I am a post-doctoral research associate in mathematics at Imperial College London.
My main interest is in arithmetic algebraic geometry. Most of my work is on unlikely intersections in Shimura varieties, for example the André-Oort and Zilber-Pink conjectures. I am also interested in abelian varieties and the Mumford-Tate conjecture.
Algebraic Geometry. 2016-7: notes and problem sheets, 2017-8: course outline.
Shimura Varieties: In Autumn 2014, Andrei Yafaev and I taught a graduate course on Shimura Varieties for the London School of Geometry and Number Theory. An outline of the course and the problem sheets can be found on the course web page.
Finiteness theorems for K3 surfaces and abelian varieties of CM type
arXiv
With A. Skorobogatov, Preprint
Height bounds and the Siegel property
arXiv
Preprint
On compatibility between isogenies and polarisations of abelian varieties
arXiv,
journal
2017, International Journal of Number Theory 13 (3), p. 673-704
Heights of pre-special points of Shimura varieties
arXiv,
journal
With C. Daw, 2016, Mathematische Annalen 365 (3), p. 1305-1357
The proof of Lemma 2.15 in the published version of this paper is incorrect.
The correction can be found in the arXiv version of the paper.
Families of abelian varieties with many isogenous fibres
arXiv,
journal
2015, Journal für die reine und angewandte Mathematik 705, p. 211-231
There is a gap in the proof of Lemma 3.3 in the published version of this paper.
The gap was found and fixed by Gabriel Dill.
The corrections can be found in the arXiv version of the paper.
Lower bounds for ranks of Mumford-Tate groups
arXiv,
journal
Minoration des rangs de groupes de Mumford–Tate
2015, Bulletin de la Société Mathématique de France 143 (2), p. 229-246
Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem
pdf
Survey article, in O-minimality and Diophantine Geometry, ed. G. O. Jones, A. J. Wilkie, 2015, LMS Lecture Notes
The André-Pink conjecture : Hecke orbits and weakly special subvarieties
pdf
La conjecture d'André-Pink : orbites de Hecke et sous-variétés faiblement spéciales
PhD thesis, Université Paris Sud, 2013
Errata for my thesis
I write a blog with expositions on pieces of maths which interest me. Currently it is rarely updated.
The best part of the blog is the series on abelian varieties and topics related to the Mumford-Tate conjecture and absolute Hodge classes. This now has its own series index.
July 2015 - present |
Post-doctoral research associate, Imperial College London
Supervisor: Alexei Skorobogatov Funded by EPSRC grant EP/M020266/1 Brauer-Manin obstruction, K3 surfaces and families of twists of abelian varieties |
2013 - 2015 |
Post-doctoral research associate, University College London
Supervisor: Andrei Yafaev Funded by ERC grant 307364 Some Problems in Geometry of Shimura Varieties |
2010 - 2013 |
PhD student, Université Paris Sud
Supervisor: Emmanuel Ullmo Funded by the Doctoral School of Mathematics Paris Sud |
Each year since 2008 I have been a tutor at the UKMT National Mathematics Summer School. This is a five-day residential summer school for students aged 15 and 16. It is a nice opportunity to introduce able students to mathematics beyond the school curriculum, and especially how to think like a mathematician. Topics I have taught include inequalities, cyclic quadrilaterals, the pigeonhole principle, and graph theory.
I am a marker for the British Mathematical Olympiad and the UK Mathematical Olympiad for Girls, both organised by the United Kingdom Mathematics Trust.
During my PhD in Orsay, I participated as a jury member and team leader in the Tournoi Français de Jeunes Mathématicien(ne)s (2012 and 2013) and in the International Tournament of Young Mathematicians (2012). In these competitions, students in their final year of secondary school work in teams of five over a period of several months to solve open-ended problems set by the organisers, and then present their work at a regional, national or international event.
Department of Mathematics
Imperial College London
South Kensington Campus
London
SW7 2AZ
United Kingdom
Office: 681, Huxley Building
m.orr@imperial.ac.uk