My research this summer will be focused on Inverse Theory using Fredholm integrals; a mathematical concept with broad and exciting real-world applications. 

Inverse theory is a branch of mathematics that deals with determining the unknown causes from known effects. This is particularly useful in fields like medical diagnostics, where symptoms (such as tumors) are observed, but the underlying cause cannot be identified. Fredholm integrals are integral equations that are instrumental in addressing such inverse problems. They provide a framework to interpret complex data and uncover hidden relationships between cause and effect.

The research will primarily focus on applying Fredholm integrals to practical scenarios involving inverse problems. This includes exploring their use in science and technology where they can hopefully improve predictive models. By investigating these applications, the goal is to demonstrate how these theoretical concepts can be translated into effective solutions for real-life challenges.