Dr. Alexei Miasnikov, Director of the Department of Mathematical Sciences at Stevens Institute of Technology, recently received the prestigious and competitive Marsden Fund Award as a Principal Investigator on the project, “From automatic groups to automatic structures and beyond,” an international collaboration with PI Dr. Bakh Khoussainov from the University of Auckland in New Zealand, and Dr. Olga Kharlampovich from McGill University.
“The Marsden Award is well deserved recognition of Dr. Miasnikov’s dedication to international collaboration and the advancement of mathematics,” says Dr. Michael Bruno, Dean of the Charles V. Schaefer, Jr. School of Engineering and Science. “Alexei’s partnerships are crucial to fostering the exchange of knowledge and ideas that ignite discovery and we look forward to their forthcoming achievements.”
Dr. Miasnikov’s project aims to investigate mathematical structures described by finite state machines such as automata and beyond. These structures have nice algorithmic and algebraic properties. In group theory, automatic groups are equipped with automata representing multiplication by generators. The typical examples are hyperbolic and Braid groups, perhaps the most-studied objects in modern group theory. In general, automatic structures come equipped with automata representing their atomic relations. Examples here include fragments of the arithmetic and state spaces of computer programs, the cornerstones of modern computing. Automaticity implies nice algorithmic properties and makes the objects algorithmically tractable.
The award coincides with Professor Khoussainov’s visit to the Department of Mathematical Sciences and the Algebraic Cryptography Center at Stevens November 21–26, 2010.
Born and raised in Russia, Dr. Miasnikov first met Dr. Kharlampovich at St. Petersburg University and later they worked together on famous Tarski Problems from group theory at McGill University. The award is partly based on their solutions to those problems. Dr. Miasnikov met Dr. Khoussainov, the host recipient of the award, at Cornell Math Institute, where they discussed problems on automata and structures. Says Dr. Miasnikov, “Strangely enough and typically enough, different ideas from different areas came together and we got something interesting.”
The Marsden Fund Award
Administered by the Royal Society of New Zealand, the Marsden Fund Award is a highly competitive fund widely regarded as a hallmark of excellence. The fund invests in investigator-initiated research aimed at generating new knowledge and contributing to the development of people with advanced skills. The annual awards support research excellence in science, technology, engineering and math.