The Simons Foundation congratulates the awardees who have been selected as Simons Investigators in mathematics, physics, astrophysics, theoretical computer science, the mathematical modeling of living systems, andMath+X.

The Simons Investigators program provides a stable base of support for outstanding scientists, enabling them to undertake long-term study of fundamental questions.

### 2017

**MATHEMATICS**

**Simon Brendle**

*Columbia University* Simon Brendle has achieved major breakthroughs in geometry including results on the Yamabe compactness conjecture, the differentiable sphere theorem (joint with R. Schoen), the Lawson conjecture and the Ilmanen conjecture, as well as singularity formation in the mean curvature flow, the Yamabe flow and the Ricci flow.

**Ludmil Katzarkov**

*University of Miami* Ludmil Katzarkov has introduced novel ideas and techniques in geometry, proving long-standing conjectures (e.g., the Shavarevich conjecture) and formulating new conceptual approaches to open questions in homological mirror symmetry, rationality of algebraic varieties and symplectic geometry.

**Igor Rodnianski**

*Princeton University* Igor Rodnianski is a leading figure in the field of partial differential equations. He has recently proven theorems concerning the full nonlinear dynamics of the Einstein equations, in both the weak and strong field regimes, and has obtained new results regarding gravitational radiation associated to black hole spacetimes.

**Allan Sly**

*University of California, Berkeley* Allan Sly resolved long-standing open problems on the computational complexity of phase transitions and on the dynamics of the Ising model.

**PHYSICS**

**Nigel Cooper**

*Cambridge University* Nigel Cooper has shown how to design optical lattices for cold atoms that provide controllable laboratories for exploring the physics of interacting particles in the presence of gauge fields. He is also known for foundational works on the topological Kondo effect and on quantum oscillations in topological insulators.

**Steven Gubser**

*Princeton University* Steven Gubser is known for foundational work on the gauge-string duality and its applications to heavy-ion and condensed matter physics, including a gravitational dual of superconductivity and studies of bulk flows of quark-gluon plasmas. He is also noted for work on semi-classical strings in anti-de Sitter space.

**Shamit Kachru**

*Stanford University* Shamit Kachru’s work includes the discovery of string dualities in N=2 supersymmetry, foundational studies of flux compactification of string theory; mathematical studies of connections between automorphic forms, black holes and string vacua; and quantum field theories describing ‘non-fermi-liquid’ behavior in condensed matter physics.

**Anders Sandvik**

*Boston University* Anders Sandvik is widely recognized for his development of stochastic series expansion methods for quantum problems and for his creative applications of these and related methods to topics including deconfined quantum criticality and optimization problems.

**Eva Silverstein**

*Stanford University * Eva Silverstein’s research connects the mathematical structure of string theory to predictions for cosmological observables, with implications for dualities, space-time singularities and black hole physics. Her work on axion monodromy provided a theoretically consistent model of large-field inflation.

**ASTROPHYSICS**

**Eve Ostriker**

*Princeton University* Eve Ostriker has made major contributions to our understanding of the role of the interstellar medium in star formation and galactic structure and evolution, with a focus on the role of turbulence and on the effects of energy returned by massive stars to the interstellar medium.

**Wayne Hu**

*University of Chicago* Wayne Hu has shown how cosmological observations can provide information about fundamental physics topics such as neutrino masses and dark energy.

**THEORETICAL COMPUTER SCIENCE**

**Scott Aaronson**

*University of Texas at Austin* Scott Aaronson has established fundamental theorems in quantum computational complexity and inspired new research directions at the interface of theoretical computer science and the study of physical systems.

**Boaz Barak**

*Harvard University* Boaz Barak has worked on cryptography, computational complexity and algorithms.

He developed new non-black-box techniques in cryptography and new semidefinite programming-based algorithms for problems related to machine learning and the unique games conjecture.

**James R. Lee**

*University of Washington* James R. Lee is one of the leaders in the study of discrete optimization problems and their connections to analysis, geometry and probability. His development of spectral methods and his work on convex relaxations has led to breakthroughs in characterizing the efficacy of mathematical programming for combinatorial optimization.

**MATHEMATICAL MODELING OF LIVING SYSTEMS**

**Arvind Murugan**

*The University of Chicago * Arvind Murugan works on how organisms enhance information uptake from the environment by using inference from past experience and has applied such ideas to self-assembly dynamics, olfaction, circadian clocks and stress-response pathways.

**David Schwab**

*Northwestern University* David Schwab has developed theories of signaling and social aggregation in the social amoeba Dictyostelium and has shown how tensor-network methods from computational quantum physics can be used in machine learning.

**Aryeh Warmflash**

*Rice University* Aryeh Warmflash has developed systems to mimic embryonic development in vitro using human embryonic stem cells and is developing dynamical system models of cell fate patterning and morphogenesis that can be rigorously compared with quantitative data on in vitro development.

**Daniel Weissman**

*Emory University* Daniel Weissman has shown that the generation of ‘irreducible complexity’ happens most frequently in large populations and that the speed of adaptation is limited by the frequency of genetic recombination.

**MATH+X**

**Andrea Bertozzi**

*University of California, Los Angeles* Andrea Bertozzi has contributed to many areas of applied mathematics including the theory of swarming behavior, aggregation equations and their solution in general dimension, the theory of particle-laden flows in liquids with free surfaces, data analysis/image analysis at the micro and nano scales and the mathematics of crime.

**Amit Singer**

*Princeton University* Amit Singer is one of the leaders in the mathematical analysis of noisy data provided by cryo-EM.

### 2016

**MATHEMATICS**

** Vladimir Markovic**

*California Institute of Technology* Vladimir Markovic has made fundamental contributions to the theory of three-dimensional manifolds, resolving several long-standing problems, among them the proof of the Thurston conjecture concerning immersed almost-geodesic surfaces in closed hyperbolic three-manifolds.

**James McKernan**

*University of California, San Diego*James McKernan, in collaboration with Caucher Birkar, Paolo Cascini, and Christopher D. Hacon, has established one of the cornerstones of the Minimal Model Program: the finite generation of canonical rings in all dimensions.

**Bjorn Poonen**

*Massachusetts Institute of Technology*Bjorn Poonen has contributed decisively to many areas revolving broadly around the study of Diophantine equations. Among his achievements are the construction of examples of threefolds without rational points but vanishing local and global obstructions, new heuristics concerning rational points on elliptic curves and results about rational points on curves of higher genus.

**PHYSICS**

**Mina Aganagic**

*University of California, Berkeley*Mina Aganagic applies insights from quantum physics to mathematical problems in geometry and topology. She made deep and influential conjectures in enumerative geometry, knot theory and mirror symmetry using predictions from string theory and from M-theory.

**Andrea Alù**

*The University of Texas at Austin*Andrea Alù’s work on the manipulation of light in artificial materials and metamaterials has shown how clever designs may surpass what had previously been thought to be limitations on wave propagation in materials. He has developed new concepts for cloaking, one-way propagation of waves in materials, dramatic enhancement of nonlinearities in nanostructures and ultrathin optical devices based on metasurfaces and twisted metamaterials.

**Andrei Beloborodov**

*Columbia University*Andrei Beloborodov applies first-principles physics to astrophysical systems, and his work provides crucial new insights on how exotic astronomical objects work. He has done important research on compact objects like neutron stars and black holes and is particularly well-known for his studies of gamma-ray bursts, magnetars and pulsars.

**B. Andrei Bernevig**

*Princeton University*Andrei Bernevig is a leader in the lively field of topological electronic states in solids. His initial proposal of the quantum spin Hall effect in HgTe quantum wells was soon followed by dramatic experimental confirmation. He has developed a theoretical framework for topological insulators and written a highly regarded book on the subject. His work on topological superconductivity in metal chains on superconducting surfaces, as well as his prediction of two types of Weyl semimetal states in transition metal monophosphides and WTe2, has stimulated considerable theoretical and experimental activity.

**Garnet Chan**

*California Institute of Technology*Garnet Chan’s research lies at the interface of theoretical chemistry, condensed matter physics and quantum information theory, and is concerned with the phenomena and simulation methods associated with quantum many-particle systems. Some current problems of interest include metalloenzymes and biological catalysts, transition metal oxides and superconductivity, and conjugated organic systems and light harvesting. He has contributed to a wide range of quantum simulation methods, including density matrix renormalization and tensor network algorithms, quantum embedding theories and local correlation approximations.

**Daniel Eisenstein**

*Harvard University*Daniel Eisenstein is a leading figure in modern cosmology. He is known for utilization of the baryon acoustic oscillations (BAO) standard ruler for measuring the geometry of the universe, which underpins several large upcoming ground and space missions. Eisenstein blends theory, computation and data analysis seamlessly to push the boundaries of current-day research in cosmology.

**Anton Kapustin**

*California Institute of Technology*Anton Kapustin’s work lies at the interface of physics and mathematics. He applied ideas from gauge theory to the study of the geometric Langlands program in mathematics and has applied sophisticated mathematics to the classification of exotic quantum states of matter.

**THEORETICAL COMPUTER SCIENCE**

** Madhu Sudan**

*Harvard University* Madhu Sudan is known for his work in computational complexity theory. He has made fundamental contributions in the areas of probabilistically checkable proofs, nonapproximability of optimization problems and computational aspects of error-correcting codes. More recently, he initiated the study of universal semantic communication.

** David Zuckerman**

*University of Texas at Austin* David Zuckerman is a leader in pseudorandomness and randomness extraction, an area that his early work pioneered. He has a number of beautiful and important results in construction and application of extractors, including applications to coding theory, computational complexity and cryptography, as well as his recent breakthrough result with two-source extractors.

** MATHEMATICAL MODELING OF LIVING SYSTEMS**

** Surya Ganguli**

*Stanford University* Surya Ganguli’s work combines theory with computation, recording, analysis of data, and modeling, contributing to our understanding of how the brain works. He has made fundamental contributions to the mechanisms of short- and long-term memory. His work also addresses difficult problems in machine learning.

** Kirill Korolev**

*Boston University* Kirill Korolev works at the interface of biophysics, statistical physics, soft condensed-matter physics and ecology. He develops elegant theories and combines them with the results of controlled experiments to address topics ranging from spreading of cell populations on a 2-D substrate, cancer progression, and ecology. His work is unified by the theme of how complex interactions determine the dynamics of biological systems.

** Madhav Mani**

*Northwestern University* Following thesis work on fluid mechanics and soft matter physics, Madhav Mani transitioned to studying the mechanics of development and gene regulation in organisms. In collaboration with experimentalists, he combined mathematical modeling with quantitative analysis of growing tissues to shed light on how cells collectively develop preferred orientations. Using model-based forced-inference techniques, he also reconstructed the dynamics of networks that drive cellular flows during early embryonic development.

** M. Lisa Manning**

*Syracuse University* Lisa Manning started her research career in the physics of glasses, i.e., how a disordered group of molecules or particles freezes into a rigid solid at a well-defined temperature. She then turned her attention to morphogenesis, the process by which embryos transform from a spherical egg to a shape we recognize as an insect, plant or mammal, showing that aspects of this process could be modeled by surface tension in analogy with the description of immiscible liquids. Her most recent work uses ideas from the physics of glasses to describe the mobility of cells organized in sheets and applies to a broad class of biological tissues, including embryos and cells from asthma patients.

**MATH+X**

** Ingrid Daubechies**

*Duke University* Ingrid Daubechies constructed the first example of what mathematicians call “wavelets,” which have had an immense impact on pure and applied mathematics. She has made and continues to make creative applications of wavelets to a large variety of problems in engineering and other fields.

### 2015

**MATHEMATICS**

**Ian Agol**

*University of California, Berkeley*Ian Agol has made major contributions to three-dimensional topology and hyperbolic geometry, completing some of Thurston’s problems elucidating the structure of 3-manifolds. He proved several deep and long-standing conjectures, including the Virtual Haken conjecture, the Marden Tameness conjecture and the Simon conjecture.

**Ben Green**

*University of Oxford*Ben Green is an expert in analytic number theory. Among his achievements is the Green–Tao theorem, establishing that primes contain arbitrarily long arithmetic progressions.

**Raphaël Rouquier**

*University of California, Los Angeles*Raphaël Rouquier has initiated a new field in mathematics, ‘higher representation theory.’ He constructed novel categories of geometric and representation-theoretic interest and applied these to problems in the theory of finite groups, Lie theory, algebraic geometry and mathematical physics.

**Christopher Skinner**

*Princeton University*Christopher Skinner works in number theory and arithmetic geometry. One of his striking recent results is a proof, in joint work with collaborators, that a positive proportion of elliptic curves defined over the rational numbers satisfy the Birch–Swinnerton-Dyer conjecture.

** THEORETICAL COMPUTER SCIENCE**

**Dan Boneh**

*Stanford University*Dan Boneh is an expert in cryptography and computer security. One of his main achievements is the development of pairing-based cryptography, giving short digital signatures, identity-based encryption and novel encryption systems.

**Subhash Khot**

*New York University*Subhash Khot initiated a new direction in computational complexity theory and approximation algorithms, based on his Unique Games conjecture, which is currently one of the most important conjectures in theoretical computer science.

**Christopher Umans**

*California Institute of Technology*Christopher Umans works on complexity theory, in particular, algorithms and randomness in computations. He has established new upper bounds for the complexity of matrix multiplication and developed a novel algorithm for polynomial factorization.

** PHYSICS**

**Jonathan Feng**

*University of California, Irvine*Jonathan Feng is recognized as one of the leaders in the theoretical study of dark matter, known for his work in constructing theoretical models, deducing observational consequences, and motivating and interpreting experimental searches for dark matter.

**Alexei Kitaev**

*California Institute of Technology*Alexei Kitaev’s work on topologically protected states of matter helped found the field of topological quantum computing; his prediction that topological superconductors may sustain Majorana fermions has initiated a major experimental activity. His ongoing work concerns the mathematical classification of the possible quantum phases of matter.

**Andrea Liu**

*University of Pennsylvania*Andrea Liu is making foundational contributions to the field of mechanics, in particular to the behavior of disordered packings of particles ranging in size from atoms or molecules (glass) to sand grains. With Nagel, she introduced the concept of jamming, explaining how random assemblies of closely packed objects become rigid. Building on this work and her subsequent analysis of the jamming transition, Liu has provided new insights into the elastic and flow properties of highly defected solids, identifying the topological defects whose motion allows flow and the soft modes associated with them.

**Mark Van Raamsdonk**

*University of British Columbia*Mark Van Raamsdonk uses the holographic insights from the gauge-gravity duality to obtain new results in the theory of quantum gravity. He is particularly known for his recent results relating the geometrical structure of spacetime to entanglement structure of the holographically dual boundary quantum field theory.

**Ashvin Vishwanath**

*Harvard University*Ashvin Viswanath is a leading quantum condensed matter physicist, known for his work on quantum phase transitions beyond the Landau–Wilson–Fisher paradigm, his recent theoretical prediction of Weyl semimetals and his generalizations of the topological insulator concept beyond the single-particle approximation.

**Anastasia Volovich**

*Brown University*Anastasia Volovich’s work on gauge and gravity theories has introduced a new perspective on Feynman diagram calculations along with powerful and extremely efficient methods for their evaluation. Her ongoing work is uncovering deep mathematical structures within the gauge theories of particle physics.

**Matthieu Wyart**

*New York University*Matthieu Wyart’s work has created a new scientific understanding of the physics of disordered and glassy systems. His study of soft modes controlled by random geometry in systems of closely-packed particles is recognized as a major advance, and his introduction of the idea of marginal stability unifies a wide range of phenomena, providing new insights into the statics and dynamics of glassy systems. Wyart resigned his Investigatorship in 2015 to move to a position at EPFL, Lausanne.

** MATHEMATICAL MODELING OF LIVING SYSTEMS**

**Michael Desai**

*Harvard University*Michael Desai combines theoretical and experimental work to bring quantitative methodology to the field of evolutionary dynamics; he and his group are particularly known for their contributions in the area of statistical genetics.

**Andrew Mugler**

*Purdue University*Andrew Mugler works on sensing and information processing in cells. He is particularly known for work demonstrating that spatial effects at the molecular level, such as protein clustering, can alter sensing and computation at the cellular level. His future research will involve combining the analysis of single-cell sensing with cell-cell communication to develop a theory of collective sensing, applicable to multicellular processes such as cancer metastasis.

**James O’Dwyer**

*University of Illinois at Urbana-Champaign*James O’Dwyer is known for his innovative work bringing new ideas from statistical physics to bear on the analysis of ecological problems. His very recent work on coevolution in microbial communities is recognized as opening a new direction for research.

** MATH+X**

**Michael Weinstein**

*Columbia University*Michael Weinstein’s work bridges the areas of fundamental and applied mathematics, physics and engineering. He is known for his elegant and influential mathematical analysis of wave phenomena in diverse and important physical problems. His and his colleagues’ work on singularity formation, stability and nonlinear scattering has been central to the understanding of the dynamics of coherent structures of nonlinear dispersive wave equations arising in nonlinear optics, macroscopic quantum systems and fluid dynamics. This led to work on resonances and radiation in Hamiltonian partial differential equations, with applications to energy flow in photonic and quantum systems. Recently, he has explored wave phenomena in novel structures such as topological insulators and metamaterials.

### 2014

**MATHEMATICS**

**Alex Eskin**

*University of Chicago*

Alex Eskin is a leading geometer with important contributions to geometric group theory, ergodic theory and number theory. He has applied ideas from dynamical systems to solve counting problems in the theory of Diophantine equations, the theory of the mapping class group and mathematical billiards on rational polygons.

**Larry Guth**

*Massachusetts Institute of Technology*

Larry Guth is a geometer with outstanding contributions to Riemannian geometry, symplectic geometry and combinatorial geometry. In Riemannian geometry, he solved a long-standing problem concerning sharp estimates for volumes of k-cycles. In symplectic geometry, he disproved a conjecture concerning higher-dimensional symplectic invariants by constructing ingenious counterexamples. In combinatorial geometry, he adopted a recent proof of the finite field analog of the Kakeya problem to the Euclidean context. He and Bourgain established the best current bounds to the restriction problem. Extending this work, he and Katz essentially solved one of the most well-known problems in incidence geometry, Erdős’s distinct distance problem, which was formulated in the 1940s.

**Richard Kenyon**

*Brown University*

Richard Kenyon’s central mathematical contributions are in statistical mechanics and geometric probability. He established the first rigorous results on the dimer model, opening the door to recent spectacular advances in the Schramm–Loewner evolution theory. In most recent work, he introduced new homotopic invariants of random structures on graphs, establishing an unforeseen connection between probability and representation theory.

**Andrei Okounkov**

*Columbia University*

Andrei Okounkov’s work spans a wide range of topics at the interface of representation theory, algebraic geometry, combinatorics and mathematical physics. He has made major contributions to enumerative geometry of curves and sheaves, the theory of random surfaces and random matrices. His papers reveal hidden structures and connections between mathematical objects and introduce deep new ideas and techniques of wide applicability.

**THEORETICAL COMPUTER SCIENCE**

**Moses Charikar**

*Princeton University*

Moses Charikar is one of the world’s leading experts on the design of approximation algorithms. He gave an optimal algorithm for the unique games, a central problem in complexity theory. His work sheds light on the strengths and limitations of continuous relaxations for discrete problems. He has uncovered new obstructions to dimension reduction and compression of geometric data. His algorithms for locality-sensitive hash functions are now *de facto* standard in real-life applications.

**Shang-Hua Teng**

*University of Southern California*

Shang-Hua Teng is one of the most original theoretical computer scientists in the world, with groundbreaking discoveries in algorithm design, spectral graph theory, operations research and algorithmic game theory. In joint work with Dan Spielman, Shang-Hua introduced smoothed analysis, a new framework that has served as a basis for advances in optimization, machine learning and data mining. His work laid foundations for many algorithms central in network analysis, computational economics and game theory.

**PHYSICS**

**Patrick Hayden**

*Stanford University*

Patrick Hayden’s work on the requirements for secure communication through quantum channels transformed the field of quantum information, establishing a general structure and a set of powerful results that subsumed most of the previous work in the field as special cases. More recently, he has used quantum information theory concepts to obtain new results related to the quantum physics of black holes.

**Marc Kamionkowski**

*The Johns Hopkins University*

Marc Kamionkowski is one of the leading theorists working at the intersection of particle physics, cosmology and astrophysics. His early work helped found the field of precision cosmology, showing how observations of the angular structure of the cosmic microwave background revealed information about fundamental-physics effects in the early Universe. He has also done work that has been crucial to our understanding of the physics of dark matter. His review articles and talks have helped define this new and growing field. Kamionkowski’s recent work centers on the development of new methods for the use of astrophysical measurements to probe properties of fundamental physical interest.

**Leo Radzihovsky**

*University of Colorado at Boulder*

Leo Radzihovsky is a condensed matter physicist whose work bridges the divide between the classical and quantum aspects of the subject, using mathematical tools and insights developed in one field to make seminal contributions in the other. His focus is on systems where fluctuations and heterogeneity play qualitative roles. He is known for his work on bent-core and other exotic liquid crystals; on fluctuating membranes and driven elastic media in the presence of quenched disorder, including the prediction of the transverse smectic phase; and on degenerate atomic gasses, where his rigorous work on the BCS-BEC crossover, particularly in systems with narrow Feshbach resonances, with and without “spin” imbalance, uncovered a host of new phenomena including topological phase transitions.

**Rachel Somerville**

*Rutgers University*

Rachel Somerville is a theoretical astrophysicist known for her contributions to the development of `semianalytic modeling’ methods that combine computational and pencil-and-paper theory, and her use of these methods, to further our understanding of the physical mechanisms of the formation, structural evolution and nuclear activity of galaxies. Her work has enabled, for example, the development of a comprehensive picture of the way in which the growth of supermassive black holes, and the energy they release during their formation, is linked with the structural properties of galaxies as well as their star formation activity.

**Anatoly Spitkovsky**

*Princeton University*

Anatoly Spitkovsky’s large-scale computer simulations of astrophysical plasmas have been instrumental in bringing a new level of quantitative precision to the field. His work on particle acceleration in astrophysical shocks is changing the way we understand high-energy astrophysics, and he is also known for his work on pulsar magnetospheres.

**Iain Stewart**

*Massachusetts Institute of Technology*

Iain Stewart works in the physics of elementary particles, investigating fundamental questions in quantum chromodynamics, i.e., the interactions of quarks and gluons via the strong force. He is particularly known for his role in inventing soft collinear effective field theory, a theoretical tool for understanding the particle jets produced by high energy collisions in accelerators such as the LHC. He has established factorization theorems that enable the clear interpretation and physical understanding of the collision products. Methods he has developed have been used in the search for the Higgs boson, to gain new insights into effects of CP violation in B-meson production and to test for beyond-standard-model physics.

**MATHEMATICAL MODELING OF LIVING SYSTEMS**

**Paul François**

*McGill University*

Paul François is known for his work on physical aspects of embryonic development, in particular his analysis of the mechanisms underlying embryonic patterning, for example, the role of genetic oscillators in the development of vertebrae. His research plans involve investigations of the physical bounds for information processing in the immune system and further investigation of the physical mechanisms of vertebrae formation.

**Oskar Hallatschek**

*University of California, Berkeley*

Oskar Hallatschek studies how large-scale patterns such as collective motion, synchronization, random genetic drift or Darwinian selection emerge in populations from the joint actions of heterogeneous individuals. He is particularly known for his work on the influence of spatial structure on biological processes, for example, how noisy traveling waves control the speed of many important dynamical processes, including biochemical reactions, range expansions, epidemic outbreaks or biological evolution. Hallatschek’s research plan involves extending his work to study the feedback between ecology and evolution, for example, how populations can evolve to become invasive, using growing biofilms as a model system.

**Pankaj Mehta**

*Boston University*

Pankaj Mehta works on collective behaviors in cell dynamics. He is particularly known for his information theoretic analysis of quorum sensing (where groups of many cells are much more sensitive to changes in environment than single cells). His theoretical work, in collaboration with the Bassler experimental group, demonstrated the importance of interference between different signaling channels and provided a mathematical model of the concentrations of receptor cells, which adjust themselves in response to multiple and time-varying signals so as to respond optimally to environmental cues. His research plans include the development and testing of a new quantitative framework for modeling high-dimensional ‘epigenetic landscapes’ and work on understanding collective behavior in cell populations.

**Olga Zhaxybayeva**

*Dartmouth College*

Olga Zhaxybayeva’s work focuses on how horizontal gene transfer influences (or influenced) the evolution of bacteria and archaea. Her work developing and implementing statistical techniques for monitoring the evolution of all of the genes in a bacterial genome showed that horizontal gene transfer has affected the evolution of much of the genomes of cyanobacteria, thermophilic bacteria and halophilic archaea. This and related work established horizontal gene transfer as an important driver of microbial evolution. Her research plan involves studying gene transfer agents (virus-like particles produced by some bacteria and archaea) to explore the possibility that horizontal gene transfer can provide an evolutionary force favoring cooperation and the emergence of complexity.

### 2013

**MATHEMATICS**

**Ngô Bảo Châu**

*The University of Chicago*

Ngô’s proof of the fundamental lemma, a deep conjecture of Langlands, inaugurated a new geometric approach to problems in harmonic analysis based on arithmetic geometry. His ideas have already inspired work in many areas, including mathematical physics and geometric representation theory.

**Maryam Mirzakhani**

*Stanford University*

Mirzakhani’s work is focused on Teichmüller theory and dynamics of natural geometric flows over the moduli space of Riemann surfaces. One of her major results, in joint work with Eskin and Mohammadi, is a proof that stationary measures for the action of SL_{2}(R) on the space of flat surfaces are invariant, a deep and long-standing conjecture.

**Kannan Soundararajan**

*Stanford University*

Soundararajan is one of the world’s leaders in analytic number theory and related areas. His work is focused on understanding the zeros and value distribution of L-functions, and on analyzing the behavior of multiplicative functions. In particular, his work (together with co-authors) has led to weak subconvexity bounds for general L-functions and to the proof of the holomorphic quantum unique ergodicity conjecture of Rudnick and Sarnak.

**Daniel Tataru**

*University of California, Berkeley*

Tataru’s work on nonlinear waves has been deep and influential. He proved difficult well-posedness and regularity results for many new classes of equations. This includes geometric evolutions such as wave and Schrödinger maps, quasilinear wave equations, some of which are related to general relativity, as well as other physically relevant models.

**Rajeev Alur**

*University of Pennsylvania*

Rajeev Alur is a leading researcher in formal modeling and algorithmic analysis of computer systems. A number of automata and logics introduced by him have now become standard models with great impact on both the theory and practice of verification. His key contributions include timed automata for modeling of real-time systems, hybrid automata for modeling discrete control software interacting with the continuously evolving physical environment, and visibly pushdown automata for processing of data with both linear and hierarchical structure such as XML documents.

**Piotr Indyk**

*Massachusetts Institute of Technology*

Piotr Indyk is noted for his work on efficient approximate algorithms for high-dimensional geometric problems. This includes the nearest neighbor search, where given a data point, the goal is to find points highly similar to it without scanning the whole data set. To address this problem, he co-developed the technique of locality sensitive hashing, which proved to be influential in many applications, ranging from data mining to computer vision. He has also made significant contributions to sublinear algorithms for massive data problems. In particular, he has developed several approximate algorithms for massive data streams that use very limited space. Recently, he has co-developed new algorithms for the sparse Fourier transform, which compute the Fourier transform of signals with sparse spectra faster than the FFT algorithm.

**Salil P. Vadhan**

*Harvard University*

Salil Vadhan has produced a series of original and influential papers on computational complexity and cryptography. He uses complexity-theoretic methods and perspectives to delineate the border between the possible and impossible in cryptography and data privacy. His work also illuminates the relation between computational and information-theoretic notions of randomness, thereby enriching the theory of pseudorandomness and its applications. All of these themes are present in Vadhan’s recent papers on differential privacy and on computational analogues of entropy, which are elegant, impressive, and far-reaching.

**PHYSICS**

**Victor Galitski**

*The University of Maryland*

Victor Galitski is a creative and productive scientist who at an early stage in his career has made many important contributions to diverse areas of quantum many-body physics, including applications of quantum theory to cold atomic gases, the theory of exotic spin models, topological insulators and topological superconductivity, quantum fluctuation phenomena, and the dynamics of periodically pumped systems. He is particularly known for his predictions of topological Kondo insulators (supported by recent experiments in samarium hexaboride), as well as his proposals for using multiple laser beams to realize spin-orbit physics in cold atomic gasses, which led to the discovery by Spielman and collaborators of the spin-orbit coupled Bose condensates he predicted.

**Randall Kamien**

*University of Pennsylvania*

Randall Kamien* *is a leading figure in the theory of topological effects in condensed matter physics, known for the mathematical rigor he brings to his work and in particular for the use of sophisticated and elegant geometrical methods to obtain insight into fundamental aspects of the structure of polymers, colloids, liquid crystals and related materials and into the topological defects occurring in these materials.

**Joel Moore**

*University of California, Berkeley*

Joel Moore* *is one of the leaders in the study of the topological aspects of electronic physics, particularly known for this work with Balents on strong topological insulators and his work with Orenstein and Vanderbilt on magnetoelectric couplings and optical responses induced by geometric and topological terms in various material classes. He has also obtained significant results on nonequilibrium dynamics of interacting quantum systems, significantly elucidating the role of quantum entanglement in these phenomena.

**Dam Thanh Son**

*The University of Chicago*

Dam Thanh Son is one of the rare theorists whose work has deep impact across several subfields of physics. He has written important papers in quantum chromodynamics, theoretical nuclear physics, condensed matter physics and atomic physics. Perhaps the most significant of his many contributions concern the duality between black holes in anti-de Sitter space and strongly interacting fluids. His initial work with Policastro and Starinets on the viscosity of the quark-gluon plasma opened new research directions in heavy ion physics and in string theory, and his subsequent work with Sachdev, Herzog and others established the AdS/CFT duality as a crucial theoretical tool of condensed matter physics.

**Senthil Todadri**

*Massachusetts Institute of Technology*

Senthil Todadri’s work with Fisher on Z2 topological order in models of spin liquid states provided key insights and initiated the systematic investigation of gauge structures in many-body systems, now a vital subfield of condensed matter physics. Senthil and co-workers also pioneered the theory of deconfined quantum criticality as a new paradigm for some phase transitions. Senthil and collaborators also introduced the concept of fractionalized Fermi liquids and developed a theory of continuous electronic Mott transitions. His most recent work in the theory of symmetry-protected topological phases and on combining ideas of quantum entanglement and many-body physics continues to move the boundaries of the field quantum many-body physics.

**Xi Yin**

*Harvard University*

Xi Yin is one of the outstanding members of the new generation of theoretical physicists, known for his work on fundamental problems of quantum gravity, including new insights into black hole entropy, for his work with Giombi on higher spin gravity, and for helping to establish the Klebanov–Polyakov conjecture and extensions of the gauge/gravity dualities. He is also credited with important work on supersymmetric Chern–Simons theories and associated connections to M-theory.

### 2012

**MATHEMATICS**

**Manjul Bhargava**

*Princeton University*

Manjul Bhargava pursues algebraic number theory and the geometry of numbers in the tradition of Gauss and Minkowski. Bhargava has inspired an extraordinary resurgence of this field, with wonderful applications. His overarching goal in this work is to count the basic objects of number theory and to make computational conclusions about their asymptotics. For example, it is conjectured that, in a certain natural sense, the average rank of the group of rational points of an elliptic curve defined over the rationals is 1/2. Bhargava and his student Shankar recently showed that it is less than 1. Previously, it was not even known whether the average rank is finite. In joint work with Dick Gross, Bhargava has also shown that the number of rational points on the majority of hyperelliptic curves is bounded by a certain small number independent of the genus of the curve. This work opens up remarkable new vistas in arithmetic and suggests exciting conjectures.

**Alice Guionnet**

*Massachusetts Institute of Technology*

Alice Guionnet has done very important work on the statistical mechanics of disordered systems (and in particular the dynamics and aging of spin glasses), random matrices (with an emphasis on the combinatorics of maps), and operator algebra/free probability. Her work on large deviations for spectra of random matrices has been very influential. She has extended the large deviation principle to the context of Voiculescu’s free probability theory, and in collaboration with Cabanal-Duvillard, Capitaine, and Biane she proved various large deviation bounds in this more general setting. These bounds enabled her to prove an inequality between the two notions of free entropy given by Voiculescu, settling half of the most important question in the field. With her former students M. Maida and E. Maurel-Segala and more recently with Vaughan Jones and D. Shlyakhtenko, Guionnet has studied statistical mechanics on random graphs through multimatrix models. Their work on the general Potts models on random graphs branches out in promising directions within operator algebra theory. Guionnet resigned her Investigatorship in 2016 to move to the École normale supérieure de Lyon in France.

**Christopher Derek Hacon**

*The University of Utah*

Christopher Hacon’s works are among the most important contributions to higher-dimensional algebraic geometry since Mori’s in the 1980s. Hacon and his co-authors have solved major problems concerning the birational geometry of algebraic varieties, including the characterization of irregular varieties, boundedness theorems for pluricanonical maps, a proof of the existence of flips, the completion of the minimal model program for varieties of general type, and bounds for the order of automorphism groups of varieties of general type. His work has also led to solutions of other problems, such as the existence of moduli spaces for varieties of general type and the ascending chain condition for log canonical thresholds.

**Paul Seidel**

*Massachusetts Institute of Technology*

Paul Seidel has done major work in symplectic geometry, in particular on questions inspired by mirror symmetry. His work is distinguished by an understanding of abstract algebraic structures such as derived categories, in sufficiently concrete terms to allow one to derive specific geometric results. On the abstract side, Seidel has made substantial advances towards understanding Kontsevich’s homological mirror symmetry conjecture and has proved several special cases of it. In joint papers with Smith, Abouzaid and Maydanskiy, he has investigated the symplectic geometry of Stein manifolds. In particular, work with Abouzaid constructs infinitely many nonstandard symplectic structures on any Stein manifold of sufficiently high dimension.

**Amit Singer**

*Princeton University*

Amit Singer works on a broad range of problems in applied mathematics, solving specific applied problems and employing sophisticated theory to allow the solution of general classes of problems. Among the areas to which he has contributed are diffusion maps, cryo-electron microscopy, random graph theory, sensor networks, graph Laplacians, and diffusion processes. His recent work in electron microscopy combines representation theory with a novel network construction to provide reconstructions of structural information on molecules from noisy two-dimensional images of populations of the molecule. He works with a widely varied group of collaborators and graduate students in several disciplines. His work is increasing the range of applicable mathematics.

**Terence Tao**

*University of California, Los Angeles*

Terry Tao is one of the most universal, penetrating and prolific mathematicians in the world. In over 200 publications (in just 15 years) spanning collaborations with nearly 70 mathematicians, he has established himself as a major player in the disparate fields of harmonic analysis, partial differential equations, number theory, random matrices, and more. He has made deep contributions to the development of additive combinatorics through a blend of harmonic analysis, ergodic theory, geometry and number theory, establishing this field as central to the modern study of many mathematical subjects. This work has led to extraordinary breakthroughs in our understanding of the distribution of primes, expanders in groups, and various questions in theoretical computer science. For example, Green, Tao, and Ziegler have proved that any finite set of linear forms over the integers, of which no two are linearly dependent over the rationals, all take on prime values simultaneously infinitely often, provided there are no local obstructions.

**Horng-Tzer Yau**

*Harvard University*

Horng-Tzer Yau is one of the world’s leading probabilists and mathematical physicists. He has worked on quantum dynamics of many-body systems, statistical physics, hydrodynamical limits, and interacting particle systems. Yau approached the problems of the quantum dynamics of many-body systems with tools he developed for statistical physics and probability. More recently, he has been the main driving force behind some stunning progress on bulk universality for random matrices. With Laszlo Erdős and others, Yau has proven the universality of the local spectral statistics of random matrices, a problem that was regarded as the main challenge of random matrix theory. This argument applies to all symmetry classes of random matrices. In the special Hermitian case, Terence Tao and Van Vu proved bulk universality concurrently. Yau’s work has been extended in many directions, for instance in his recent results on invariant beta ensembles with Paul Bourgade and Laszlo Erdős.

**Sanjeev Arora**

*Princeton University*

Sanjeev Arora has played a pivotal role in some of the deepest and most influential results in theoretical computer science. He started his career with a major contribution to the proof of the PCP theorem, widely regarded as the most important result in complexity theory in the last 40 years. The PCP theorem states roughly that every proof, of any length, can be efficiently converted into a special format, in which correctness can be verified with high probability by reading small parts of it. The PCP theorem revolutionized our understanding of optimization problems and opened new directions in coding, cryptography and other areas. Arora is also known for his breakthroughs in approximation algorithms, having solved longstanding open problems. Notable examples include his algorithms for the Euclidean traveling salesman problem and for the sparsest cut in a graph. Arora has made important contributions on many other topics, including the unique games conjecture (a conjectured strengthening of the PCP theorem) and the power and limitations of hierarchies of linear and semidefinite programs.

**Shafrira Goldwasser**

*Massachusetts Institute of Technology*

Shafi Goldwasser has had tremendous impact on the development of cryptography and complexity theory. Starting with her thesis on “semantic security”, she laid the foundations of the theory of cryptography. She created rigorous definitions and constructions of well-known primitives such as encryption schemes (both public and private key versions) and digital signatures, and of new ones that she introduced, such as zero-knowledge interactive proof systems invented with Micali and Rackoff. Continuing her work on interactive proofs which allow a probabilistic polynomial time algorithm to verify mathematical proofs via interaction with a powerful prover, Shafi and her co-authors extended the notion of interactive proofs to two-prover systems. The original motivation was cryptographic, but they turned out to be of great significance in complexity theory, paving the way to the equivalent formulation of PCP (probabilistically checkable proofs). The expressive power of two-prover systems is huge (non-deterministic exponential time). furthermore, Shafi and her co-authors showed the connection between a scaled down variant of these systems and the hardness of approximation results for NP-hard problems, which led to the PCP theorem. On the algorithmic front, a problem of great significance is that of recognizing (and generating) prime numbers. Shafi and Kilian designed efficient probabilistic primality provers, which output short proofs of primality, based on the theory of elliptic curves. Together with Goldreich and Ron, Shafi originated the field of combinatorial property testing, devising a class of sub-linear algorithms to test properties in dense graphs.

**Russell Impagliazzo**

*University of California, San Diego*

Russell Impagliazzo has made many deep contributions to cryptography and complexity theory. Russell and collaborators showed that one-way functions exist if and only if pseudorandom generators exist. In other words, one can generate sequences of bits for which it is computationally hard to predict the next bit with accuracy much better than random guessing if and only if there are easy-to-compute functions that are hard to invert on the average. Russell also showed that there are worlds in which certain cryptographic primitives are strictly inequivalent. For example, there are worlds where one-way functions exist but public-key encryption is not possible. One of Russell’s major contributions in complexity theory is the exponential-time hypothesis and its implications. The hypothesis states that there are problems where it is hard to speed up the brute-force solution even by a small amount. Russell helped establish the first complete problem for this class. In joint work with Avi Wigderson, Russell showed that if there are problems in exponential time that require exponential-sized circuits to solve, then any efficient algorithm that uses randomization has an equivalent, efficient one that does not.

**Jon Kleinberg **

*Cornell University*

Jon Kleinberg is noted for his creativity, intellectual ability, research scholarship, diversity of research interests and the impact of his work. He is best known for his contributions in establishing the computational foundations for information retrieval and social networks. His information retrieval work includes the use of link analysis (e.g., hubs and authorities) for ranking, classification and identifying web communities, the web as a graph, and understanding the success of latent semantic analysis. His work in algorithmic social networks (a field that he can be said to have started) includes the understanding of “small worlds” and decentralized search, analysis of bursty streams and influence spread in social networks. Kleinberg has done work in many other fields, including approximation algorithms, communications networks, queuing theory, clustering, computational geometry, bioinformatics, temporal analysis of data streams, algorithmic game theory, online algorithms and distributed computing. His influence is augmented by popular papers in Science and Nature and by two widely used texts, one with Tardos, Algorithm Design, and one with Easley, Networks, Crowds, and Markets: Reasoning about a Highly Connected World.

**Daniel Spielman**

*Yale University*

Daniel Spielman’s work has been important to three distinct research communities: theoretical computer science, applied mathematics, and operations research. His work on smoothed analysis of linear programming provides mathematical justification for why the simplex method to solve problems works well in practice even though worst-case analysis shows that there are instances in which it takes exponential time. A small random perturbation converts any linear programming instance into one that, with high probability is solved efficiently by the simplex algorithm. Similar perturbation results hold for many other problems and provide an alternative to worst-case analysis, which may be too pessimistic. His codes based on expander graphs achieve near-optimal rate and nearly linear time encoding and decoding algorithms. In joint work with Teng, Spielman gave a method of preconditioning a Laplacian matrix A, which yields a near-linear-time algorithm for solving the system Ax = b. This leads to highly efficient algorithms for circuit analysis and network flow computations.

**Igor Aleiner**

*Columbia University*

Igor Aleiner is an influential leader of condensed matter theory research, renowned both for his fundamental contributions to our understanding of the quantum mechanical interplay of electron-electron interactions and disorder in condensed matter systems (in particular many-body localization) and for the theoretical power displayed in his tour de force calculations. He has used a variety of quantum field theoretic and random matrix methods to obtain profound results in the theory of quantum chaos, the study of mesoscopic fluctuation effects in interacting electron systems, the theory of transport in interacting disordered systems, and the properties of graphene.

**Michael Brenner**

*Harvard University*

Michael Brenner is a versatile theoretical physicist whose diverse contributions involve collaborations with biologists, physicists, and engineers from a variety of subfields. His work seamlessly integrates analytical and computational approaches to solve problems ranging from fundamental issues in fluid mechanics to engineering design to the evolution of protein functionality and from the aerodynamics of whale flippers to the ejection of fungal spores. He is known for generating creative and original questions and answers. Particularly noteworthy are his achievements in understanding the singularities and nonlinearities that control how droplets, jets and sheets of fluid change shape and break up. His work in this area has potential impact for optimizing devices ranging from inkjet printers to cell sorters. His research has also led to the development of general methods for simplifying the dynamical models of many coupled oscillators that arise in contexts such as atmospheric chemistry.

**Sharon Glotzer**

*University of Michigan*

Sharon Glotzer is a leader in the use of computer simulations to understand how to manipulate matter at the nano- and meso-scales. Her work in the late 1990s demonstrating the nature and importance of spatially heterogeneous dynamics is regarded as a breakthrough. Her ambitious program of computational studies has revealed much about the organizing principles controlling the creation of predetermined structures from nanoscale building blocks, while her development of a conceptual framework for classifying particle shape and interaction anisotropy (patchiness) and their relation to the ultimate structures the particles form has had a major impact on the new field of “self-assembly’’. Glotzer recently showed that hard tetrahedra self-assemble into a quasicrystal exhibiting a remarkable twelve-fold symmetry with an unexpectedly rich structure of logs formed by stacks of twelve-member rings capped by pentagonal dipyramids.

**Matthew Hastings**

*Duke University*

Matthew Hastings’ work combines physical insight and mathematical power to make profound contributions to a range of topics in physics and related fields. His Ph.D. thesis produced breakthrough insights into the multifractal nature of diffusion-limited aggregation, a problem that had stymied statistical physicists for more than a decade. Hastings’ recent work has focused on proving rigorous results on fundamental questions of quantum theory, including the stability of topological quantum order under local perturbations. His results on area laws and quantum entanglement and his proof of a remarkable extension of the Lieb-Schulz-Mattis theorem to dimensions greater than one have provided foundational mathematical insights into topological quantum computing and quantum mechanics more generally. Hastings resigned his Investigatorship in 2013 to move to Microsoft Research.

**Chris Hirata**

*California Institute of Technology*

Chris Hirata is an outstanding young cosmologist and astrophysicist whose research ranges from purely theoretical investigations to original data analysis. He is known for his sophisticated analysis of radiative transfer through the epoch of reionization. He has also shown that primordial dark matter fluctuations can impact contemporary observations. His work with experimental and observational groups on systematizing the extraction of cosmological data from cross correlation of different extragalactic surveys is having an important impact on precision cosmology.

**Charles Kane**

*University of Pennsylvania*

Charles Kane and co-workers showed, extending earlier work by Thouless and collaborators, that the electronic band structures of all crystals could be classified in terms of the momentum space topology of the electronic states, and that as a consequence there exist protected states at interfaces between topologically nontrivial crystals and topologically trivial crystals. Along with related work by Shou-Cheng Zhang and others, Kane’s results have created a large and vibrant research field focused on the search for and measurement of topologically nontrivial materials, including materials that are topologically nontrivial as a result of broken symmetries. Kane’s recent work has turned towards applications for example the use of interfaces between topological insulators and ordinary superconductors to achieve a solid-state realization of Majorana fermions and the exploration of possible applications of these excitations in topological quantum computing.

**Hirosi Ooguri**

*California Institute of Technology*

Hirosi Ooguri is a mathematical physicist and string theorist of exceptional creativity and breadth. His work on Calabi-Yau manifolds has yielded important new insights into the D-brane structures crucial to string theory, while his work on the relationship of supersymmetric gauge theories to string theory and to gravity has fostered the rapid development of the AdS/CFT correspondence, which relates quantum properties of gauge theories to solutions of higher-dimensional classical field equations in the presence of black holes and curved space-time. He is perhaps best known for his innovations in the use of topological string theory to compute Feynman diagrams in superstring models.

**Frans Pretorius**

*Princeton University*

Frans Pretorius has made seminal contributions to the numerical solution of the equations of general relativity, in particular inventing a new computational scheme based on harmonic decomposition of the Ricci tensor, which is now a textbook method in the field. Thanks in large part to Pretorius’ innovations, accurate computer simulations of such general relativistic phenomena as the merger of two black holes have become possible for the first time after several decades of effort. These results enable the calculation of expected gravitational-wave signals that may be detected by present or planned gravitational wave observatories. Pretorius has also contributed to mathematical issues in general relativity such as the no-hair theorem in higher dimensions and the Gregory-Laflame instability of black strings.

**Eliot Quataert**

*University of California, Berkeley*

Eliot Quataert is an outstanding theoretical astrophysicist whose research combines many areas of physics, including gas dynamics, plasma physics, radiative transfer and nuclear physics. He is also known as a particularly effective mentor of students and postdocs. He has made fundamental contributions to the theory of astrophysical turbulence and transport properties in hot plasmas, as well as to stellar and black-hole astrophysics.