Algebraic geometry: Algebraic groups, Singularity theory Geometric invariant theory

Representation theory of real and p-adic groups: Harmonic analysis on Spherical varieties, Gelfand pairs, asymptotic representation theory

Functional analysis: Distributions and generalized functions, Microlocal analysis, Topological vector spaces.

Active sensing: Mechanisms of closed loop perception.

Biomimetic technology for active vibrissal touch

Object localization

Sensory substitution - from vision to touch

Weakly coupled versions of the AdS/CFT correspondence and possible derivations

General properties of field theories with quenched disorder

Dualities between field theories in various dimensions

Conformal bootstrap at large N and quantum gravity

Planetary Science

Genetic Regulation of Metabolic Pathways and its Co-ordination with Developmental and Stress Response Programs in Plant Biology

Antibodies that recognize crystal surfaces and 2-dimensional organized patterns.

Mechanisms of crystal nucleation and modulation of crystal growth and properties in biomineralization (bone, mollusk shells, echinoderms).

Mechanism of cell adhesion using crystal substrates.

Understanding how breakdown of this process results in autoimmunity.

Deciphering the molecular and cellular mechanisms that control the establishment of central immune tolerance.

Multi-level computational methods, scientific computation.

Quantification of atoms, groups and molecules electronegati using metal substituted bacteriochlorophylls and application to chemical reactivity.

Resolving the forces which drive membrane protein assembly.

The mechenism behind generation of reactive oxygen species (ROS) by illuminating novel bacteriochlorophyll derivatives and their application in photodynamic therapy (PDT) of tumors.

Study and application of molecular biorecognition