The monodromy groups of the n-th order hypergeometric differential equations are characterized as the subgroups of the general linear group GL(n), which are generated by the companion matrices of two monic co-prime polynomials f (x) and g(x) of degree n.

My research interest lies in the field of linear and nonlinear wave propagation. More specifically, my interest is in the study of partial differential equations of hyperbolic type. Most of the systems of PDEs (of practical interest) are not solvable exactly to get closed form solutions and therefore an approximation procedure needs to be adopted. Also, since the solution spaces of these systems are often vast (for instance the space of BV functions in the case of hyperbolic system of conservation laws), any qualitative analysis becomes more challenging.

"Plates are plane structural elements with a small thickness compared to the planar dimensions. De-pending on the length to thickness ratios, plates are classified into moderately thick, thin and very thin plates. One of my primary research interests has been to employ finite element methods to determine approximations to deformation and stresses in thin and very thin plates when they are subject to loads. A Kirchoff model is used for the thin elastic plates and this leads to fourth order elliptic equations with the transverse displacement as the unknown variable.

(1) Asymptotic analysis of PDEs: Most of the physical phenomena are modeled by Hyperbolic PDEs and in many of them feature multiple characteristics. Roughly it corresponds to studying crossings of eigenvalues of operators parametrized by a vectorial parameter. We are studying some of such situations.

(2) Conservation laws: We are studying the question of convergence generalized viscous approximations to entropy solutions of hyperbolic conservation laws.

Extension of Recent Contributions for Wider Applications in Computational Biology/Drug Discovery/Immunoinformatics/Automated Pulse-Diagnostics

(1) ParaDes: AI Software for Epitope-Paratope Designing (Copyright: GoI No. SW-698/2002) deploying knowledge-based correlation mapping on Hopfield Network.

(2) Efficient ab-initio Protein Structure Prediction using AI & Nonparametric Statistics.[Web-server: www.math.iitb.ac.in/~epropainor/ ]

My research area is Reliability Theory. Currently, I have been working on research problems that deal with Multi-state coherent systems. These systems are such that their components and systems themselves can be in one of (M + 1) possible states 0, 1, 2, • • • , M at any given time, where the extreme states 0 and M represent completely failed and completely working states respectively, and others are intermediate states that decrease in performance level as the system or a component makes a transition from state i to (i − 1), i = M, (M − 1), • • • , 1.

Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables Y and X equals the marginal measure of association. We have discussed the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure.

Our current question of philosophical enquiry is that how emotion, mostly empathy, plays a key role in moral cognition. The role of feelings in cognition is a subject of investigation in philosophy. The cognitive, aesthetical, ethical and psychological functions of feelings are discussed among others to underline our behavioural, cognitive, ethical and existential meaning. In the text books of philosophy moral cognition has often been considered a rational activity where one makes moral judgments based on a rational assessment.

Working in an institution of higher education, we worry about whether students are really ‘getting it’. Is our teaching effective in exciting students into learning about core concepts? Are they able to develop, apply and transfer the required concepts and skills to solve problems? In our research, we design and develop technology enhanced learning systems to promote students’ pan-domain thinking skills. We focus on engineering and science domains, using disciplinary content as a vehicle to develop the relevant thinking skills.

A general purpose circuit simulation packaged called SEQUEL has been developed at IIT Bombay. SEQUEL is particularly suitable for teaching coursesin electronics and power electronics. It has a graphical user interface (GUI) which allows the user to enter the circuit in a schematic form, set component values and simulation parameters, and view the simulation results. It also allows exporting of circuit schematics and the simulation plots so that they can be included in reports and presentations.

Did you know that many molecules have a ‘handedness’? That is, these molecules are distinguishable from their mirror image, like our left and right hand. But why should we care about it? It turns out that certain drugs and medicines may have their “mirror-twin” which could be toxic rather than medicinal! Through his theoretical contribution to quantum mechanics and ultrafast optics, Prof.

A novel theoretical framework for a magnetic field tunable radio frequency oscillator has been developed.The proposed device, when realised, would play a major role in  the nanoelectronics field, specifically as integrable clocks in futuristic logic circuits.

IIT Bombay and TIFR researchers demonstrate a method to turn heat into usable spin current