The main idea of the mathematics unit is to develop research that draws inspiration from and connects to different mathematical disciplines and also to encourage collaborations with scientists in areas such as biology, physics, social sciences, earth sciences, computer science, and many others, thus making it an integral part of the scientific ecosystem within ICTS.

The group pursues a wide range of **mathematical, statistical and computational** research themes. In particular, current research includes dynamical systems, probability, nonlinear partial differential equations, geometry and mathematical physics.

Main research areas:

**Analysis of partial differential equations and applications:**Analytical and numerical methods for PDEs. Boundary-value problems, stability of solutions to nonlinear PDEs, reduced and asymptotic models. Applications in surface gravity waves, geophysical fluid dynamics, monsoon modelling, inverse and observer problems for PDEs. Experimental fluid dynamics**Faculty involved:**Vishal Vasan

**Data assimilation:**Bayesian data assimilation and inverse problems, consistency and convergence rates of posterior measures, Markov Chain Monte Carlo (MCMC) sampling methods, particle filtering, variational methods and observers for PDE models**Faculty involved:**Amit Apte

**Differential geometry:**Constant mean curvature surfaces, Minimal surfaces, Solitons; Maximal surfaces in Minkowski space**Faculty involved:**Rukmini Dey

**Dynamical systems:**Hamiltonian systems, nontwist maps, bifurcations, transition to chaos and renormalization; Nonlinearity and non-Gaussianity in data assimilation and nonlinear filtering; Monsoon modelling**Faculty involved:**Amit Apte

**Mathematical physics:**Quantization (especially geometric quantization) and coherent states; Geometric quantization of various moduli spaces of solutions of equations coming from physics; Study of path spaces and loop spaces; Integrable systems, e.g. the quantum Toda system; Study of moduli spaces of vortices, Higgs bundles, Generalized Seiberg-Witten equations, Fueter equations**Faculty involved:**Rukmini Dey

**Monsoon dynamics:**Conceptual models of monsoon dynamics, including ODE, PDE, and stochastic models; Data based studies of monsoon dynamics; Dynamics of cloud formation**Faculty involved:**Amit Apte, Rama Govindarajan, Samriddhi Sankar Ray, Vishal Vasan

**Activities (past and near future):**

- The Legacy of Emmy Noether: Aug 29-30, 2016
- Summer Research Program on Dynamics of Complex Systems: May 23 - Jul 23, 2016
- Airbus Day at ICTS-TIFR: Jan 11, 2015
- Nonlinear filtering and data assimilation: Jan 08-11, 2014
- Mathematical Perspectives on clouds, climate, and tropical meteorology: Jan 22-26, 2013
- Data Assimilation Research Program (DARP): July 04-23, 2011
- Scientific discovery through intensive data exploration: Feb 02-11, 2011

**Opportunities:**

The group envisions a significant and sustained growth in many areas and at all levels. Specific research areas that we would like to grow include, but are not limited to, probability and stochastic analysis, geometry and topology, mathematical physics, dynamical systems and differential equations, scientific computing, and discrete mathematics. ICTS would also like to develop a theoretical computer science group as part of this unit.

Please click here for more information about the faculty positions.

For information about ICTS graduate program in mathematics (as part of the TIFR deemed university), please click here