Explorations in Geometry and Mathematical Physics: From Symplectic Geometry to String Theory

Understanding how faults slip during an earthquake is still a grand challenge in seismology.

Exploring Qualitative Mathematical Modelling and the Mathematics of Traditional and Indigenous Cultures

Exterior Differential Systems and Hyperbolic PDE

As we move into exascale computing, and beyond, the chance of a fault occurring in the system increases. Traditional approaches to building resilience into the system, such as check-pointing, may become too expensive.

Higher arithmetic. The failure of unique factorization in generalized number systems. Integer and rational solutions to algebraic equations. Fermat's Last Theorem.

It is proposed that the student presents a review of the theory of black hole formation, and a critical evaluation of the arguments used to deduce their existence in the universe.

Explore the analogy between the Galois theory of fields and the theory of covering spaces in topology.

Generalized geometry, whose definition was inspired in particular by duality symmetries in String Theory, was recently put into a rigorous mathematical framework by Hitchin [Hi] and his students [Ca, Gu].

Geometric Control Theory

This project is to explore various new topological invariants using topological field theory and dualities arising from gauge theory and string theory

This project would lay down some of mathematical ground for string theory.

Why are the trace and the determinant of a matrix special, as opposed to some other random function of the matrix entries? Why should the discriminant $b^2-4ac$ play a fundamental role, and not, say $a^2+4bc$? One answer (among many) is that the trace, the determinant, and the discriminant are distinguished functions

Group Theory in Quantum Computation

Approximation of High Dimensional Data Sets using Sparse Grid Techniques.