The University's Mathematics and Physics departments celebrated Leonard Eisenbud's 100th birthday on Tuesday and Wednesday of last week with three lectures on the use of geometry in string theory. The Eisenbud lectures, which happen once a year, are a result of a donation from Leonard and Ruth-Jean Eisenbud, whose son, David Eisenbud, was a Mathematics professor at Brandeis. The donation allows the Mathematics and Physics departments to have a leading mathematician or physicist give a lecture on topics pertaining to the boundary between the two fields.

This year's recipient, Cumrun Vafa, the Donner Professor of Science at Harvard University, has his own connections to Brandeis. His dissertation adviser was Brandeis alumnus Edward Witten '71.

Vafa is a leading string theorist who studies the geometry behind the tiny, vibrating "strings" that supposedly make up the universe. The strings themselves are simply an interpretation of the abstract mathematics that surround string theory. The math behaves similarly to the vibrating strings on a violin and so physicists named the theory after them. Vafa studies the physical consequences of these strings to describe unexplained phenomena such as the entropy behind black holes, duality and quantum fields.

The first of these lectures was an introduction to Vafa's research called "String Theory and the Magic of Extra Dimensions." String theory is a hypothesis that tries to combine the incredibly small scale of quantum mechanics with the immense mass of Albert Einstein's general relativity. The theory asserts that the substances that make up fundamental particles, such as quarks, or particles that make up protons and neutrons, are made up of tiny vibrating strings. One of the main hindrances of string theory is that these so called strings are approximately a nonillionth of a meter with energy of around a 10 quadrillion tetra-electron volts. Today's scientific equipment cannot measure anywhere near that scale; the Large Hadron Collider in Switzerland measures particles with energy approximately 10 tetra-electron volts. That, however, has not deterred theoretical physicists exploring the consequences of string theory.

Vafa discussed how string theory was a "re-emergence of geometry" in physics after the "fuzziness" of quantum mechanics. He described how the interactions between strings are not described by a complex set of equations, but a simple geometric picture. He added that where geometry seems to fail in string theory is its requirement of 10 dimensions. The math behind string theory fails unless there are 10 dimensions whereas classical physics only uses four dimensions: length, width, height and time.

If the universe actually consists of 10 dimensions, string theorists wonder why only four are used in classical physics. Up until recently, physicists have ignored this question claiming that the extra six dimensions are "curled up" and unobservable. Vafa advocates that scientists use them to explain other puzzles in physics such as black hole entropy. "When [physicists] get something extra, we don't throw it out," explained Vafa as to why his research involves a particular focus on the existence of these extra dimensions.

Vafa also explained M-theory during his lecture, a recent advance in string theory that Witten suggested in 1995. M-theory, or membrane theory, is the idea that rather than the 10 dimensions previously described, there is another dimension hidden within.

It is similar to looking at the cross section of a plane and only seeing a line, but then by shifting slightly one can see the whole plane. In M-theory, the lines scientists thought of as strings become flat planes known as membranes, or "branes." The membranes follow the same simple geometrical models that the strings do but have fixed some of the problems of string theory.

The two lectures following the one on Tuesday went into more detail of Vafa's work on M-theory and, more specifically, the geometry of interacting membranes.

When asked why scientists do not stop at the 10 dimensional strings but continue to study M-theory as well, Vafa replied that this is how physics progresses. While M-theory currently answers all the puzzles given to it explained Vafa, there may be other puzzles not yet thought of that it cannot answer. As Vafa said, "that's why [physics is] good, otherwise it would be very boring."