The Departments of Physics and Mathematics and Brandeis are incredibly excited to announce that this year’s Eisenbud Lectures in Mathematics and Physics will be given by the world-renowned theoretical physicist Prof. Cumrun Vafa, the Donner Professor of Science Harvard University. Prof. Vafa is one of the leading figures in the fields of string theory and quantum gravity, and he has been on the forefront of the exchange between string theory and geometry that has revolutionized both fields over the last thirty years. He is known for his immense intuition, creativity, and depth of thinking in physics and mathematics.

The Eisenbud Lectures are the result of a bequest by Leonard and Ruth-Jean Eisenbud, and this year marks the 100th anniversary of Leonard Eisenbud’s birth. Leonard Eisenbud was a mathematical physicist at SUNY-Stony Brook; upon his retirement he moved to the Boston area, as his son David was a member of the Mathematics faculty at Brandeis, and was given a desk here. The bequest is for an annual lecture series by physicists and mathematicians working on the boundary between the first two fields.

The Eisenbud lectures consist of three lectures. The first is a colloquium-style lecture meant for a broad scientific audience. The following two lectures are more technical lectures meant for experts in the field. The schedule is:

Lecture 1: “String Theory and the Magic of Extra Dimensions”, Tuesday, March 11 at 4PM in Abelson 131. Tea, coffee, and refreshments will be served at 3:30 outside of the lecture hall. A reception will follow the talk.

Lecture 2: “Recent Progress in Topological Strings I”, Wednesday, March 12 at 11 AM in Abelson 333.

Lecture 3: “Recent Progress in Topological Strings II”, Wednesday March 12 at 4 PM in Abelson 229.

We hope to see you all at what promises to be a very exciting series of talks!

— Albion Lawrence, Dept. of Physics. and Bong Lian, Dept. of Mathematics

## Eisenbud Lectures in Mathematics and Physics, March 11 – 12, 2014

## Brandeis in Aspen I: String theory and quantum information

The Aspen Center for Physics is a physics retreat in which groups of researchers in a given field gather for a few weeks during the summer to discuss the latest developments and create the next ones. This May, a record four Brandeis physicists — almost a quarter of the department — visited the Center at the same time, attending two different workshops. This posting is about a workshop attended by string theorists Matthew Headrick and Albion Lawrence (and co-organized by Headrick); another posting will describe a workshop attended by condensed-matter theorists Aparna Baskaran and Bulbul Chakraborty (a member of the Center’s advisory board). Entry into Aspen workshops is competitive, so this strong Brandeis representation is remarkable; as always, we punch above our weight.

Headrick and Lawrence attended the workshop Quantum information in quantum gravity and condensed matter physics. This was a highly interdisciplinary workshop, which brought together specialists in quantum gravity, including Headrick and Lawrence; experts in quantum information theory; and experts in “hard” condensed matter physics (who study material properties for which quantum phenomena play a central role).

Quantum information theorists study how the counterintuitive features of quantum mechanics — such as superpositions of states, entanglement between separated systems, and the collapse of the wave function brought on by measurement — could be exploited to produce remarkable (but so far mostly hypothetical) technologies like teleportation of quantum states, unbreakable encryption, and superfast computation. What does this have to do with gravity? When we try to formulate a consistent quantum-mechanical theory of gravity — which would subsume Einstein’s classical general theory of relativity — the concept of information crops up in numerous and often puzzling ways. For example, Stephen Hawking showed in the 1970s that, on account of quantum effects, black holes emit thermal radiation. Unlike the radiation emitted by conventional hot objects, which is only approximately thermal, pure thermal radiation of the kind that Hawking’s calculation predicted cannot carry information. Many physicists (including Hawking) therefore originally interpreted his result as implying that black holes fundamentally destroy information, challenging a sacred principle of physics. Today, based on advances in string theory, physicists (including Hawking) generally believe that in fact black holes do not destroy the information they contain. Rather, black holes hide information in very subtle ways, by scrambling, encryption, and perhaps quantum teleportation — in other words, the same kinds of tricks that the quantum information people have been inventing and studying independently at the same time.

Another connection between gravity and information is provided by the so-called “holographic principle”, which also arose in the study of black holes and which has been given a precise realization in the context of string theory. This principle posits that, due to a combination of gravitational and quantum effects, there is a fundamental limit to the amount of information (i.e. the number of bits) that can be stored in a region of space, and furthermore that limit is related to its surface area, not its volume. String theorists, beginning with the seminal work of Juan Maldacena, have uncovered a number of precise implementations of this principle, in which certain quantum theories without gravity are holograms of theories of quantum gravity. This should provide an avenue for uncovering the “tricks” gravity uses to hide information, a subject Lawrence is active in. An additional benefit of these implementations is that calculations in the nongravitational theories which seemed prohibitively difficult become fairly simple in the gravitational side; these include the computation of interesting quantities in quantum information theory, an area in which Headrick has done influential work.

All of these issues and many others were discussed in Aspen. This rather unique workshop was a very fruitful exchange of ideas, with physicists from three fields learning from each other and forging new interdisciplinary collaborations, in a setting where the scenery matched the grandeur of the subject.

## Physics students present research at 20th Annual Berko Symposium on May 16

On Monday, May 16, the Physics Department will hold the Twentieth Annual Student Research Symposium in Memory of Professor Stephan Berko in Abelson 131. The symposium will end with talks by the two Berko Prize winning students, undergraduate Netta Engelhardt and graduate student Tim Sanchez. The whole department then gathers for a lunch of cold cuts, cookies and conversation. “It’s a great way to close out the academic year,” said Professor of Astrophysics and Department Chair John Wardle. “We come together to celebrate our students’ research and hear what the different research groups are doing.”

The undergraduate speakers will describe their senior thesis honors research. This is the final step in gaining an honors degree in physics, and most of them will also be co-authors on a paper published in a mainline science journal. The graduate student speakers are in the middle of their PhD research, and will disucss their progress and their goals.

The prize winners are nominated and chosen by the faculty for making particularly noteworthy progress in their research. Graduate student winner Sanchez’ talk is titled “Reconstructing cilia beating from the ground up.” He works in Professor Zvonimir Dogic’s lab studying soft condensed matter. Undergraduate winner Engelhardt’s talk is titled “A New Approach to Solving the Hermitian Yang-Mills Equations”. She works with Professors Matt Headrick and Bong Lian (Math) on problems in theoretical physics and string theory. The schedule for Monday morning and abstracts of all the talks can be found on the Physics Department website.

Sanchez’ research very much represents the growing interdisciplinary nature of science at Brandeis. Here, a physicist’s approach is used to study a biological organism. Professor Zvonimir Dogic says of his work “He has made a whole series of important discoveries that are going to have a measurable impact on a number of diverse fields ranging from cell biology, biophysics, soft matter physics and non-equilibrium statistical mechanics. His discoveries have fundamentally transformed the direction of my laboratory and probably of many other laboratories as well.”

Engelhardt’s research is much more abstract and mathematical, and concerns fundamental problems in string theory, not usually an area tackled by undergraduates. Professor Headrick says “Netta really, really wants to be a theoretical physicist, preferably a string theorist. She has a passion for mathematics, physics, and the connections between them.” He adds that she is utterly fearless in tackling hard problems. Netta has been awarded an NSF Graduate Research Fellowship based on her undergraduate work here. Next year she will enter graduate school at UC Santa Barbara and will likely work with eminent string theorist Gary Horowitz, who has already supervised the PhD research of two other Brandeis physics alumni, Matthew Roberts ’05, and Benson Way ’08.

This Student Research Symposium is now in its 20th year. The “First Annual…..” (two words which are always unwise to put next to each other) was initiated in 1992 by Wardle to honor Professor Stephan Berko, who had died suddenly the previous year. Family, friends and colleagues contributed to a fund to support and celebrate student research in his memory. This provides the prize money which Netta and Tim will share.

Stephan Berko was a brilliant and volatile experimental physicist who was one of the founding members of the physics department. He was born in Romania in 1924 and was a survivor of both the Auschwitz and Dachau concentration camps. He came to the United States under a Hillel Foundation scholarship and obtained his PhD at the University of Virginia. He came to Brandeis in 1961 to establish a program in experimental physics and worked tirelessly to build up the department. Together with Professors Karl Canter (dec. 2006) and Alan Mills (now at UC Riverside) he established Brandeis as a world center for research into positrons (the anti-matter mirror image of ordinary electrons). In a series of brilliant experiments they achieved many “firsts,” culminating in election to the National Academy of Sciences for Steve, and, it has been rumored, in a Nobel Prize nomination for the three of them. Steve was as passionate about teaching as he was about research, and when he died, it seemed most appropriate to honor his memory by celebrating the research of our graduate and undergraduate students. During the coffee break on Monday, we will show a movie of Steve lecturing on “cold fusion,” a headline-grabbing but phony claim for producing cheap energy from 1989.

## NSF CAREER Award for Headrick

Assistant Professor of Physics Matthew Headrick has received a Faculty Early Career Development (CAREER) award from the National Science Foundation. Headrick’s project “* CAREER: Holography, Quantum Information, and Elliptic Relativit*y” will fund his research exploring issues in string theory and classical and quantum gravity. The two projects address 1) study of the thermal and statistical physics of holographic systems, and quantum gravity more generally, through the lens of quantum information theory, and 2) continuing the development of practical, general methods for numerically solving the elliptic Einstein equation to find static, stationary, and Euclidean metrics for higher-dimensional black holes and compactification spaces. NSF grants require broader impact activites. Headrick will participate in TheoryNet, an NSF-funded program in which high-energy physicists visit high-school science classrooms, and will also work with the Brandeis Science Posse program.

Associate Professor Zvonimir Dogic, also in the Physics department, was a 2010 recipient of an NSF CAREER award.

## Chiral Equivariant Cohomology

Prof. Bong Lian from Math writes:

In the 1950’s, French mathematicians Henri Cartan and Armand Borel defined a new topological invariant that was capable of distinguishing symmetries of certain geometric spaces known as G-manifolds. Cartan and Borel called their invariant the

Equivariant Cohomology of a G-manifold. It was new in that it was able to capture essential aspects of geometric operations, called Lie group actions (after Sophus Lie), on manifolds that ordinary cohomology theory was unable to detect. Hence it provides a new conceptual framework for studying symmetries of spaces on the one hand, and offers a powerful tool for computing ordinary cohomology of these spaces, on the other.In the late 80’s, physicists invented String Theory in their attempt to construct a grand unified field theory. They found that certain solutions to String Theory are essentially governed by an algebraic structure called a Chiral Algebra. This turns out to be a new structure that generalizes many fundamental algebraic constructs in mathematics, including commutative algebras and Lie algebras. A question was then raised as to whether there exists a natural theory that integrates both the Cartan-Borel invariant and Vertex Algebras. This hypothetical theory, which I learned about as a graduate student at Yale University, was dubbed the

stringy analogue of the Equivariant Cohomologytheory.In 2004, Andrew Linshaw, a Brandeis PhD student (now Research Fellow, U. Darmstadt), and I constructed such a theory, which we coined the

Chiral Equivariant Cohomology(CEC) of a G-manifold. In our latest paper, joint with another Brandeis PhD student, Bailin Song (now Assoc. Prof., Univ. of Science and Technology of China), we showed that not only does the CEC subsumes the Cartan-Borel theory, it goes well beyond that. For example, we have found an infinite family of Lie group actions on spheres that the Cartan-Borel theory is too weak to distinguish, but have non-isomorphic CEC. This proves that the CEC theory is strictly stronger as a topological invariant than the Cartan-Borel invariant. The paper appears in the December 2010 issue of the American Journal of Mathematics (Volume 132, Number 6).