The focus will be on broader understanding of algebraic varieties, constructing reliable and powerful methods to secure digital information and leading research in Quantum Analysis.
The area of study of this project lies within Algebraic Geometry, the branch of mathematics devoted to geometric shapes called algebraic varieties, defined by polynomial equations. While algebraic geometry has contributed applications in coding, industrial control, and computation, the topics of this project are more closely related to applications in theoretical physics, where physicists con sider algebraic varieties as components of the fine structure of our universe. This is especially true with the first topic, moduli theory. Such objects are a central object of study of this project. The other topic studied in this project is birational geometry, which is devoted to a certain abstract relationship, called birational equivalence, among algebraic varieties, which lies at the foundation of algebraic geometry. Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. The ultimate goal is a broader understanding of algebraic varieties from three different perspectives.
Principal Investigator: Arijit Dey
Cryptography, Cybersecurity and Distributed Trust
Our goal is to construct reliable, fast and powerful methods to secure digital information and distribute points of trust so as to minimize risk of failure caused either by accident or malice. Our focus will comprise post-cryptography to future-proof cryptographic systems and make them quantum resilient, Byzantine fault tolerant distributed computing to build resilient network platforms for distributed trust applications, and cryptography for cloud computing to design algorithms and construct systems with provable security to enable secure cloud computing.
Principal Investigator: Shweta Agrawal
We investigate connections between representations of groups and properties of operator algebras, investigate mathematical aspects of quantum channels and study quantum resonances and scattering through the geometric approach. We focus on structural properties of operator algebras, results related to Duflo theorems in quantum scattering theory.
Principal Investigator: Kunal Krishna Mukherjee