Faculty

Computational finance, Monte Carlo methods for derivate pricing, Financial risk management, Real Options.

Immuno-engineering, Biomaterials, Drug Delivery

Tau pathology, Neuroinflammation, Neurodegenerative diseases

My research interest is in studying constrained and related stochastic dynamical systems with computational mathematical tools. Current work includes applications to problems of data assimilation and rough path behaviour.

Space dynamical systems (such as satellite orbit estimation) and biochemical reactions are examples of fields of application.

Artificial intelligence, Neuromorphic circuits, In-memory computing, Molecular electronics, Nanoelectronics, Nonlinear dynamics and chaos

How does our brain enable us to pay attention selectively to some things, and to ignore others? What happens in the brain when we make important decisions? Our research focuses on understanding the neural basis of cognitive phenomena such as selective attention and decision making. To address these questions we follow a quantitative approach that combines neuroscience experiments, model-based analyses (e.g., linear/nonlinear dynamical systems, control theory, machine learning) as well as large-scale computer simulations. We directly measure or perturb brain activity with a variety of techniques, including functional neuroimaging (fMRI), diffusion imaging (dMRI), high-density electro-encephalography (EEG), and transcranial electrical and magnetic stimulation (tES/tMS). The overarching goal is to develop a unified framework that describes how cognitive phenomena emerge from neural computations by a systematic analysis of brain and behavior.

Theoretical and applied probability, statistics, branching particle systems, random geometric graphs, mathematical finance, credit-risk modelling, time-series analysis, Monte Carlo simulatio.

Understanding immune cell social behaviour and immunosurveillance in diseases and therapies.

Automatic Modulation Classification for OFDM and MIMO-OFDM Systems

Mathematical signal processing, statistical inference and learning, applied to communication systems, network sciences, and computational imaging

I received a B.Tech in Electrical Engineering from IIT Kanpur and a PhD in Biomedical Engineering from the Johns Hopkins School of Medicine. My postdoctoral training was in the department of Neurobiology at Harvard Medical School with Dr. John Maunsell. I joined the Center for Neuroscience, IISc, in June 2011. From 2012 onwards, I have also been an associate faculty in the Electrical Engineering Department at IISc.
Our lab studies the neural basis of selective attention, with a focus on a brain rhythm called “gamma” (30-80 Hz), which is modulated by attentional load and is thought to be linked to high-level cognitive processes. Attentional mechanisms have been studied at several different recording scales – from single neurons in monkeys to diffuse population measures such as electro-encephalography (EEG) in humans. However, the relationship between signals recorded from such different scales is poorly understood. The long-term goal of this research is to elucidate the mechanisms of attention by linking the neural recordings obtained from these vastly different scales. This involves recordings from both humans and non-human primates using a variety of techniques while they are engaged in certain cognitive tasks, development of advanced signal processing techniques to build the “links” across recording scales, and mathematical modelling of brain signals, including gamma oscillations, using dynamical system approach as well as detailed biophysical models. Establishment of this cross-species, cross-scale link between brain signals has far reaching applications, such as in Brain-computer Interfacing (BCI) and clinical diagnosis of brain disorders.

Research Interests: Mechanisms of attention and gamma oscillations; Modeling and Signal Processing, Brain-Computer Interfacing.

Intelligent flight control system, Autonomous Systems, Applied Game Theory, Computer Vision and Robotics, Machine learning and AI

Calculus of Variations, Partial Differential Equations and geometric analysis.

Variational models and PDE models are widely employed in different branches of physics and engineering applications, from models in material sciences ( fracture models, micro-magnetics ) to image reconstruction, impedance tomography, invisibility cloaking etc. A theoretical understanding of the relevant functional from the calculus of variation and PDE perspective both facilitates and in turn is facilitated by the qualitative understanding of the physical phenomena involved.

I am also interested in some toy models in quantum field theory that leads to interesting geometric variational problems, like nonlinear sigma-models etc.

Intersection of Genetics and Data Science

Experimental mechanics, Image based def.rmation measurements, Large strain plasticity, Granular mechanics.

Numerical Analysis for Partial Differential Equations.

Compilation for multicores and accelerators, Automatic parallelization, Programming language and runtime system design

Cell division and fate in plants and yeasts.

Organ Morphogenesis, Developmental Biology, Plant Biology

Computer Vision, Deep-learning, Video Analytics, Multimedia