Simons Collaborations in Mathematics and the Physical Sciences

Simons Collaborations in Mathematics and the Physical Sciences bring together groups of outstanding scientists to address topics of fundamental scientific importance in which significant new developments have created novel areas for exploration in the fields of mathematics, theoretical physics and theoretical computer science. See the latest Simons Collaborations Request for Applications.

Algorithms and Geometry (2014-2021)

The Simons Collaboration on Algorithms and Geometry addressed fundamental questions at the interface of mathematics and theoretical computer science.

Director

Assaf Naor

The Many Electron Problem (2014-2023)

The Simons Collaboration on the Many Electron Problem developed new ways to solve the quantum mechanical behavior of systems comprised of many interacting electrons, to revolutionize our ability to calculate and understand the properties of molecules and solids important in chemistry, physics and everyday life.

Director

Andrew Millis

Homological Mirror Symmetry and Applications (2015-2022)

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

Director

Tony Pantev

It from Qubit: Quantum Fields, Gravity, and Information (2015-2022)

“It from Qubit” was a large-scale effort by some of the leading researchers in the fundamental physics and quantum information theory communities to foster communication, education and collaboration between them, thereby advancing both fields and ultimately solving some of the deepest problems in physics.

Director

Patrick Hayden

Cracking the Glass Problem (2016-2023)

This collaboration, addressing such fundamental issues as disorder, nonlinear response and far-from-equilibrium dynamics, built upon three powerful approaches: the study of marginal stability at jamming, the mean-field theory of glasses in infinite dimension, and the dynamics of systems in complex landscapes.

The Non-perturbative Bootstrap (2016-2023)

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 The critical challenge for the 21st century is to map and understand the whole space of QFTs, including strongly coupled models. This was the main goal of the Simons Collaboration on the Nonperturbative Bootstrap.

Special Holonomy in Geometry, Analysis, and Physics (2016-2023)

This collaboration worked to 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.

Arithmetic Geometry, Number Theory, and Computation (2017-2024)

This collaboration sought to accelerate research in number theory and arithmetic geometry through the computational realization of deep theory, and to use the computational tools to probe our conceptual understanding of complex arithmetic objects.