Maria Francis

Currently, I am an Assistant Professor at the Computer Science and Engineering department at the Indian Institute of Technology, Hyderabad. Previously, I was a postdoctoral researcher at the Institute for Algebra at the Johannes Kepler University (JKU), Linz, Austria where I worked under the supervision of Prof. Manuel Kauers. Prior to that, I was a doctoral student at the Computer Science and Automation department at the Indian Institute of Science (IISc), Bangalore, India. My research supervisor was Dr.Ambedkar Dukkipati. During the period 2007 - 2009, I had worked with Microsoft India (R &D) as a Program Manager. I completed my undergraduate degree in Computer Science and Engineering from the National Institute of Technology, Calicut.

My research interests are in Computer Algebra, Symbolic Computation, Commutative Algebra and Lattice Cryptography. My CV can be found here.


Publications

  1. M. Francis and T. Verron. “On Two Signature Variants Of Buchberger’s Algorithm Over Principal Ideal Domains”, To appear in International Symposium on Symbolic and Algebraic Computation (ISSAC) 2021. arXiv preprint : arXiv:2102.03339.

  2. M. Francis and T. Verron. “A Signature-based Algorithm for Computing Gröbner Bases over Principal Ideal Domains”, Mathematics in Computer Science (2020). arXiv preprint : arXiv:1802.01388.

  3. M. Francis and A. Dukkipati. “On Ideal Lattices, Gröbner Bases and Generalized Hash Functions ”, Journal of Algebra and its Applications, Vol. 17, No. 06, 1850112 (2018).

  4. M. Francis and A. Dukkipati. “On Computing Krull Dimension of Residue Class Polynomial Rings over Integral Domains using Gröbner Bases”, Journal Of Symbolic Computation, 86:1-19, 2018.

  5. M. Francis and A. Dukkipati. “ On Reduced Gröbner Basis and Macaulay-Buchberger Basis Theorem Over Noetherian Rings ”, Journal Of Symbolic Computation, 65:1-14, 2014.

Preprints/Submitted:

  1. M. Francis and T. Verron. " Signature-based Möller's Algorithm for strong Gröbner bases over PIDs, arXiv preprint: arXiv:1901.09586

  2. A. Dukkipati, N. Pai and M. Francis. “Border Bases for Polynomial Rings over Noetherian Rings”, arXiv preprint: arXiv:1405.0472.