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 2007 2018

- 13 Finished

### 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

### Support of Joint Research Group (Scheme 3) COW Algebraic Geometry Seminar

1/10/13 → 30/09/14

Project: UK charity

## Research Output 2000 2019

### Regular cylindrical algebraic decomposition

Davenport, J., Locatelli, A. & Sankaran, G., 27 Jun 2019, (Accepted/In press) In : Journal of the London Mathematical Society.Research output: Contribution to journal › Article

### Teaching of computing to mathematics students: Programming and discrete mathematics

Betteridge, J., Davenport, J. H., Freitag, M., Heijtljes, W., Kynaston, S., Sankaran, G. & Traustason, G., 9 Jan 2019,*Proceedings of the 3rd Conference on Computing Education Practice, CEP 2019.*Association for Computing Machinery, 12

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

### Weighted Castelnuovo-Mumford Regularity and Weighted Global Generation

Malaspina, F. & Sankaran, G. K., 28 Feb 2019, In : Journal of Algebra and its Applications. 18, 2, 15 p., 1950028.Research output: Contribution to journal › Article

### Fast matrix operations in computer algebra

Tonks, Z., Sankaran, G. & Davenport, J. H., 9 Nov 2018,*Proceedings - 2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2017.*Ida, T., Jebelean, T., Petcu, D., Watt, S. M., Negru, V. & Zaharie, D. (eds.). IEEE, p. 67-70 4 p. 8531267

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

### Fundamental groups of toroidal compactifications

Kasparian, A. K. & Sankaran, G. K., 9 Nov 2018, In : Asian Journal of Mathematics. 22, 5, p. 941-954 13 p.Research output: Contribution to journal › Article

## Datasets

### Data for 'Fast Matrix Operations in Computer Algebra'

Tonks, Z. (Creator), University of Bath, 13 Dec 2017

DOI: 10.15125/BATH-00460

Dataset

## Thesis

## Computations and bounds for surfaces in weighted projective four-spaces

Author: Rammea, L., 1 Oct 2009Supervisor: Sankaran, G. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Irreducible holomorphic symplectic manifolds and monodromy operators

Author: Onorati, C., 22 Nov 2018Supervisor: Sankaran, G. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Moduli of deformation generalised Kummer manifolds

Author: Dawes, M., 2 Mar 2016Supervisor: Sankaran, G. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Non-simple abelian varieties and (1; 3) Theta divisors

Author: Borowka, P., 21 Nov 2012Supervisor: Sankaran, G. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## On the degenerations of (1,7)-polarised abelian surfaces

Author: Marini, A., 1 Jan 2002Supervisor: Sankaran, G. (Supervisor)

Student thesis: Doctoral Thesis › PhD