L. Gurvits

activity

20022005

most citedHigh-resolution radio imaging of the most distant radio quasar SDSS J0836+0054

37 citations · 112 across the 8 of their papers we have counts for

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4 papers · 1 filter

math.CO2005★ 10 cited

A proof of hyperbolic van der Waerden conjecture : the right generalization is the ultimate simplification

Leonid Gurvits

Consider a homogeneous polynomial $p (z_{1}, ..., z_{n})$ of degree $n$ in $n$ complex variables . Assume that this polynomial satisfies the property : \\ $|p(z_1,...,z_n)| \geq \prod_{1…

math.CO2004★ 8 cited

Van der Waerden Conjecture for Mixed Discriminants

Leonid Gurvits

We prove that the mixed discriminant of doubly stochastic $n$ -tuples of semidefinite hermitian $n \times n$ matrices is bounded below by $\frac{n !}{n ^{n}}$ and that this bound is u…

math.CO2004★ 24 cited

Combinatorial and algorithmic aspects of hyperbolic polynomials

Leonid Gurvits

Let $p (x_{1}, ..., x_{n}) = \sum_{(r_{1}, ..., r_{n}) \in I_{n, n}} a_{(r_{1}, ..., r_{n})} \prod_{1 \leq i \leq n} x_{i}^{r_{i}}$ be homogeneous polynomial of degree $n$ in $n$ real variables with in…

math.CO2004★ 12 cited

Combinatorics hidden in hyperbolic polynomials and related topics

Leonid Gurvits

The main topic of this paper is various "hyperbolic" generalizations of the Edmonds-Rado theorem on the rank of intersection of two matroids. We prove several results in this direc…