Awardees by year

The Simons Foundation congratulates the awardees who have been selected as Simons Investigators in 2015 in mathematics, physics, theoretical computer science, mathematical modeling of living systems, and Math+X.

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

**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**

*University of California, Berkeley*

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.

### 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.