Julius Ross

A study of the Hilbert-Mumford criterion for the stability of projective varieties

We make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties

Unstable products of smooth curves

(X,L)

K-stability for Kähler manifolds

; in particular for K- and Chow stability. For each type of stability this leads to a concept of slope

The Hele-Shaw flow and moduli of holomorphic discs

\mu

Variation of Gieseker moduli spaces via quiver GIT

for varieties and their subschemes; if

A note on positivity of the CM line bundle

(X,L)

Asymptotics of Partial Density Functions for Divisors

is semistable then

Semi-continuity of Stability for Sheaves and Variation of Gieseker Moduli Spaces

\mu(Z)\le\mu(X)

On the maximal rank problem for the complexhomogeneous Monge–Ampère equation

for all

Balanced metrics on twisted Higgs bundles

Z\subset X