NSA Grant Funds New Methods in Metabelian Theory

Revising classical mathematics from the viewpoint of modern computer science

12/17/2013

A new, two-year grant from the National Security Agency has been awarded to Alexei Miasnikov, Distinguished Professor and Department Director, and Alexander Ushakov, Assistant Professor in the Department of Mathematical Sciences at Stevens Institute of Technology.

Various mathematical methods are centered on the theory of metabelian groups, one of the most meaningful parts of group theory. This theory is rich with remarkable theorems, precise examples and counter-examples whose interactions raise questions that invite research. 

Members of the Algebraic Cryptography Center at Stevens, the two researchers will develop techniques and methods for frameworks that manage massive computations for solving problems that are formulated in the paradigm of the theory of metabelian groups.

Revising the classical algorithmic theory of metabelian groups, Miasnikov and Ushakov will consider new applications that require a revision of old solutions—and produce new solutions. They will study some completely new open problems in an interesting mixture of classical mathematics and very recent algorithmic approaches coming from computer science.  In other words, they will revise classical mathematics from the viewpoint of modern computer science.

The proposal addresses the broad spectrum of natural algorithmic problems with unknown complexity. Possible approaches include, in particular, the methods of commutative algebra, algebraic geometry over groups and rings, number theory, linear groups, and free differential calculus.

“Previous solutions are not satisfactory anymore says Dr. Miasnikov. “Time has changed and so have the applications.”