Invited Talk by Dr. Maria Francis on Polynomial Rings over Commutative Rings - Algorithmic techniques and Applications
Polynomial rings over commutative rings have applications in several areas like cryptography, control theory, coding theory and algebraic geometry. For example, in lattice based cryptography, most arithmetic operations are over integers, and in control theory parametric equations with polynomials themselves as coefficients are very common.
Algorithmic techniques for polynomial rings over fields are well studied with Groebner bases being one of the fundamental tools. Even though various approaches have been proposed to extend Groebner bases theory to polynomial rings over rings, these techniques have only looked at extending basic definitions and concepts.
Maria Francis is a postdoctoral researcher at the Institute for Algebra at the Johannes Kepler University (JKU), Linz, Austria where she works under the supervision of Prof. Manuel Kauers. Previously, she was a doctoral student at the Computer Science and Automation department at the Indian Institute of Science (IISc), Bangalore, India. Her research supervisor was Dr.Ambedkar Dukkipati. Her research interests are in Computer Algebra, Symbolic Computation, Commutative Algebra and Lattice Cryptography.