Eliashberg, Yakov M., 1946-
professor of math, Stanford
NAS, 2003
Yakov Eliashberg, professor of mathematics, is a leading geometer who has done fundamental work in symplectic geometry, complex analysis and singularity theory. He is a founder of the new and rapidly developing field of symplectic topology, employed to solve long-standing problems in classical mechanics and geometric optics, particularly about the existence and stability of periodic orbits of mechanical systems. In recent years, he and others have discovered deep connections between symplectic topology and other areas of mathematics and theoretical physics, such as differential topology and string theory.
Eliashberg obtained his doctoral degree at Leningrad University in 1972, the same year he joined Syktyvkar University in the northern Soviet Union as an associate professor. He became chair of the math department in 1975. He lost that position in 1979 when he became a "refusenik" that is, he was refused permission to emigrate to the United States to join family members. From 1981 to 1987, despite many difficulties while heading a computer software group, Eliashberg continued his mathematical research, and in 1986 he was invited to speak in Berkeley, Calif., at the International Congress of Mathematicians. As he was not allowed to leave the former Soviet Union, his lecture was read for him at that congress. In 1988, he emigrated with his family to the United States and spent a year at the Mathematical Sciences Research Institute in Berkeley before joining the Stanford faculty in 1989. He received a Guggenheim Fellowship in 1995 and was awarded the Oswald Veblen Prize in 2001 from the American Mathematical Society
Professor Yakov Eliashberg of Stanford University will deliver the 2001 Alfred Brauer Lectures in Mathematics. Professor Eliashberg will give three lectures, with the general title Holomorphic Curves in Symplectic Geometry: From Gromov's Width to Symplectic Field Theory. Titles of each lecture, room numbers, and schedules are found on the main page.
Alfred Brauer (l894-l985) had a profound impact on the Mathematics Department at UNC. Born in Germany, he held a position at the University of Berlin until the advent of the Nazis during the l930's; he fled the country in l939, accepting Hermann Weyl's invitation to the Institute for Advanced Study in Princeton. He came to North Carolina in l942, teaching here until his retirement in l966. During this time he founded the Mathematics and Physics Library, using his knowledge and expertise to establish a superb collection. In appreciation for this effort, the Library was named for him in l976. Alfred Brauer was honored by the University with the award of a Kenan Professorship in l959, the Tanner Award for excellence in undergraduate teaching in l965, and an honorary Doctor of Legal Letters degree in l972. He has also received honors from outside the University, including the Oak Ridge Science Award and the G.W.F. Hegel Medal from the University of Berlin. In l975 an Alfred T. Brauer Instructorship was created at Wake Forest University, where he taught after his retirement from the University of North Carolina. The Alfred Brauer Fund was established by the Department of Mathematics in l984 on the occasion of his ninetieth birthday.
Professor Yakov Eliashberg received his Ph.D. from Leningrad University in 1972 under V. A. Rokhlin. A winner of the Leningrad Math Society prize for young mathematicians in 1973, he spent his Soviet-era years at Syktyvkar University and Leningrad Institute of Accounting. Since 1989, he has been Professor of Mathematics at Stanford University; during that time he has also held visiting positions at Princeton, Orsay, Harvard, ETH, IHES, and RIMS. He has been twice invited to speak at the International Congress of Mathematicians, first in 1986 in Berkeley (he was not permitted to attend, but his lecture was delivered), and then speaking in 1998 in Berlin. Among the distinguished talks he has given are the Porter Lectures at Rice, the Marston Morse Lectures at the Institute for Advanced Study in Princeton, and the Rademacher Lectures at Penn. This past January, he won the prestigious Veblen Prize in Geometry, awarded by the American Mathematical Society.
Professor Eliashberg has been a major figure in symplectic geometry, which grew originally from the Hamiltonian approach to classical mechanics. This subject has exploded recently as an independent area of mathematics, providing the natural language for problems arising from physics and other parts of mathematics (e.g., Gromov-Witten invariants, quantum cohomology, etc.) One of the seminal results in the modern area of "symplectic topology" is Eliashberg's proof of symplectic rigidity--the group of symplectomorphisms of a symplectic manifold is closed (in the C^0-topology) in the group of all volume-preserving diffeomorphisms. In addition, he has made major advances in contact geometry, (the odd-dimensional analogue of symplectic geometry), specifically the classification of contact structures on 3-manifolds. He is currently working with H. Hofer and A. Givental on "Symplectic Field Theory," a new subject on which he will speak at the Brauer Lectures.
The Alfred Brauer Lectures were established in l985. Previous Brauer Lecturers have been Daniel Gorenstein, Richard Stanley, Barry Mazur, Armand Borel, Benedict Gross, Persi Diaconis, Grigorii Margulis, Yuri I. Manin, Joe Harris, John Conway, Clifford Taubes, Friedrich Hirzebruch, Ian Macdonald, Andrew Wiles, Nigel Hitchin, and Bertram Kostant.
