

in either nature or engineering are typically very large. It is therefore

tempting to want to reduce such networks by excluding a part of their

elements while preserving some important characteristic(s) of the original

network. Such fundamental characteristic is the spectrum (collection of all

eigenvalues) of the network's weighted adjacency matrix. Moreover, this

matrix often contains all the known information about a network. Can one

hope to reduce a network while maintaining its spectrum? It seems that

there is no hope because of the Fundamental Theorem of Algebra which says

that the spectrum of MxM matrix contains M eigenvalues. Therefore the

spectrum of a smaller matrix (corresponding to a smaller network) contains

fewer eigenvalues. However, it is possible to do and the recently developed

theory of isospectral networks' reduction suggests new ways of networks'

analysis and synthesis. In particular, a new equivalence relation in the

class of all networks was found. Besides (as a "byproduct") the theory of

isospectral networks transformations allowed to advance some classical

areas of Mathematics as e.g. estimation of matrices' spectra. Another good

news is that numerical implementation of the procedure of isospectral

reduction is very simple and straightforward.**Bio:**

Prof. Leonid Bunimovich is a Regents' Professor of Mathematics at

Georgia Tech. His research concerns a wide array of problems at the

intersection of dynamical systems and statistics. He is known for his

discovery of focusing chaotic billiards (the "Bunimovich stadium") and for

the Bunimovich mushroom, a billiard with mixed regular and chaotic

dynamics. He became a Regents’ Professor and given the Exemplary Senior

Faculty Award, in 2000 receiving the Outstanding Faculty Research Author

Award. He was made a Fellow of the Institute of Physics in 2004, and was

named a Chartered Physicist and Fellow of the UK Institute of Physics in

1999. He received the Humboldt Prize in 2003. Prof. Bunimovich received his

PhD from the University of Moscow (1973) and a Doctorate of Sciences from

the Institute for Theoretical Physics of the Academy of Sciences of USSR,

Kiev (1986).