[Turkmath:3042] Jonathan Leake at IMBM, Friday, June 8, 2018, 14:00

[Mohan Ravichandran]

Dear All,

   Jonathan Leake will give a talk on the Polya-Schur theory tomorrow.

 Speaker :Jonathan Leake, UC Berkeley
Time and date : 14:00, June 8, Friday, IMBM


Applications and Extensions of Real Stability Preservers

Linear operators on polynomials which preserve the property of having only
real roots have been studied since the seminal work of Polya and Schur in
the early 20th century. Various progress has been made in the direction of
this problem, culminating in 2009 in the Borcea-Branden characterization of
all such real-rootedness preservers. Their result relies on a multivariate
generalization of real-rootedness called "real stability", a concept which
has recently had a strong influence on fields including combinatorics,
optimization, and theoretical computer science. In all applications, the
Borcea-Branden characterization has become an essential and
heavily-utilized tool. In this talk, we will discuss this characterization,
and a number of its most interesting theoretical consequences. We will
further discuss a few combinatorial implications of the theory,
particularly related to matchings of a graph. If time permits, we will also
discuss the relation of this theory to that of "mesh polynomials", which
are real-rooted polynomials with a certain minimum spacing between
consecutive roots.

Thanks,
Mohan
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