Mini courses on three fascinating topics in the area of probability and stochastic processes will be offered in this workshop, namely Martingales, Percolation and Heavy-tailed Distributions. Martingales, one of the most fundamental concepts in probability, finds myriad applications in financial mathematics such as in arbitrage-free pricing, in martingale optimal transport, in probabilistic methods implemented for solving various problems in graph theory, in the swiftly expanding subfield of elephant random walks in probability. Percolation, an area of immense interest to researchers in both mathematics and statistical physics, finds wide applications elsewhere as well, such as in ecology (modeling the spread of infections, understanding the impact of environment fragmentation on animal habitats, modeling the spread of forest fires etc.), in biochemistry and physical virology (predicting fragmentation thresholds for biological virus shells), to name just a few. Heavy-tailed probability distributions are indispensable in the area of risk analysis in financial mathematics (such as for understanding ruin probabilities in insurance risk models). Apart from a thorough introduction to each of these areas via lectures and tutorial sessions, certain topics deemed as prerequisites, such as Markov chains, simple random walks, branching processes and the basics of measure theory (including the notion of conditional expectation), will also be discussed as needed.

 

Venue: IISER Pune campus

Dates: July 10-18, 2025

More details related to registration, lectures can be found in the given link below.

https://www.atmschools.org/school/2025/NCMW/dsc