The best-understood special holonomy spaces are the so-called Calabi–Yau spaces; over the past 30 years, the study of these from various viewpoints and geometry, analysis, algebra and physics has been one of the most active and influential parts of mathematics and its applications to physics. Meanwhile, the exceptional cases, which share some important features with Calabi–Yau spaces, remain the most challenging and the least understood, both mathematically and physically. Exceptional holonomy spaces are key ingredients in extracting physics from M-theory and F-theory (generalizing the role that Calabi–Yau 3-folds play in string theory), where they provide models for the extra dimensions of space. Progress in understanding the physical applications crucially depends on a better understanding of spaces, especially singular ones, with exceptional holonomy.

Advances in understanding geometric structures associated with exceptional holonomy spaces have often required insights from apparently disparate parts of the field, or from outside the field entirely. This collaboration brings together the leading mathematics researchers in the various geometric incarnations of exceptional holonomy with experts on the applications to physics. We will capitalize on several recent mathematical breakthroughs related to the geometric structures associated with exceptional holonomy spaces and also make use of powerful, new tools for analyzing singular spaces.

The Simons Foundation will support more collaborations in future years; groups interested in applying should review the Request for Applications available on our website.

]]>Quantum field theory (QFT) is a universal language for theoretical physics, describing phenomena ranging from the Standard Model of particle physics and early universe inflation to phase transitions and superconductivity in terrestrial materials. A triumph of 20th Century physics was the understanding of weakly coupled QFTs. However, weakly interacting systems represent a tiny island in theory space and do not capture many of the most interesting physical phenomena. The critical challenge for the future and the main goal of the new Simons collaboration is to map and understand the whole space of QFTs, including strongly coupled models. Meeting this challenge requires new physical insight, new mathematics, and new computational tools. The starting point is the astonishing discovery that the space of QFTs can be determined by using only general principles of symmetry and quantum mechanics. By analyzing the full implications of these general principles, one can make sharp predictions for many physical observables without resorting to approximations. This strategy is called the *bootstrap*.

The bootstrap idea has its roots in work done in the 1960s on the S-matrix approach to the strong nuclear force and reappeared in the 1970s and 1980s with the formulation of the *conformal bootstrap*, which was applied with great success to rational conformal field theories (CFTs), a special class of two-dimensional models with enhanced symmetry. The collaboration is motivated by the recent discovery of new bootstrap techniques that apply to far more general classes of QFTs and have been applied to a wide variety of seemingly unrelated problems: to perform the world’s most precise analysis of the 3-D Ising model (which describes the water-ice critical point), to constrain strongly coupled theories of physics beyond the Standard Model, to aid in classifying superconformal field theories, to derive locality and black hole thermality in models of quantum gravity, and to prove irreversibility of renormalization group flows. This is the beginning of a much larger enterprise, crossing traditional boundaries between string theory, condensed matter physics, and phenomenology, and making strong connections to modern mathematics and computer science. More information about the collaboration can be found here.

The Simons Foundation will support more collaborations in future years; groups interested in applying should review the Request for Applications available on our website.

]]>At the Story Collider, the audience hears from scientists about all the times things went wrong in their labs, but the show also presents stories from people who haven’t had a formal connection to science since high school. Storytellers have included physicists, comedians, neuroscientists, writers, actors and doctors.

The Story Collider presents its flagship show monthly in New York City and also hosts shows in Boston, Washington, D.C., and other cities across the U.S. and in the U.K. Its podcast is available on SoundCloud, iTunes and the NPR One app and will pass 5 million downloads in 2016.

]]>A meeting was recently organized by Accelerating Science and Publication in Biology (ASAPbio) to discuss the merits and drawbacks of preprints in the biological sciences. The attendees — including scientists, journal representatives and funders — published a commentary summarizing their perspectives. In June four foundations, including the Simons Foundation Autism Research Initiative, announced support for ASAPbio and its preprint plan.

In support of this initiative within the Simons Foundation, the Simons Collaboration on the Global Brain (SCGB) will now give investigators the option of including preprints in our applications and progress reports, and we will take these manuscripts into consideration during reviews.

Preprints have many advantages. They speed access to new findings and the provide an opportunity for authors to receive feedback from a larger group of scientists instead of being limited to the anonymous peer reviewers. Preprint servers have the potential to increase communication and collaboration among investigators in the SCGB.

The scientific community is concerned that posting preprints may decrease the authors’ chances of being published in the top peer-reviewed journals, increase their chances of getting scooped, or introduce low-quality data to the field. The discussion in our community, and the example from physics, has addressed many of these fears and convinced us that preprints are worth trying in the biological sciences. We recognize that certain experiments and experimental preparations raise unique questions for preprints, and these issues should be discussed further.

There are many investigators in the SCGB who already support and post preprints. We encourage you to look at the work available on preprint servers (like bioRxiv) and consider providing feedback.

]]>If your favorite number is 712, mathematician Andrew Granville will quickly compute that 712 is 2 times 356, 4 times 178, 8 times 89, or 2 times 2 times 2 times 89. “Every number has a unique way of being written down as a product of primes,” Granville says. “When we study an object in chemistry, we go to atoms; in biology, we go to DNA. For number theorists, it is prime numbers.”

Granville says prime numbers are an example of a deep mathematical idea with the potential to transform other realms of research. But he cautions that an overemphasis on practicality can be dangerous.

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