About Us

About Us

Solomon Lefschetz, 1884 - 1972Solomon Lefschetz, 1884 - 1972

The Lefschetz Center for Dynamical Systems is one of the leading research groups in dynamical systems and stochastic  systems theory. The Center was established when a group of mathematicians and control theorists came to Brown from the Research Institute for Advanced Studies (RIAS) in Baltimore, Maryland, in 1964.  RIAS was founded in 1955 by George Bunker of the  Glenn L. Martin Company,  a  division of Lockheed Martin.  Bunker was convinced that advances in aerospace would depend heavily upon well supported research in mathematics.   The Soviet launch of Sputnik in 1958  led to  considerable  national appreciation of the  importance of  dynamical systems and  control.  It also convinced Solomon Lefschetz , a 73 year old acclaimed  mathematician, to come out of retirement, and lead the mathematics division of RIAS.  Although it was technically part of the Martin Corp, it was funded by government mathematics  funding agencies, and virtually completely independent.

As a young mathematicianAs a young mathematician

Despite his youthful passion for mathematics, Lefschetz did not go directly into it.  He had studied mechanical engineering at the Ecole Centrale des Arts et Manufactures in Paris, but since he was not a  French citizen, a professorship was unattainable,  so  following his additional interest   in  Electrical Engineering he came to the Westinghouse Corporation in the US  in  1905.    Unfortunately, while at work, a laboratory explosion  led to the loss of both of his hands. Following convalescence, his interest in mathematics was   rekindled, and he obtained the Ph.D. (algebraic geometry)  at Clark  University  in 1922.   He then taught at Nebraska and Kansas, and moved to Princeton in 1924, where he was chairman  for many years.  Lefschetz is best known for his ground breaking work on algebraic geometry   and nonlinear differential equations, in which his name is associated with many fundamental results. 

He  was  joined at RIAS  by Joseph LaSalle, Jack Hale, and other prominent  mathematicians. Stochastic Control  was the  other component of RIAS,  led by Rudy Kalman who was joined by Richard Bucy,  John Florentin, Harold Kushner, Murray Wonham, among others.    Owing to the extensive contacts of Lefschetz, LaSalle, Hale, and Kalman in the Soviet block,  RIAS  was  a useful  point of contact between mathematicians  during those years of the cold war. Its flavor was that of a very good free-wheeling academic department, with numerous visitors and seminars. At that time, RIAS probably had the largest concentration of researchers in its areas in the world. 

Joe LaSalle (standing center) collaborates with fellow mathematiciansJoe LaSalle (standing center) collaborates with fellow mathematicians

In 1964, prompted by a shift in the goals of the Martin Company,  the  group broke up, with the largest number coming  to the  Division of applied Mathematics at  Brown  University,  and founding the Center  for Dynamical Systems, with LaSalle as the director.  (He was also the Division Chairman from  1968—1973.)  Many other eminent mathematicians such as Constantine and Stella Dafermos, Wendell Fleming, Walter Strauss, Tom Banks, Ettore Infante, John Mallet-Paret, joined them.  The center continued to grow, with a very large  number of visitors, post docs, and graduate students,  and very good new permanent appointments.  On Lefschetz’s death in 1972,  the center was renamed “Lefschetz Center for Dynamical Systems.” 

Jack Hale, 1928-2009Jack Hale, 1928-2009

Among its well-known members, Jack Hale played a major role.  An excellent researcher and teacher, he was an enthusiastic supporter of young talent, and his spirit played a central part in the excitement.    The stochastic systems  group with  intellectual leaders Wendell Fleming and Harold Kushner continued the RIAS  traditions and, together with new appointments,  is well known as one of the most paramount research groups anywhere.

 (Essay by Professor Emeritus Harold Kushner, April 2015)