Groups

  • Causal set theory is an attempt to reconcile General relativity with Quantum Theory. It is what is called a theory of quantum gravity. It assumes that the fundamental reality is not a smooth manifold but is rather a discrete structure called a causal set. Some wonderful results have already come out of the causal set idea. Although a...
  • Stochastic Portfolio Theory is a branch of Mathematical Finance. Robert Merton studied the portfolio allocation problem as a Stochastic Control Problem. In his model, an investor allocates his/her wealth between a risky asset and a riskless asset, then chooses the consumption rate to maximize the total expected utility. Dr. Hussain is...
  • Spectral theory can be seen as a generalization of the ideas and concepts of eigenvalues and eigenvectors of a square matrix to a broader class of operators acting in different spaces. Dr. Usman’s research interest lies in the spectral theory of Quantum graphs. A quantum graph is a metric graph with one-dimensional Schrödinger operato...
  • Modeling of complex biological phenomena has become fashionable over the past two decades, as the computing power required to analyze such models has become available. On the other side, non-local calculus has gained significance owing to its applications in various biological and physical phenomena. The theory of non-local calculus h...
  • Algebraic Geometry is the study solutions of multivariate polynomial equations. The solutions of these polynomial equations which are the geometric objects of study in Algebraic Geometry are called algebraic varieties. Dr. Qureshi is interested in classification of families of algebraic varieties. In particular he is interested the cl...
  • Real world problems can be formulated in mathematical terms (modeling), as the models have grown complex, a great deal of computing power is required to study these models. Scientific computation involves investigation of robust and efficient methods for studying problems that require heavy computations. Dr. Sial’s has been working on...
  • Evolution equations can be interpreted as differential laws describing the development of a system.  Beginning with the study of differential equations investigators now look at these in a more abstract setting. Dr. Imran Naeem studies exact solutions of evolution equations using Lie Symmetry methods.  Lie symmetry analysis...
  • C* Algebras were first studied in connection with modeling observables in quantum mechanics. They have subsequently generated a lot of interest as an area of research. Fixed point theory is the investigation of existence, uniqueness and approximation of fixed points of mappings. From economics (Nash’s theorem) to physics (phase transi...
  • Using ideas from algebra, how can one classify topological spaces?  This is the fundamental question which investigators in Algebraic Topology try to address. Dr. Haniya is interested in the cohomology of n-pointed configuration spaces of complex projective varieties and rational models for the cohomology of s...

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