Design and development of muti-functional, hierarchically structured, and highly ordered materials is the key to the advancement in the field of materials nanochemistry, and bionanotechnology. These fields are likely to play an important role in driving markets, and economies in the developing countries by fulfilling their high demand towards the improvement in health, and energy sector. Specifically, the formation of biodegradable materials with novel properties, multiple functions, improved efficiency, and higher sensitivity can cater to the demand of health and diagnostics industry.

■   Metal nanoparticles of gold (Au), ruthenium (Ru), rhodium (Rh) and palladium (Pd) supported by a carbon nanotube (CNT): supramolecular assembly are highly efficient heterogeneous catalysts for various organic reactions
■   Oxidation of alcohols, phenols, silanes, hydroxylamines and olefins, reductive amination and N-formylation of aldehydes,  reduction of N-oxides and nitroaromatics as well as coupling reactions have been successfully carried out with the above M      CNT catalyst

We have been involved in understanding the mechanism of transport in crowded and active medium. For this, we build statistical mechanical models and solve it either analytically or on a computer, when complicacy of the problem does not allow exact analytical solutions. Availability of single molecule data also makes it possible to compare our results with experiments. A realistic example would be biological cell where presence of cell organelles makes it highly crowded.

Touch screens have become the ubiquitous interface for controlling contemporary electronic devices and incorporated into almost all the new technologies starting from smart phones, computers, flat panel televisions to personal gadgets and household appliances. One of the key components of touch screen is a transparent conducting electrode (TCE) which is optically transparent and electronically conductive. TCEs are also the backbone of optoelectronic devices eg. organic light emitting devices (OLEDs), photovoltaics (PVs), liquid crystal devices (LCDs) electro chromical devices (ECDs) etc.

Our research focuses on chemical reactivity and catalysis. When two molecules react to form product(s), there are different likely pathways that one can think of. Energies of various intermediates and transition states connecting such intermediates involved in the reaction has an enormous effect on the pathway a reaction would proceed through. We employ ab initio and density functional theory computational methods to identify the nature of intermediates and transition states involved in catalytic reactions.

Surface enhanced Raman scattering (SERS) spectroscopy, a powerful contemporary tool for studying low-concentration analytes via surface plasmon induced enhancement of local electric field, is of utility in biochemistry, material science, threat detection, and environmental studies. We have developed a simple, fast, scalable, and relatively low-cost optical method of fabricating and characterising large-area, reusable and broadband SERS substrates with long storage lifetime.

‘High-resolution and non-intrusive’ experimental measurements are indispensible for study of complex fluid flows that are frequently encountered in industrial and environmental situations. In today’s age and technology, it is possible to do so with the help of laser-based optical imaging. Our research focuses on using non-intrusive techniques to study instabilities, mixing, and turbulence in complex flows by capturing a spectrum of length-scales ranging from micrometer to centimeter. This ensures that both large-and small-scale flow features are resolved with considerable accuracy.

Semiconductors and superconductors are generally thought to be two very different types of materials. Indeed superconductors are usually metals, alloys and certain oxides with high electron densities. Semiconductors have much lower electron densities. However there are some semiconductors which become superconducting at low temperatures.

Often rapid and precise identification of composition of raw and finished products (on and off the site) are vital in several industries like mining, pharmaceutical, petrochemical, agriculture and food processing, etc. Our laboratory offers solutions for in situ analysis of materials in such challenging environments using reflectance, emission (optical) and X-ray fluorescence spectroscopic techniques.

Black hole is a region exhibiting such strong gravitational pull that nothing, including particles and light can escape from it. It is formed when the inward gravitational collapse of a massive star cannot be halted. It grows by capturing matter, energy, or by merging with other black holes.

Event horizon of black hole: Surface around black hole through which, matter and light can only pass inward. Therefore, if event occurs within this boundary, then the information from the event cannot reach an outside observer; due to which, it is impossible to determine if the event occurred.

Spin transfer torque magnetic random access memory (STT-MRAM) is a new memory technology based on electron spin. MRAM promises to bring non- volatile, low-power, low cost and high speed memory and has the potential to replace FLASH, DRAM and even hard-discs. The basic building cell of the STT-MRAM is the magnetic tunnel junction (MTJ) device.

Newton’s laws of motion are based on calculus. Einstein unified gravity with Special Theory of Relativity using Riemannian geometry. We see that mathematics provides a language by means of which physical laws can be formulated to explain nature. Einstein’s theory of General Relativity inspired developments in the area of Differential Geometry. This interplay of mathematics applied to physics and physics inspiring development in mathematics has intensified in the last five decades.

Systems of partial differential equations (PDEs) are usually solved by nu- merical methods. As opposed to this standard practice, in this project, we have been building tools that are capable of solving PDEs symbolically with the help of algebraic computations. The main motivation behind this endeav- our is the quest for exact solutions of PDEs.

A natural and important question representation theory is to understand how a representation of group restricts to a given subgroup. It was realized, almost three decades ago, that closely related questions in the context of p-adic and adelic groups have significant number theoretic aspects. In the case of p-adic group, one is interesting in finding out which representation of group admit non-trivial linear forms that are invariant under the fixed group of an involution.

Following results were proved: 1. For any non-trivial action of (C, +) on the polynomial ring C[X,Y,Z] the ring of invariants C[X,Y,Z]Ga is isomorphic to a polynomial ring in two variables.

2. (Jointly with Avinash Sathaye) Let (C,+) act regularly and non-trivially on a smooth affine 3-fold X with trivial integral homology, Then the quotient X/(C,+) is smooth. The proof of (1) is much more accessible than the original proof of M. Miyanishi.

Let A be a commutative Noetherian ring and P be a finitely generated projective A-module. We say that P has a unimodular element or P splits off a free summand of rank 1 if P is isomorphic to A⊕Q. If A = R[X, Y ±1] is Laurent polynomial ring and rank of P is > d = dimension of R, then it is well known that P has a unimodular element. In each case below P has a unimodular element.

The broad area of my research is commutative algebra. I also use some non-commutative algebra which is useful in my work. I work in the following four areas:

My primary interests centre around characterising L-functions by means of their analytic properties and in establishing the desired analytic properties for L-functions associated to automorphic forms. Recent work has involved the exterior square L-functions associated to GLn (over local and global fields) and primitivity results for the L-functions of cusp forms associated to GL3 in the extended Selberg class.