Some people say they don’t need math. String theorists do – but some of it hasn’t been invented yet. Isadore Singer is working on the problem.
Dr. Isadore Singer, a professor at MIT and one of the nation’s leading mathematicians, visited UCSB from Jan. 14 to Feb. 14 to give a series of lectures on advanced topics in mathematics and their applications to theoretical physics. He also met with graduate students to discuss research and teaching experiences and presented a seminar with UCSB math professor Xianzhe Dai.
“Isadore Singer is a world-renowned mathematician. It was really wonderful to have him visiting UCSB and truly inspirational to work with him,” Dai said.
In 2000, Singer was awarded the prestigious Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. The Society bestowed its award on him “for his many years of contributions to index theory, geometry and mathematical physics, and for his work to further collaboration between mathematics and theoretical physics.”
Singer’s research is of particular interest to UCSB’s Institute for Theoretical Physics. Researchers at the ITP are working to find a unified field theory – a theory that unites all of the elemental forces in the universe. For physicists, the unified field theory has become something of a Holy Grail and it may require math that does not yet exist. Singer’s work could be the foundation of the new math required by the institute for its research into the superstring theory – the latest and most promising candidate for a unified field theory.
According to Doug Moore, chair of the Mathematics Dept., “Singer’s lectures here on noncommutative geometry were filled with amazing insights. We hope that Singer will return many times in the future and facilitate the interactions between mathematicians and physicists at UCSB.”
This visit was not Singer’s first to UCSB.
“Actually, I’ve been visiting UCSB on and off for almost 20 years, beginning with my term on the ITP advisory board in the early ’80s. ITP has frequent programs at the interface of geometry and physics. I attend when I can, and often lecture in the math dept. as well,” Singer said. He also served on the UCSB Math Dept. Visiting Committee two years ago.
Singer is best known for his index theorem, which he worked on in the 1960s. The index theorem is considered to be one of the greatest mathematical discoveries of the 20th century. It sheds light on many of the complex partial derivatives that come up when dealing with real life equilibrium situations.
He is also a recipient of the National Medal of Science, which was awarded to him in 1983. The honor was bestowed on him “for his inspired revival of differential geometry and its connections to analysis, for his contribution to the discovery and applications of the index theorem for differential operators, and for his leadership in using geometric and topological methods in connection with theoretical physics.”