Two Brandeis Professors Receive 2017 Simons Fellowships, part II

20 06 2017
Spectral Flow

Spectral Flow (full caption below)

Two Brandeis professors have been awarded highly prestigious and competitive Simons Fellowships for 2017. Daniel Ruberman received a 2017 Simons Fellowship in Mathematics. Matthew Headrick was awarded a 2017 Simons Fellowship in Theoretical Physics. This is the second of two articles where each recipient describes their award-winning research.

Daniel Ruberman’s research asks “What is the large-scale structure of our world?” Einstein’s unification of physical space and time tells us that the universe is fundamentally 4-dimensional. Paradoxically, the large-scale structure, or topology, of 4-dimensional spaces, is much less understood than the topology in other dimensions. Surfaces (2-dimensional spaces) are completely classified, and the study of 3-dimensional spaces is largely dominated by geometry. In contrast, problems about spaces of dimension greater than 4 are translated, using the technique called surgery theory, into the abstract questions of algebra.

Ruberman will work on several projects studying the large-scale topology of 4-dimensional spaces. His work combines geometric techniques with the study of partial differential equations arising in physics. One major project, with Nikolai Saveliev (Miami) is to test a prediction of the high-dimensional surgery theory, that there should be `exotic’ manifolds that resemble a product of a circle and a 3-dimensional sphere. The proposed method, which would show that this prediction is incorrect, is to compare numerical invariants derived from the solutions to the Yang-Mills and Seiberg-Witten equations, by embedding both in a more complicated master equation. The study of the Seiberg-Witten invariants is complicated by their instability with respect to varying geometric parameters in the theory. A key step in their analysis is the introduction of the notion of end-periodic spectral flow, which compensates for that instability, as illustrated below.

Other projects for the year will apply techniques from 4-dimensional topology to classical problems of combinatorics and geometry about configurations of lines in projective space. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects (“lines”) and other objects (“points”) can be realized by actual points and lines in a projective plane. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. Ruberman’s work with Laura Starkston (Stanford) gives new topological restrictions on the realization of configurations of spheres in the complex projective plane.

Caption: Solutions to the Seiberg-Witten equations of quantum field theory provide topological information about 4-dimensional spaces. However, the set of solutions, or moduli space, can undergo a phase transition as a parameter T is varied, making those solutions hard to count. This figure illustrates a key calculation: the phase transition is equal to the end-periodic spectral flow, a new concept introduced in work of Mrowka-Ruberman-Saveliev. In the figure, the spectral set, illustrated by the red curves, evolves with the parameter T. Every time the spectral set crosses the cylinder, the moduli space changes, gaining or losing points according to the direction of the crossing.



Two Brandeis Professors Receive 2017 Simons Fellowships, part II

20 06 2017
Spectral Flow

Spectral Flow (full caption below)

Two Brandeis professors have been awarded highly prestigious and competitive Simons Fellowships for 2017. Daniel Ruberman received a 2017 Simons Fellowship in Mathematics. Matthew Headrick was awarded a 2017 Simons Fellowship in Theoretical Physics. This is the second of two articles where each recipient describes their award-winning research.

Daniel Ruberman’s research asks “What is the large-scale structure of our world?” Einstein’s unification of physical space and time tells us that the universe is fundamentally 4-dimensional. Paradoxically, the large-scale structure, or topology, of 4-dimensional spaces, is much less understood than the topology in other dimensions. Surfaces (2-dimensional spaces) are completely classified, and the study of 3-dimensional spaces is largely dominated by geometry. In contrast, problems about spaces of dimension greater than 4 are translated, using the technique called surgery theory, into the abstract questions of algebra.

Ruberman will work on several projects studying the large-scale topology of 4-dimensional spaces. His work combines geometric techniques with the study of partial differential equations arising in physics. One major project, with Nikolai Saveliev (Miami) is to test a prediction of the high-dimensional surgery theory, that there should be `exotic’ manifolds that resemble a product of a circle and a 3-dimensional sphere. The proposed method, which would show that this prediction is incorrect, is to compare numerical invariants derived from the solutions to the Yang-Mills and Seiberg-Witten equations, by embedding both in a more complicated master equation. The study of the Seiberg-Witten invariants is complicated by their instability with respect to varying geometric parameters in the theory. A key step in their analysis is the introduction of the notion of end-periodic spectral flow, which compensates for that instability, as illustrated below.

Other projects for the year will apply techniques from 4-dimensional topology to classical problems of combinatorics and geometry about configurations of lines in projective space. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects (“lines”) and other objects (“points”) can be realized by actual points and lines in a projective plane. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. Ruberman’s work with Laura Starkston (Stanford) gives new topological restrictions on the realization of configurations of spheres in the complex projective plane.

Caption: Solutions to the Seiberg-Witten equations of quantum field theory provide topological information about 4-dimensional spaces. However, the set of solutions, or moduli space, can undergo a phase transition as a parameter T is varied, making those solutions hard to count. This figure illustrates a key calculation: the phase transition is equal to the end-periodic spectral flow, a new concept introduced in work of Mrowka-Ruberman-Saveliev. In the figure, the spectral set, illustrated by the red curves, evolves with the parameter T. Every time the spectral set crosses the cylinder, the moduli space changes, gaining or losing points according to the direction of the crossing.



Physics department mourns passing of Professor Emeritus Sam Schweber

22 05 2017

Sam SchweberSam Schweber, Professor Emeritus of Physics, died May 14th at the age of 89. A theoretical physicist and historian of science, Sam was among that first generation of Brandeis faculty whose genius turned a fledgling institution into a university of the first rank. He published his first book in 1956, when not yet thirty, and his last in 2012, in his mid-eighties. His was an extraordinary life and career.

Sam was born in Strasbourg and came to this country at the age of 14. Like many immigrants and children of immigrants, he attended college at City College of New York, and he then went on to earn an M.S. from the University of Pennsylvania and a Ph.D. from Princeton. A postdoctoral fellowship at Cornell gave him the special opportunity to work under Hans Bethe (whose biography he wrote, many years later). Sam came to Brandeis in 1955 as associate professor of physics and quickly became involved in building the young department. In 1957, the Physics Department started a graduate program, and the following year it established, at Sam’s initiative, a summer institute in theoretical physics, bringing to campus leading physicists as well as selected graduate students and postdocs, for weeks of seminars and colloquia. The institute ran annually for fifteen years, until the federal funding ceased.

The young Sam Schweber had clearly impressed Hans Bethe. In 1955 he co-authored with Bethe (and a third physicist) the two-volume Mesons and Fields, and in 1960, the same three authors published Quantum Theory of Fields. A year after that, in his foreword to Sam’s new book, An Introduction to Relativistic Quantum Field Theory, Bethe observed, “It is always astonishing to see one’s children grow up, and to find that they can do things which their parents no longer fully understand.” This book remains in print five decades after its initial publication.

Sam continued to conduct research and publish in the field of quantum field theory, while also playing an integral part in the growth of Brandeis University. His scholarly interests then started to shift. Volunteering to teach a course on how probability entered the sciences, he became fascinated with the history of science and chose to spend his next sabbatical in the History of Science Department at Harvard. In the third decade of his career, Sam became a historian of science. He joined our interdepartmental program in History of Ideas, and in 1982 was appointed to the Koret Chair in the History of Ideas.

Sam became equally eminent in his new field, publishing a series of significant books and helping to found and then lead the Dibner Institute for the History of Science and Technology at MIT. Sam brought to his writing not only rigorous historical research and a deep understanding of science, but also a strong interest in the human dimension and social consequences of scientific research and discovery. Among his many books were Einstein and Oppenheimer: The Meaning of Genius, In the Shadow of the Bomb: Oppenheimer, Bethe and the Moral Responsibility of the Scientist, and Nuclear Forces: The Making of the Physicist Hans Bethe. Describing another of Sam’s books, Freeman Dyson wrote that “he has produced a lively and readable narrative history, with a lightness of touch than can come only to one who is absolute master of his subject.”

Sam continued to be an active scholar and author after his retirement from Brandeis in 2003. In 2011, he won the Abraham Pais Prize for History of Physics. The citation spoke of “his sophisticated, technically masterful historical studies” and his “broadly insightful biographical writing on several of the most influential physicists of the 20th century.” Sam was a Fellow of the American Physical Society, the American Association for the Advancement of Science, and the American Academy of Arts and Sciences. A further measure of his stature and influence came in the past few days, from the Max-Planck-Institut fur Wissenschaftsgeschichte: “It is with deep regret that we announce the passing on May 14, 2017 of the distinguished historian of science, Professor Sam S. Schweber. Sam was a dear colleague and mentor of many at the Institute and will be sorely missed by all those who had the great fortune and pleasure of knowing him.”

That sentiment will surely be echoed by the many former Brandeis colleagues and students who greatly admired Sam and learned from him.



Pump without pumps

14 04 2017

By Kun-Ta Wu, Ph.D.

Pumping water through a pipe solves the need to provide water in every house. By turning on faucets, we retrieve water at home without needing to carry it from a reservoir with buckets. However, driving water through a pipe requires external pressure; such pressure increases linearly with pipe length. Longer pipes need to be more rigid for sustaining proportionally-increased pressure, preventing pipes from exploding. Hence, transporting fluids through pipes has been a challenging problem for physics as well as engineering communities.

To overcome such a problem, Postdoctoral Associate Kun-Ta Wu and colleagues from the Dogic and Fraden labs, and Brandeis MRSEC doped water with 0.1% v/v active matter. The active matter mainly consisted of kinesin-driven microtubules. These microtubules were extracted from cow brain tissues. In cells, microtubules play an important role in cell activity, such as cell division and nutrient transport. The activity originates from kinesin molecular motors walking along microtubules. In cargo transport, microtubules are like rail tracks; kinesin motors are like trains. When these tracks and trains are doped in water, their motion drives surrounding fluids, generating vortices. The vortices only circulate locally; there is no global net flow.

Wu-Pump without Pumps

Figure: Increasing the height of the annulus induces a transition from locally turbulent to globally coherent flows of a confined active isotropic fluid. The left and right half-plane of each annulus illustrate the instantaneous and time-averaged flow and vorticity map of the self-organized flows. The transition to coherent flows is an intrinsically 3D phenomenon that is controlled by the aspect ratio of the channel cross section and vanishes for channels that are either too shallow or too thin. Adapted from Wu et al. Science 355, eaal1979 (2017).

To create a net flow like rivers, Wu et al. discovered that confining such an active fluid in a toroid triggers a transition from turbulent to coherent flowing states (Figure, above left). Unlike rivers, which gain kinetic energy from their gravitational potential, such a fluid is driven by kinesin motors consuming internal chemical energy (adenosine triphosphate), self-pumping without external pressure. However, not all toroidal geometries sustain coherent flows. Wu et al. pointed out that sustaining coherent flows requires the toroidal cross section to have a shape similar to a square or circle. In a thin and wide toroid, the coherent flow is suppressed (Figure, above right). Wu et al. demonstrated that with a proper (circular) cross section, the coherent flow can persist for meters, proving the feasibility of transporting fluids at a macroscopic scale without external pressure.

In conclusion, Wu et al. invented self-pumping fluids. The fluids flow in a pipe without external pressure. However, the knowledge of self-pumping fluids remains limited. For example, why does the transition from turbulent to coherent flow depend on the shape of the pipe cross section, rather than its absolute size? How does the coherent flow respond to external pressure? Answering these questions are the key to understanding underlying principles of self-organization of active fluids; however, Wu et al.’s invention already opens the door to pumping fluids without a pump.

Kun-Ta Wu, Jean Bernard Hishamunda, Daniel T.N. Chen, Stephen J. DeCamp, Ya-Wen Chang, Alberto Fernández-Nieves, Seth Fraden, and Zvonimir Dogic. Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355, eaal1979 (2017). doi:10.1126/science.aal1979.



Physics Graduate Student Receives Kavli Fellowship

12 04 2017

Cesar Agon at Kavli Institute Cesar Agon, a graduate student in the High-Energy and Gravitational Theory group, was awarded a prestigious Graduate Fellowship at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara. KITP is one of the world’s leading centers for research in all areas of theoretical physics. In addition to having its own faculty and postdocs, it hosts visiting faculty from around the world and holds conferences and semester-long programs on topics of current interest. The Graduate Fellowship program allows exceptional students to benefit from this activity and the scientific ambience of KITP by spending a semester there. This is a very competitive program, with only about half a dozen students coming from around the world each semester. Agon, who is advised by Profs. Matthew Headrick, Albion Lawrence, and Howard Schnitzer, is currently spending the spring term at KITP, before heading off to Stony Brook University as a postdoc in the fall.

Back in the summer of 2015, Agon had the opportunity to visit KITP during two important programs on the physics frontiers, both of special interest to him, namely ”Entanglement in Strongly-Correlated Quantum Matter” and ”Quantum Gravity Foundations: UV to IR”. That was a great opportunity to meet in person the leaders of the field from around the world in the relaxed and friendly atmosphere of the KITP. Discussions among the researchers and students were tremendously common all around the institute and there were many activities that facilitated such discussions such as daily coffees, lunches, and dinners.

In his new visit as a Graduate Fellow in 2017, Agon has found once again most of what he saw in his previous visit. The current program, “Scattering Amplitudes and Beyond”, expands his current knowledge of Quantum Field Theory and is of help in his preparation for his upcoming postdoctoral job. Scattering amplitudes are quantities of interest in quantum field theory since they encode the basic information one needs to make predictions and test them against accelerator experiments. In addition, being a local now allows him to explore more of what KITP and UCSB have to offer. Faculty, postdocs, and grad students discuss physics every day over lunch overlooking the beautiful lagoon. Furthermore, two seminars are programmed weekly, as well as colloquia and postdoc and graduate student journal clubs. These kinds of activities are extremely useful, as they facilitate the essential but difficult process of being up to date on the relevant current work in the field (broadly defined), and making collaborations with various members of both KITP and UCSB easier and more natural for him.

During his stay, Agon has had the opportunity to give talks at local events (Pacific Gravity Meeting) as well as at the weekly group seminar, and he has started a collaboration with KITP postdoc Tomonori Ugajin on some interesting entanglement entropy related projects. One of them seeks to study the gravitational duals to certain contributions to the entanglement entropy of excited CFT states, while the second looks for a better understanding of the universal behavior of the ground state entanglement entropy between disjoint regions in the small separation regime. His preliminary work has been dedicated to studying some of the techniques that have proved useful in previous work (related to bulk emergence and the proofs of energy conditions on quantum field theories) and which they believe will be also useful in solving these problems.

Although the scientific activity was Agon’s main motivation to visit KITP, one has to also acknowledge the beauty that Santa Barbara and its surroundings offer. The most remarkable for him was the enormous diversity of the natural environment, which is not limited to the gorgeous beaches but also includes a variety of fauna and flora in the nearby mountains, which range from the tropical to dessert-like, and the vast flat lands that fill the space in between, all of this in an almost invariant perfect weather all year long. The city itself keeps a beautiful Spanish Colonial architecture, an authentic and large variety of delicious Mexican cuisine, and a considerable amount of cultural activities with special emphasis on art in all its forms.



Physics Graduate Student Receives Kavli Fellowship

12 04 2017

Cesar Agon at Kavli Institute Cesar Agon, a graduate student in the High-Energy and Gravitational Theory group, was awarded a prestigious Graduate Fellowship at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara. KITP is one of the world’s leading centers for research in all areas of theoretical physics. In addition to having its own faculty and postdocs, it hosts visiting faculty from around the world and holds conferences and semester-long programs on topics of current interest. The Graduate Fellowship program allows exceptional students to benefit from this activity and the scientific ambience of KITP by spending a semester there. This is a very competitive program, with only about half a dozen students coming from around the world each semester. Agon, who is advised by Profs. Matthew Headrick, Albion Lawrence, and Howard Schnitzer, is currently spending the spring term at KITP, before heading off to Stony Brook University as a postdoc in the fall.

Back in the summer of 2015, Agon had the opportunity to visit KITP during two important programs on the physics frontiers, both of special interest to him, namely ”Entanglement in Strongly-Correlated Quantum Matter” and ”Quantum Gravity Foundations: UV to IR”. That was a great opportunity to meet in person the leaders of the field from around the world in the relaxed and friendly atmosphere of the KITP. Discussions among the researchers and students were tremendously common all around the institute and there were many activities that facilitated such discussions such as daily coffees, lunches, and dinners.

In his new visit as a Graduate Fellow in 2017, Agon has found once again most of what he saw in his previous visit. The current program, “Scattering Amplitudes and Beyond”, expands his current knowledge of Quantum Field Theory and is of help in his preparation for his upcoming postdoctoral job. Scattering amplitudes are quantities of interest in quantum field theory since they encode the basic information one needs to make predictions and test them against accelerator experiments. In addition, being a local now allows him to explore more of what KITP and UCSB have to offer. Faculty, postdocs, and grad students discuss physics every day over lunch overlooking the beautiful lagoon. Furthermore, two seminars are programmed weekly, as well as colloquia and postdoc and graduate student journal clubs. These kinds of activities are extremely useful, as they facilitate the essential but difficult process of being up to date on the relevant current work in the field (broadly defined), and making collaborations with various members of both KITP and UCSB easier and more natural for him.

During his stay, Agon has had the opportunity to give talks at local events (Pacific Gravity Meeting) as well as at the weekly group seminar, and he has started a collaboration with KITP postdoc Tomonori Ugajin on some interesting entanglement entropy related projects. One of them seeks to study the gravitational duals to certain contributions to the entanglement entropy of excited CFT states, while the second looks for a better understanding of the universal behavior of the ground state entanglement entropy between disjoint regions in the small separation regime. His preliminary work has been dedicated to studying some of the techniques that have proved useful in previous work (related to bulk emergence and the proofs of energy conditions on quantum field theories) and which they believe will be also useful in solving these problems.

Although the scientific activity was Agon’s main motivation to visit KITP, one has to also acknowledge the beauty that Santa Barbara and its surroundings offer. The most remarkable for him was the enormous diversity of the natural environment, which is not limited to the gorgeous beaches but also includes a variety of fauna and flora in the nearby mountains, which range from the tropical to dessert-like, and the vast flat lands that fill the space in between, all of this in an almost invariant perfect weather all year long. The city itself keeps a beautiful Spanish Colonial architecture, an authentic and large variety of delicious Mexican cuisine, and a considerable amount of cultural activities with special emphasis on art in all its forms.



Two Brandeis Professors Receive 2017 Simons Fellowships

11 04 2017
Bit threads in a holographic spacetime

Bit threads in a holographic spacetime

Two Brandeis professors have been awarded Simons Fellowships for 2017. Daniel Ruberman received the 2017 Simons Fellows in Mathematics. Matthew Headrick was awarded the 2017 Simons Fellows in Theoretical Physics. This is the first of two articles where each recipient’s award-winning research is described.

Matthew Headrick’s research studies the phenomenon of entanglement in certain quantum systems and its connection to the geometry of spacetime in general relativity. This very active area of research is the culmination of three developments in theoretical physics over the past 20 years.

First, in 1997, string theorists discovered that certain quantum systems involving a large number of very strongly interacting constituents — whose analysis would normally be intractable — are secretly equivalent to general relativity — a classical theory describing gravity in terms of curved spacetime — in a space with an extra dimension. For example, if the quantum system has two dimensions of space, then the general relativity has three; the phenomenon is thus naturally dubbed “holography”.

This equivalence between two very different-looking theories is incredibly powerful, and has led to much progress in understanding both strongly-interacting quantum systems and general relativity. However, it is still not fully understood how or precisely under what conditions such an equivalence holds.

Meanwhile, around 15 years ago, theorists began studying entanglement as a way to understand the behavior of quantum systems. “Entanglement” refers to correlations between two parts of a quantum system that occurs at the level of the wave function (unlike more familiar classical, or statistical, correlations). Entanglement is responsible for much of the apparent weirdness of quantum mechanics, as well as the power of such potential technologies as quantum cryptography and quantum computers. Although the concept of entanglement has been recognized almost since the birth of quantum mechanics, only recently has it been understood how quantifying entanglement (using certain kinds of entropies) provides powerful insights into the behavior of quantum systems ranging from many-body condensed-matter systems to theories of particle physics.

These two developments came together in 2006, when two physicists, Ryu and Takayanagi — one a condensed-matter theorist and the other a string theorist — made a dramatic conjecture connecting them. They posited that, in a holographic system, the entanglement is directly related to the geometry of space on the general relativity side; more specifically, given a decomposition of the quantum system into two parts, the amount of entanglement is given by the area of a certain minimal surface on the general relativity side. This development has led to many advances in our understanding of entanglement in strongly-interacting systems, and has provided a new framework for thinking about the emergence of space out of quantum constituents.

Since the Ryu-Takayanagi conjecture was originally made, Headrick has been a leader in testing, generalizing, and applying it. Working with Michael Freedman (Microsoft Research), he recently discovered a new way to understand entanglement in holographic systems in terms of microscopic “bit threads” running through space; using the so-called max flow-min cut theorem from network theory, they showed that this picture precisly reproduces the predictions of the Ryu-Takayanagi formula. With his students and other collaborators, Headrick is currently building on this picture. A major focus, for example, is to understand the subtle role that time plays in entanglement and holography.



“Exceptionally Helpful” Matthew Headrick Receives Award

9 03 2017

Associate Professor of Physics Matthew Headrick was named by the American Physical Society as an Outstanding Referee for 2017. The award recognizes “scientists who have been exceptionally helpful in assessing manuscripts for publication in the APS journals”. Headrick, who works in string theory and related areas of theoretical physics, is one of 150 Outstanding Referees named this year, out of about 60,000 active referees for the APS journals. Headrick is not the only Brandeis physicist to receive this honor; Robert Meyer, now Emeritus Professor, was named an Outstanding Referee in 2011.

Headrick’s research is primarily focused on the intersection of quantum gravity, quantum field theory, and quantum information theory. He is specifically interested in information-theoretic aspects of holographic field theories (field theories that are dual to higher-dimensional gravitational theories), such as entanglement entropies and related quantities.






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