Projects per year
Personal profile
Research interests
I do research in algebraic geometry and some related areas of pure mathematics. Most of my research is concerned with the geometry of moduli spaces and their compactifications. It is possible to use ideas and techniques from number theory (modular forms especially) and algebraic topology to control the geometric behaviour of moduli spaces, and I have been studying this in relation to moduli of abelian varieties, K3 surfaces and hyperkahler manifolds. The geometry associated with those varieties themselves is therefore also of interest to me.
The compactifications I work with are mostly toroidal compactifications and much of my research is directed towards finding new ways to exploit the flexibility of this construction. This leads to questions on such matters as birational geometry, Hodge theory and symmetric spaces, as well as toric geometry.
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Projects

Algebraic geometry and number theory for development
Engineering and Physical Sciences Research Council
1/04/20 → 31/03/21
Project: Research council

Support of Joint Research Group: Algebraic Geometry Seminar (COW)
1/08/17 → 30/09/18
Project: UK charity

Support of Joint Research Group: Algebraic Geometry Seminar (COW)
1/08/16 → 31/07/17
Project: UK charity


Research Output

Blowups with log canonical singularities
Sankaran, G. & Santos, F., 23 Feb 2020, (Arxiv).Research output: Working paper

Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
Nair, A., Davenport, J. & Sankaran, G., 8 Jul 2020, Mathematical Software – ICMS 2020  7th International Conference, Proceedings. Bigatti, A. M., Carette, J., Davenport, J. H., Joswig, M. & de Wolff, T. (eds.). Singapore: Springer, Singapore, p. 1726 10 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 12097 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Regular cylindrical algebraic decomposition
Davenport, J., Locatelli, A. & Sankaran, G., 25 Feb 2020, In: Journal of the London Mathematical Society. 101, 1, p. 4359 17 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile21 Downloads (Pure) 
Lazard's CAD exploiting equality constraints
Nair, A., Davenport, J., Sankaran, G. & McCallum, S., 30 Sep 2019, In: ACM Communications in Computer Algebra. 53, 3, p. 138141 4 p.Research output: Contribution to journal › Article › peerreview

On Benefits of Equality Constraints in LexLeast Invariant CAD (Extended Abstract
Nair, A. S., Davenport, J. & Sankaran, G., Sep 2019, Proceedings SC2 2019. 8 p.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
File35 Downloads (Pure)
Datasets

Data for 'Fast Matrix Operations in Computer Algebra'
Tonks, Z. (Creator), Davenport, J. (Editor) & Sankaran, G. (Editor), University of Bath, 13 Dec 2017
DOI: 10.15125/BATH00460
Dataset