Multi-armed bandit (MAB) is a popular framework for sequential decision-making in an uncertain environment.

Algebraic Complexity Theory is a field in which one studies complexity theoretic questions surrounding algebraic objects. In this talk we will be broadly discussing two such problems.

In this thesis defense, we will discuss the following results.

Over the past few decades, probabilistic models have become an important tool for under-standing risks and decision making in practical financial systems.

The query model is a simple model of computation that has led to many deep results. One such class of results relates computational complexity measures such as query complexity/communication complexity to algebraic measures such as degree/rank.