"Non UBC"@en .
"DSpace"@en .
"Eli Shamovich"@en .
"2019-11-27T09:42:13Z"@en .
"2019-05-30T17:01"@en .
"Recall that given two complex polynomials $f$ and $g$, the Bezout matrix $B(f,g) = (b_{ij})$ of $f$ and $g$ is defined by $\frac{f(t)g(s) - f(s)g(t)}{t-s} = \sum_{i,j} b_{ij} t^i s^j$. It is a classical result of Hermite that given a polynomial $p(z)$, the Bezout matrix of $p(z)$ and $p^{\tau}(z) = \overline{p(\bar{z})}$ is skew self-adjoint. The number of common zeroes of $p$ and $p^{\tau}$ is the dimension of the kernel of $-i B(p,p^{\tau})$. Additionally, $p$ has $n_+$ roots in the upper half-plane and $n_-$ in the lower half-plane. Here $n-+$ and $n_-$ stand for the number of positive and negative eigenvalues of $-i B(p,p^{\tau})$, respectively. In this talk, I will describe how one can extend the notion of the Bezout matrix to a pair of meromorphic functions on a compact Riemann surface. If the surface is real and dividing the matrix $-i B(f,f^{\tau})$ is $J$-selfadjoint, for a certain signature matrix $J$. We the study the signature of the Bezoutian and obtain an extension of Hermite\u00C3\u00A2s theorem to quadrature domains. \n\nThis talk is based on joint work with V. Vinnikov."@en .
"https://circle.library.ubc.ca/rest/handle/2429/72430?expand=metadata"@en .
"32.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University of Waterloo"@en .
"Banff (Alta.)"@en .
"10.14288/1.0385990"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Postdoctoral"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Operations Research, Mathematical Programming, Algebraic Geometry, Control/Optimization/Operation Research"@en .
"Counting the number of zeroes of polynomials in quadrature domains"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72430"@en .