Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

Workshop Reports

### Jahresbericht | Annual Report - 2017

MFO Annual Report, 2017

### Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps (Revised Edition)

Ariyan Javanpeykar & Ljudmila Kamenova
Demailly's conjecture, which is a consequence of the Green-Griffths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to provide evidence for Demailly's conjecture by verifying several predictions it makes. We first define what an algebraically hyperbolic projective variety is, extending Demailly's definition to (not necessarily smooth) projective varieties over an arbitrary algebraically closed field of characteristic zero, and we prove that this property...

### Splitting Necklaces, with Constraints

Dusko Jojic, Gaiane Panina & Rade Zivaljevic
We prove several versions of Alon's "necklace-splitting theorem", subject to additional constraints, as illustrated by the following results. (1) The "almost equicardinal necklace-splitting theorem" claims that, without increasing the number of cuts, one guarantees the existence of a fair splitting such that each thief is allocated (approximately) one and the same number of pieces of the necklace, provided the number of thieves $r=p^\nu$ is a prime power. (2) The "binary splitting theorem" claims that if...

### Positive Line Bundles Over the Irreducible Quantum Flag Manifolds

Fredy Díaz García, Andrey Krutov, Réamonn Ó Buachalla, Petr Somberg & Karen R. Strung
Noncommutative Kähler structures were recently introduced by the third author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subsequently observed that the notion of a positive vector bundle directly generalises to this setting, as does the Kodaira vanishing theorem. In this paper, by restricting to covariant Kähler structures of irreducible type (those having an irreducible space of holomorphic $1$-forms) we provide simple cohomological criteria for positivity, offering a means...

Workshop Reports

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Workshop Reports

### Random matrix theory: Dyson Brownian motion

Gianluca Finocchio
The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John Dyson, who were both concerned with the statistical description of heavy atoms and their electromagnetic properties. In this snapshot, we show how mathematical properties can have unexpected links to physical phenomenena. In particular, we show that the eigenvalues of...

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