Number theory is a fundamental form of pure mathematics that focuses on the characteristics of numbers--particularly integers and prime numbers. MIT's research in number theory focuses on arithmetic algebraic geometry, with a specialty in p-adic analytic methods in arithmetic geometry and p-adic Hodge theory. The MIT number theorists are also working on several projects dealing with the applications of number theory in cryptography, using computer modeling to better protect electronic data for a wide variety of applications.
MIT's computational biology research examines the ways that theoretical mathematics can be applied to solving problems in the field of biological studies. Mathematical modeling is used on research projects ranging from gene sequencing and pharmaceutical development to macro-evolutionary modeling. Computational biology research has become pivotal in combining genome sequencing with evolutionary analysis to understand the evolutionary development of various species. Several projects at MIT focus on the complex nature of protein folding, primarily under the leadership of Dr. Bonnie Berger.
Representation theory primarily focuses on understanding the natural symmetries that exist in science and nature, while developing abstract systems for exploring these symmetries. In addition to working on the representation theory of infinite-dimensional groups, MIT staff members are working on a variety of research projects to identify all finite-dimensional symmetries of a quantum mechanical system and to describe these symmetries within the framework of Lie group representations. Specific research interests at MIT now include infinite-dimensional Lie algebras, vertex algebras, symmetric spaces, Hecke algebras and quantum groups.
MIT is a leader in the field of theoretical computer science, in which mathematical theory is used to predict and solve problems in the field of computer science, ultimately improving computational efficiency while developing new mathematical ideas that can be applied in other disciplines. Past research projects have resulted in the RSA cryptosystem used today in electronic commerce protocols. The staff is currently working on projects dealing with approximation algorithms, distributed computing, complexity theory and algorithms in number theory.