Department of
Mathematics

Research

Dr. Moumanti Podder's current research can be divided broadly into the following topics:

1) At the interface of combinatorics, probability, physics and theoretical computer science: Dr. Moumanti Podder studies two-player combinatorial games, which are perfect information games, on random graphs. These games bear intimate ties with topics in physics (such as percolation, various models of statistical mechanics and their Gibbs states), recursive distributional equations, probabilistic automata (such as probabilistic cellular automata and probabilistic tree automata) that are important objects in theoretical computer science, with applications to a wide range of subjects (such as in parallel computing, dynamical systems, computational cell biology, fluid mechanics etc.). A primary focus of her research remains on questions of phase transition phenomena, such as understanding how the probability of draw in many combinatorial games that she studies change from zero to strictly positive as the underlying parameter(s) are varied, whether a given probabilistic automaton changes from being non-ergodic to being ergodic, whether a model of statistical mechanics goes from being weakly spatial mixing to having multiple Gibbs states etc. Recently, she has started focusing on Maker-Breaker percolation games played on infinite random graphs generated by rumour-spreading models. Dr. Podder also often studies combinatorial games played on deterministic graphs (such as variants of the popularly studied nim games). 

2) Stochastic processes that are inspired by models of evolutionary biology.

3) Statistics: There are two kinds of research Dr. Podder delves into in statistics, the first of which involves estimation / testing of hypotheses pertaining to parameter(s) underlying models inspired by statistical mechanics, and the second involves detection of structural breaks or changepoints in time series data (such as in finance, climate change studies, medical condition monitoring) that may happen due to the occurrence of certain significant events (such as war, an outbreak of an epidemic etc.).