- Postal Address
Department of Mathematics,
Greetings friends. My name is Daniel Loughran and I am currently a research fellow in mathematics at the University of Bristol. Together with Tim Dokchitser and Jonathan Bober, I organise the Heilbronn number theory seminar.
My research interests include arithmetic geometry and analytic number theory. So far my work has revolved around the study of rational points on varieties, in particular their existence and distribution. I also have an interest in harmonic analysis, Brauer groups, L-functions and equivariant geometry. I have recently initiated a research programme on counting the number of varieties in a family which contain a rational point. As part of this programme I have formulated some conjectures, which I hope will stimulate further research (see my latest paper below).
I finished my PhD in Bristol in 2011, under the supervision of Tim Browning. I spent the academic year 2011/2012 as a postdoc at Jussieu in Paris, before coming back with avengence to Bristol as a research fellow.
For the autumn term of 2013, I will be teaching (together with Vinesh Solanki and Lee Butler) the course MATH30001/MATHM0008 - Topics in modern geometry. The course will cover topological spaces, topological groups, projective space, projective geometry, algebraic curves and elliptic curves. All teaching material for the course will appear here.
Office hours: Office 2.21, Howard House, Fridays 2pm - 4pm.
The following is a list of my publications. My thesis is essentially a collection of my first three papers, however it also contains a general introduction to del Pezzo surfaces and Manin's conjecture. It was awarded a postgraduate commendation for excellence in a doctoral thesis by the faculty of science of the University of Bristol.
- Varieties with too many rational points (with Tim Browning), submitted, [arXiv:1311.5755].
- The number of varieties in a family which contain a rational point, submitted, [arXiv:1310.6219].
- Rational points of bounded height and the Weil restriction, submitted, [arXiv:1210.1792].
- Equivariant compactifications of two-dimensional algebraic groups (with Ulrich Derenthal), Proceedings of the Edinburgh mathematical society, to appear, [arXiv:1212.3518].
- Manin's conjecture for a singular quartic del Pezzo surface, J. London Math. Soc. 86(2) (2012), 558-584, [arXiv:1109.6253].
- Manin's conjecture for a singular sextic del Pezzo surface, Journal de Théorie des Nombres de Bordeaux, 22(3) (2010), 675-701, [arXiv:1009.2364].
- Singular del Pezzo surfaces that are equivariant compactifications (with Ulrich Derenthal), Hausdorff Trimester on Diophantine equations in: Zapiski Nauchnykh Seminarov (POMI) 377 (2010), 26-43, [arXiv:0910.2717].
- Manin's conjecture for del Pezzo surfaces, (Ph.D. Thesis) 2011, pdf.
Research talksThe following is a list of invited research talks that I have given. It also includes upcoming talks.
- 03/12/2013 - Number theory seminar, University of Cambridge.
- 28/03/2013 - Research seminar, HIM, Bonn.
- 28/02/2013 - Pure mathematics seminar, Exeter University.
- 11/02/2013 - Number theory seminar, Warwick University.
- 06/12/2012 - Séminaire d'arithmétique, Université Lille 1, Lille.
- 03/12/2012 - Pure mathematics seminar, Royal Holloway, London.
- 27/11/2012 - Number theory seminar, Sheffield University.
- 22/10/2012 - Pure maths research seminar, UEA, Norwich.
- 18/10/2012 - Number theory seminar, Oxford University.
- 21/05/2012 - Analytic methods for diophantine equations, Göttingen.
- 21/05/2012 - Arithmétique en plat pays, Ghent.
- 27/04/2012 - Séminaire de théorie des nombres de Caen, Caen.
- 09/03/2012 - Séminaire variétés rationnelles, Ecole normale supérieure, Paris.
- 22/02/2012 - Séminaire de théorie des nombres, Institut Fourier, Grenoble.
- 02/02/2012 - Séminaire de géométrie algébrique, Université de Rennes 1, Rennes.
- 05/12/2011 - Rencontres de théorie analytique et élémentaire des nombres, Institut Henri Poincaré, Paris.
- 14/11/2011 - Séminaire de théorie des nombres, Institut de Mathématiques de Jussieu, Paris.