Four members of the MIT faculty representing the departments of Economics, Mathematics, and Physics were recently named recipients of the 2019 Sloan Research Fellowships from the Alfred P. Sloan Foundation. The recipients, all early-career scholars in their fields, will each receive a two-year, $70,000 fellowship to further their research.

This year’s MIT recipients are among 126 scientists who represent 57 institutions of higher education in the United States and Canada. This year’s cohort brings MIT’s total to nearly 300 fellows — more than any single institution in the history of the fellowships since their inception in 1955.

Sloan Fellows are nominated by their fellow researchers and selected from an independent panel of senior scholars on “the basis of a candidate’s research accomplishments, creativity, and potential to become a leader in his or her field.”

2019 Sloan Fellow Nikhil Agarwal, the Castle Krob Career Development Assistant Professor of Economics in the School of Humanities, Arts, and Social Sciences, studies the empirics of matching markets.

“In these marketplaces, agents cannot simply choose their most preferred option from a menu with posted prices, because goods may be rationed or agents on the other side of the market must agree to a match,” Agarwal says of markets that include medical residency programs, kidney donation, and public school choice. “My research interests lie in how the market structure, market rules, and government policies affect economic outcomes in these settings. To this end, my research involves both developing new empirical techniques and answering applied questions,” he says.

Nancy Rose, department head and Charles P. Kindleberger Professor of Applied Economics, nominated Agarwal. “Nikhil [Agarwal] has made fundamental contributions to the empirical analysis of matching markets, advancing both economic science and public policy objectives,” says Rose.

Andrew Lawrie, an assistant professor in the Department of Mathematics, is an analyst studying geometric partial differential equations. He investigates the behavior of waves as they interact with each other and with their surrounding medium.

Lawrie’s research focuses on solitons — coherent solitary waves that describe nonlinear dynamics as varied as rogue waves in the ocean, black holes, and short-pulse lasers. Together with Jacek Jendrej, a researcher at Le Centre National de la Recherche Scientifique and Université Paris 13, Lawrie recently gave the first mathematically rigorous example of a completely inelastic two-soliton collision.

“Dr. Lawrie’s mathematical versatility and knowledge recently has been put on great display,” says one of Lawrie’s nominators of his paper in the research journal Inventiones Mathematicae. “This is one of those papers that completely describe mathematically an important phenomenon.”

“He has amassed an astonishingly broad and deep body of work for somebody who is only on his second year of a tenure track,” says his nominator, who requested anonymity.

Lawrie’s colleague Yufei Zhao was also named a 2019 Sloan Fellow recipient. Zhao, the Class of 1956 Career Development Assistant Professor in the Department of Mathematics, is a researcher in discrete mathematics who has made significant contributions in combinatorics with applications to computer science.

In major research accomplishments, Zhao contributed to a better understanding of the celebrated Green-Tao theorem, which states that prime numbers contain arbitrarily long arithmetic progressions. Zhao’s proof, co-authored with Jacob Fox, Zhao’s advisor and a former professor in the mathematics department, and David Conlon at the University of Oxford, simplifies a central part of the proof, allowing a more direct route to the Green-Tao theorem. Their work improves the understanding of pseudorandom structures — non-random objects with random-like properties — and has other applications in mathematics and computer science.

“The resulting proof is clean and fits in 25 pages, well under half the length of the original proof,” says Larry Guth, Zhao’s nominator and a professor of mathematics at MIT. “His expository work on the Green-Tao theorem is a real service to the community.”

The final 2019 Sloan Research Fellow recipient is Daniel Harlow, an assistant professor in the Department of Physics. Harlow researches cosmologic events, viewed through the lens of quantum gravity and quantum field theory.

“My research is focused on understanding the most extreme events in our universe: black holes and the Big Bang. Each year brings more observational evidence for these events, but without a theory of quantum gravity, we are not able to explain them in a satisfying way,” says Harlow, whose work has helped clarify many aspects of symmetries in quantum field theory and quantum gravity.

Harlow, who is a researcher in the Laboratory for Nuclear Science, has been working with Hirosi Ooguri, Fred Kavli Professor and director of the Walter Burke Institute for Theoretical Physics at Caltech, to give improved explanations of several well-known phenomena in the standard model of particle physics.

“We are very proud of Dan’s work with Ooguri on foundational aspects of symmetries in quantum field theory,” says Peter Fisher, department head and professor of physics.

“Sloan Research Fellows are the best young scientists working today,” says Adam F. Falk, president of the Alfred P. Sloan Foundation. “Sloan Fellows stand out for their creativity, for their hard work, for the importance of the issues they tackle, and the energy and innovation with which they tackle them. To be a Sloan Fellow is to be in the vanguard of 21st century science.”

Neutron stars are among the densest-known objects in the universe, withstanding pressures so great that one teaspoon of a star’s material would equal about 15 times the weight of the moon. Yet as it turns out, protons — the fundamental particles that make up most of the visible matter in the universe — contain even higher pressures.

For the first time, MIT physicists have calculated a proton’s pressure distribution, and found that the particle contains a highly pressurized core that, at its most intense point, is generating greater pressures than are found inside a neutron star.

This core pushes out from the proton’s center, while the surrounding region pushes inward. (Imagine a baseball attempting to expand inside a soccer ball that is collapsing.) The competing pressures act to stabilize the proton’s overall structure.

The physicists’ results, published today in Physical Review Letters, represent the first time that scientists have calculated a proton’s pressure distribution by taking into account the contributions of both quarks and gluons, the proton’s fundamental, subatomic constituents.

“Pressure is a fundamental aspect of the proton that we know very little about at the moment,” says lead author Phiala Shanahan, assistant professor of physics at MIT. “Now we’ve found that quarks and gluons in the center of the proton are generating significant outward pressure, and further to the edges, there’s a confining pressure. With this result, we’re driving toward  a complete picture of the proton’s structure.”

Shanahan carried out the study with co-author William Detmold, associate professor of physics at MIT. Both are researchers in the Laboratory for Nuclear Science.

Remarkable quarks

In May 2018, physicists at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility announced that they had measured the proton’s pressure distribution for the first time, using a beam of electrons that they fired at a target made of hydrogen. The electrons interacted with quarks inside the protons in the target. The physicists then determined the pressure distribution throughout the proton, based on the way in which the electrons scattered from the target. Their results showed a high-pressure center in the proton that at its point of highest pressure measured about 10³⁵ pascals, or 10 times the pressure inside a neutron star.

However, Shanahan says their picture of the proton’s pressure was incomplete.

“They found a pretty remarkable result,” Shanahan says. “But that result was subject to a number of important assumtions that were necessary because of our incomplete understanding.”

Specifically, the researchers based their pressure estimates on the interactions of a proton’s quarks, but not its gluons. Protons consist of both quarks and gluons, which continuously interact in a dynamic and fluctuating way inside the proton. The Jefferson Lab team was only able to determine the contributions of quarks with its detector, which Shanahan says leaves out a large part of a proton’s pressure contribution.

“Over the last 60 years, we’ve built up quite a good understanding of the role of quarks in the structure of the proton,” she says. “But gluon structure is far, far harder to understand since it is notoriously difficult to measure or calculate.”

A gluon shift

Instead of measuring a proton’s pressure using particle accelerators, Shanahan and Detmold looked to include gluons’ role by using supercomputers to calculate the interactions between quarks and gluons that contribute to a proton’s pressure.

“Inside a proton, there’s a bubbling quantum vacuum of pairs of quarks and antiquarks, as well as gluons, appearing and disappearing,” Shanahan says. “Our calculations include all of these dynamical fluctuations.”

To do this, the team employed a technique in physics known as lattice QCD, for quantum chromodynamics, which is a set of equations that describes the strong force, one of the three fundamental forces of the Standard Model of particle physics. (The other two are the weak and electromagnetic force.) The strong force is what binds quarks and gluons to ultimately make a proton.

Lattice QCD calculations use a four-dimensional grid, or lattice, of points to represent the three dimensions of space and one of time. The researchers calculated the pressure inside the proton using the equations of Quantum Chromodynamics defined on the lattice.

“It’s hugely computationally demanding, so we use the most powerful supercomputers in the world to do these calculations,” Shanahan explains.

The team spent about 18 months running various configurations of quarks and gluons through several different supercomputers, then determined the average pressure at each point from the center of the proton, out to its edge.

Compared with the Jefferson Lab results, Shanahan and Detmold found that, by including the contribution of gluons, the distribution of pressure in the proton shifted significantly.

“We’ve looked at the gluon contribution to the pressure distribution for the first time, and we can really see that relative to the previous results the peak has become stronger, and the pressure distribution extends further from the center of the proton,” Shanahan says.

In other words, it appears that the highest pressure in the proton is around 10³⁵ pascals, or 10 times that of a neutron star, similar to what researchers at Jefferson Lab reported. The surrounding low-pressure region extends farther than previously estimated.

Confirming these new calculations will require much more powerful detectors, such as the Electron-Ion Collider, a proposed particle accelerator that physicists aim to use to probe the inner structures of protons and neutrons, in more detail than ever before, including gluons.

“We’re in the early days of understanding quantitatively the role of gluons in a proton,” Shanahan says. “By combining the experimentally measured quark contribution, with our new calculation of the gluon piece, we have the first complete picture of the proton’s pressure, which is a prediction that can be tested at the new collider in the next 10 years.”

This research was supported, in part, by the National Science Foundation and the U.S. Department of Energy.