Julius Ross

Research

I am a Fellow and Lecturer at Sidney Sussex College, Cambridge. Starting in Oct 2011, I will hold an EPSRC Career Acelleration Grant at the University of Cambridge.

My research is in the area of algebraic geometry, specifically looking at the notion of stability (in the sense of Geometric invariant theory) for projective varieties, with an eye to a relationship with the existence of metrics of constant scalar curvature. I am also interested in Okounkov bodies, singular metrics and pluripotential theory.

I edit a Journal

Workshop on Kahler Geometry

I am organising a workshop on Kahler Geometry, April 10-13th 2012 at Cambridge University. For information click here.

Papers and Preprints

(Joint with David Witt-Nystrom) Gradient maps and Okounkov bodies In preparation
(Joint with Julien Keller) A note on Chow stability of the projectivisation of Gieseker stable bundles arXiv:1110.4489
(Joint with Mario Garcia-Fernandez) Limits of balanced metrics on vector bundles and polarised manifolds arXiv:1111.2819
(Joint with David Witt-Nystrom) Analytic test configurations and geodesic rays. arXiv:1101.1612
(Joint with R.P. Thomas) Weighted Bergman kernels on orbifolds. Jour. Diff. Geom. 88, p.87-108, 2011. arXiv:0907.5215
(Joint with R.P. Thomas) Weighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metrics Jour. Diff. Geom. 88, p.109-160, 2011. arXiv:0907.5214
(Joint with J. Roé) An inequality between multipoint Seshadri Constants. Geometriae Dedicata Volume 140, Number 1. pp 175-181. arXiv:0804.1662
(Joint with D. Panov) Slope Stability and Exceptional Divisors of High Genus. Math. Ann. 343 No 1, 2009. arXiv:0710.4078
(Joint with D.H. Phong and J. Sturm) Deligne pairings and the Knudsen-Mumford expansion Jour. Diff. Geom. 78, p.475-496, 2008.math.DG/0612555
Seshadri constants on symmetric products of curves Math Res. Let. Vol 14 No 1. pp 63-75, 2007. math.AG/0608224.
(Joint with J. Fine) A note on Positivity of the CM line bundle IMRN, vol. 2006, Article ID 95875, 14 pages, 2006. math.AG/0605302
Unstable products of smooth curves. Invent Math. Vol. 165 No. 1 pp 153-162, 2006 math.AG/0506447.
(Joint with R.P. Thomas) A study of the Hilbert-Mumford criterion for the stability of projective varieties. Journal of Algebraic Geometry 16 (2007), 201-255. math.AG/0412519.
(Joint with R.P. Thomas) An obstruction to the existence of constant scalar curvature Kahler metrics, Jour. Diff. Geom. 72, 429-466, 2006. math.DG/0412518

Unpublished work

Canonical metrics and stability of projective varieties (Notes written for the workshop on ''Numerical invariants of singularities and higher-dimensional algebraic varieties'' at the American Institute of Mathematics, July 2006)
Instability of Polarised Algebraic Varieties. Thesis (ps file)
Stability of polarised varieties (Slides of seminar given at Seattle 2005)

Doctoral Students

Anton Isopoussu

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