Chris Daw
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+44 (0) 118 378 5352
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Associate Professor
- Library Representative
- LMS Correspondent
- Pure Group Teaching Lead
Office
Room 106Building location
MathematicsAreas of interest
- Arithmetic geometry
- Number theory
- Model theory
- Ergodic theory
- Algebraic groups
- Unlikely intersections in Shimura varieties
Teaching
Current teaching (2023/24):
Research centres and groups
Number TheoryResearch projects
My research focuses on certain mathematical objects known as Shimura varieties. Shimura varieties arise in many guises, but they may be most familiar as the parameter spaces of abelian varieties. Abelian varieties are central objects in number theory — the simplest abelian varieties, known as elliptic curves, are now at the heart of modern cryptography. For this reason, and others, questions regarding the geometry of Shimura varieties can inspire and illuminate many questions in number theory and beyond.
Background
2014 - 2016 Hodge Fellow, Institut des Hautes Etudes Scientifiques
2016 - 2017 EPSRC Postdoctoral Research Assistant, University of Oxford
2016 - 2017 Junior Research Fellow, Linacre College, Oxford
2017 - 2018 Academic Visitor, Mathematical Institute, University of Oxford
2018 - 2023 Visiting Research Fellow, Mathematical Institute, University of Oxford
Academic qualifications
MSci Mathematics, University College London (2010)
PhD Mathematics, University College London (2014)
Professional bodies/affiliations
Member, London Mathematical Society
Websites/blogs
Publications
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Daw, C.
ORCID: 0000-0002-2488-6729
,
Gorodnik, A.
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Ullmo, E.
(2023)
The space of homogeneous probability measures on Γ∖X¯¯¯¯¯¯¯¯¯¯S max is compact.
Mathematische Annalen
, 386
pp.
987-1016.
ISSN:
0025-5831
|
doi:
https://dx.doi.org/10.1007/s00208-022-02412-w
- Daw, C. and Orr, M. (2023) Lattices with skew-Hermitian forms over division algebras and unlikely intersections. Journal de l'École polytechnique — Mathématiques , 10 pp. 1097-1156. ISSN: 2270-518X | doi: https://dx.doi.org/10.5802/jep.240
- Daw, C. , Gorodnik, A. , Ullmo, E. , Li, J. (2023) The space of homogeneous probability measures on $\overline{\Gamma\backslash X}^S_{\rm max}$ is compact. Mathematische Annalen , 386 pp. 987-1016. ISSN: 0025-5831 | doi: https://dx.doi.org/10.1007/s00208-022-02412-w
- Daw, C. (2022) Zilber–Pink in Y(1)n.
- Binyamini, G. and Daw, C. (2022) Effective computations for weakly optimal subvarieties. Journal of the European Mathematical Society ISSN: 1435-9855
- Daw, C. and Orr, M. (2022) Quantitative reduction theory and unlikely intersections. International Mathematics Research Notices , 2022 (20). pp. 16138-16195. ISSN: 1073-7928 | doi: https://dx.doi.org/10.1093/imrn/rnab173
- Daw, C. and Orr, M. (2021) Unlikely intersections with ExCM curves in A2. Annali della Scuola Normale Superiore di Pisa , 22 (4). ISSN: 2036-2145 | doi: https://dx.doi.org/10.2422/2036-2145.202006_014
- Daw, C. , Gorodnik, A. , Ullmo, E. (2021) Convergence of measures on compactifications of locally symmetric spaces. Mathematische Zeitschrift , 297 (3-4). pp. 1293-1328. ISSN: 0025-5874 | doi: https://dx.doi.org/10.1007/s00209-020-02558-w
- Borovoi, M. , Daw, C. , Ren, J. (2021) Conjugation of semisimple subgroups over real number fields of bounded degree. Proceedings of the American Mathematical Society , 149 pp. 4973-4984. ISSN: 0002-9939 | doi: https://dx.doi.org/10.1090/proc/14505
- Daw, C. , Javanpeykar, A. , Kühne, L. (2020) Effective estimates for the degrees of maximal special subvarieties. Selecta Mathematica , 26 ISSN: 1420-9020 | doi: https://dx.doi.org/10.1007/s00029-019-0528-1
- Daw, C. and Ren, J. (2018) Applications of the hyperbolic Ax-Schanuel conjecture. Compositio Mathematica , 154 (9). pp. 1843-1888. ISSN: 1570-5846 | doi: https://dx.doi.org/10.1112/S0010437X1800725X
- Daw, C. (2017) The Zilber-Pink conjecture for pure Shimura varieties via o-minimality. O-Minimality and its Applications to Number Theory and Analysis. Mathematisches Forschungsinstitut Oberwolfach pp. 1405-1407. | doi: https://dx.doi.org/10.4171/OWR/2017/22
- Daw, C. and Harris, A. (2017) Categoricity of modular and Shimura curves. Journal of the Institute of Mathematics of Jussieu ISSN: 1475-3030 | doi: https://dx.doi.org/10.1017/S1474748015000365
- Daw, C. and Orr, M. (2016) Heights of pre-special points of Shimura varieties. Mathematische Annalen , 365 (3-4). pp. 1305-1357. ISSN: 0025-5831 | doi: https://dx.doi.org/10.1007/s00208-015-1328-3
- Daw, C. (2016) Degrees of strongly special subvarieties and the André–Oort conjecture. Journal für die reine und angewandte Mathematik (Crelles Journal) , 2016 (721). pp. 81-108. ISSN: 0075-4102 | doi: https://dx.doi.org/10.1515/crelle-2014-0062
- Daw, C. (2015) The Andre-Oort conjecture via o-minimality. In: Jones, G. and Wilkie, A. , (eds.) O-Minimality and Diophantine Geometry. London Mathematical Society Lecture Note Series Cambridge University Press (421). pp. 129-158. ISBN: 9781316106839 | doi: https://dx.doi.org/10.1017/CBO9781316106839.006
- Daw, C. (2012) A simplified proof of the Andre-Oort conjecture for products of modular curves. Archiv der Mathematik , 98 (5). pp. 433-440. ISSN: 1420-8938 | doi: https://dx.doi.org/10.1007/s00013-012-0372-4
- Daw, C. (2012) On torsion of class groups of CM tori. Mathematika , 58 (2). pp. 305-318. ISSN: 2041-7942 | doi: https://dx.doi.org/10.1112/S0025579312000022
- Daw, C. and Yafaev, A. (2011) An unconditional proof of the Andre-Oort conjecture for Hilbert modular surfaces. Manuscripta Mathematica , 135 (1). pp. 263-271. ISSN: 0025-2611 | doi: https://dx.doi.org/10.1007/s00229-011-0445-x