Number Theory:
While classical number theory includes some questions which are centuries old, the tools developed in this field includes some of the most modern and sophisticated ideas in modern mathematics. The research undertaken by Chinta, Jorgenson, and their numerous collaborators, addresses problems in number theory and related fields, which includes Riemannian geometry, Lie theory, spectral theory, and functional analysis.
Group Theory:
Group theory aims to capture and understand the essence of symmetries, which occur frequently in nature and physical settings, as well as in a broad range of abstract settings. Brinkmann, Cleary, and Shpilrain work on different aspects of group theory, notably on algorithmic and computational aspects, including computational complexity of various algorithms, with applications to cryptography. The latter aspects are part of collaborative work with CAISS, which is directed by Baumslag of the Computer Science Department, and involves some other members of the latter department, including two new hires in cryptography, Skeith and Fazio
Dynamical Systems Theory:
is the mathematical study of change, modeled by iterating a mapping or represented by differential equations. Arising from Newtonian physics, the different versions of dynamical systems theory have been applied to all the sciences. The popularly garbled notion of chaos is a topic studied by dynamical systems folks. Akin works in the topological aspects of the theory and its applications to biology. |
