February 2021-Present: PhD student, University of Barcelona
2015-2020: Intergrated Master's (BS-MS), Indian Institute of Science Education and Research, Thiruvananthapuram

Research activities:
2020: Master's project titled 'Syzygies of Modules' supervised by Dr. Sarbeswar Pal, IISER Tvm.
2019: Minor project titled 'Moonshine and its applications towards Conformal Field Theory' supervised by Dr. Bindusar Sahoo, IISER Tvm.


Project: Extraction of geometric primitives from 3D point clouds.

Advisors: Carlos D'Andrea, Juan Carlos Naranjo

Institution: University of Barcelona
This project has a very strong foot in Algebraic Geometry with applications to Machine Learning as a motivation. The extraction of geometric primitives from 3D point clouds is an important problem in reverse engineering. These 3D point clouds are typically obtained by means of accurate 3D scanners and there exist several methods for performing the geometric primitives extraction. Key ingredients in this approach are geometric routines that are capable of producing an instance of a given type of shape from a small number of points. The most used types of shapes are planes, spheres, cylinders, cones and tori. While devising such routines is relatively straightforward for planes and spheres, the cases of cylinders, cones and tori are much more difficult but have been worked out recently. The goal of this PhD is to investigate to what extent one can deepen these results, and also to extend them to other kind of low degree surfaces.

Expected Results: We expect to deliver algorithmic criteria for reconstructing specific surfaces given a cloud of points in 3D, as well as topological, geometric, and algebraic criteria for distinguishing them (degree, genus, Betti numbers, etc.). Generalizations to higher dimensions and non necessarily smooth algebraic objects and implementations are also part of the research plan.

The project will take place at the Mathematics Dept of the University of Barcelona.

Secondments are planned at Inria Research Center Sophia Antipolis Mediterranee, and at Faculty of Mathematics and Informatics, Vilnius University.