Simons Collaborations in Mathematics and the Physical Sciences

The frontier of research is now studying curves of higher genus, abelian surfaces, and K3 surfaces. Here, however, the development and implementation of practical algorithms has lagged behind the theory, and we seek to correct this imbalance. Available computational resources have reached a point where algorithms are now technically feasible. In contrast to the situation…

This collaboration, directed by Andrew Strominger of Harvard University, seeks to realize the holographic principle in (nearly) asymptotically flat spacetimes, guided by but not assuming AdS/CFT or string theory. Recent discoveries make this so-far-elusive goal plausibly within reach. More information on the collaboration’s research can be found on its website.

This collaboration, directed by Igor Klebanov of Princeton University, aims to improve our understanding of confinement in various gauge theories, including quantum chromodynamics (QCD), and to renew efforts to solve the large N QCD problem using recent developments in fundamental theory, in lattice gauge theory and in effective field theory for QCD strings.

The endeavor to understand the glassy state of matter forces us to consider deeply the seemingly simple question: what is a solid. Glass – the prototypic and ubiquitous amorphous solid – inhabits an incredibly ramified and complex energy landscape in which systems are often stranded far from equilibrium.

This collaboration, directed by Roger Blandford of Stanford University, will explore classical and quantum electrodynamics under the extreme conditions provided by compact astrophysical objects, such as neutron stars and black holes. More information about the collaboration’s research can be found on its website.

This collaboration, directed by Andrea Alù of the Advanced Science Research Center at The Graduate Center, CUNY, builds on the recent concerted realization that advanced symmetry principles can guide the design and synthesis of new metamaterials with exotic wave properties, providing tools for the design and implementation of groundbreaking functional properties and enabling extreme forms…

This collaboration, directed by Constantin Teleman of the University of California, Berkeley, brings together a group of physicists and mathematicians, working across disciplinary boundaries, to unlock the power of symmetry in its broadest, most general form.

The goals of this collaboration, directed by Amitava Bhattacharjee of Princeton University, include a modern stellarator optimization code that can exploit the full power of petascale and exascale computers, and a few optimal designs of next-generation stellarator experiments.

The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications.

Developments over the past ten years have shown that major advances in our understanding of quantum gravity, quantum field theory and other aspects of fundamental physics can be achieved by bringing to bear insights and techniques from quantum information theory. Nonetheless, fundamental physics and quantum information theory remain distinct disciplines and communities, separated by significant…

This collaboration, directed by Greg Bryan of Columbia University, aims to understand and determine the evolution and initial conditions of our universe, using observations via a Bayesian forward modeling approach.

The goal of this collaboration, directed by Svitlana Mayboroda of the University of Minnesota, is a unified understanding of wave localization, enabling the solution of some of the most compelling puzzles in modern condensed matter physics and gaining control over the behavior of waves in disordered media.

The Simons Collaboration on the Many Electron Problem brings together a group of scientists focused on developing new ways to solve the quantum mechanical behavior of systems comprised of many interacting electrons, with the goal of revolutionizing our ability to calculate and understand the properties of molecules and solids important in chemistry, physics and everyday…

Algebraic geometry is concerned with the study of the geometry of the zeroes of polynomials. It is a central topic with strong connections to all branches of mathematics. A fundamental and challenging problem in algebraic geometry is to classify all algebraic varieties. After fixing some discrete invariants, it remains to understand all continuous families with…

This collaboration, directed by Aaron Lauda of the University of Southern California, brings together a team of researchers, covering a variety of different perspectives, who can synthesize the interconnections between fields and overcome the barriers preventing progress in revealing the next generation of tools in low-dimensional topology.

Quantum field theory (QFT) is a universal language for theoretical physics, describing the Standard Model of particle physics, early universe inflation, and condensed matter phenomena such as phase transitions, superconductors, and quantum Hall fluids. A triumph of 20th century physics was to understand weakly coupled QFTs.

This collaboration, directed by Martin Olsson of the University of California, Berkeley, brings together experts in a wide variety of algebraic disciplines to explore new perfection techniques and their applications to major open problems across algebra, geometry, topology and number theory. More information on the collaboration’s research can be found on its

Our collaboration, initially consisting of 10 principal investigators and directed by Robert Bryant of Duke University, will advance the theory and applications of spaces with special holonomy and the geometric structures—calibrated submanifolds and instantons—associated with them, particularly in the two exceptional cases: spaces with holonomy G_2 or Spin(7) in 7 or 8 dimensions, respectively.

Superconductivity (SC) is a quantum phenomenon characterized by the ability to carry electric current without resistance and to expel magnetic fields. The conventional Bardeen-Cooper-Schrieffer (BCS) theory of SC, which attributes it to weak attractive interactions between low-energy fermions, was initially sufficient to explain the phenomenon. However, the discovery of high-temperature superconductors and SC in unconventional…

The Simons Observatory will join the Atacama Cosmology Telescope and the Simons Array in the high Atacama Desert in Chile to make observations of the cosmic microwave background and study how the universe began, what it is made of, and how it evolved to its current state.

This collaboration, directed by Omer Reingold of Stanford University, aims at establishing firm mathematical foundations, through the lens of computer science theory, for the emerging area of algorithmic fairness, following the example set by the revolutionary role of theory in cryptography, algorithmic economics, privacy, quantum information, computational biology, social sciences and more.

The goal of this collaboration, directed by Ashvin Vishwanath of Harvard University, is to fully develop the theory of ultra-quantum matter from fundamental characterization and classification to the design for realization and testing of ultra-quantum matter in the lab. To achieve this, the collaboration will bring together experts in condensed matter physics, high energy physics,…

This collaboration, directed by Jalal Shatah of New York University, is the first attempt for a systematic coordinated study of wave turbulence theory in a large-scale project, bringing together state-of-the-art skills in the areas of mathematics and physics, with theoretical, experimental and numerical expertise. It is a joint effort of several groups of researchers who…