Projects

Artificial Intelligence (AI) has the potential to accelerate scientific research and discovery in many areas of mathematics and physics. In the area of quantum physics, for instance, AI algorithms are being used to model complex quantum systems, suggest new quantum experiments, optimize quantum computations, and aid in understanding quantum gravity and chaos.

This collaborative project explores connections between AI and machine learning with quantum information and quantum gravity. In particular, some modern ideas of quantum gravity involve mathematical structures that are similar to the concepts that underlie AI techniques: tensor networks to represent quantum states and computational neural networks to represent probability distributions, locality in physics and the idea of sparse auto encoders in AI, and the role of geometry in representing information more generally.  

Principal Investigator:

^{Juan Maldacena, Carl P. Feinberg Professor, School of Natural Sciences}

Co-Investigator:

^{Xiaoliang Qi, Member, School of Natural Sciences}

The objective of this week-long workshop, to be held at the IAS in June of 2026, is to enable established and newly initiated research groups to work collaboratively on current research projects in various branches of several complex variables and adjacent fields. It will offer a platform that encourages continued collaboration and mentoring, and strengthens the community in the field of several complex variables.

The workshop will bring together junior and senior participants to work on pre-defined research projects. Participants will be assigned to project groups and will spend their time at the workshop engaged in focused and substantive research. In order to promote the exchange and interaction of ideas and methods, each research group will have two experts as co-leads and up to three participants who are not necessarily experts in the topic of their research group. The topics to be explored include holomorphic mapping theory, complex dynamics in several variables, Cauchy-Riemann geometry, operator theory, and metric geometry. This workshop is jointly supported by the Minerva Research Program and the IAS. The Nelson Center’s funding will be available as a backstop should additional support for the workshop be required.

Principal Investigator:

^{Wei Ho, Visiting Professor, School of Mathematics}

Co-Investigators:

^{Anne-Katrin Gallagher, Gallagher Tool & Instrument, Redmond, WA
Purvi Gupta, Indian Institute of Science, Bangalore, India
Liz Vivas, Ohio State University}

The Arabic Gospel texts are among the earliest sustained efforts to render the Christian scriptures in the language of Islam—a process that involved not only translation but also deep hermeneutic and theological negotiation between divergent Middle Eastern Christian groups. While traditionally viewed as a late or derivative tradition, the Arabic Gospels occupy a pivotal position in the development of Christian scriptural transmission in the Near East on the eve of the advent of Islam.

This project reframes the Arabic Gospel texts not as marginal translations—as they have been treated by academic biblical scholarship thus far—but as central witnesses to the vibrant processes of interlingual and intercultural engagement that shaped the Christian Middle East in dialogue with its Greek, Syriac, and Coptic antecedents. By integrating philology, manuscript studies, translation theory, and digital tools, this interdisciplinary project aims to produce a new scholarly paradigm for understanding the Arabic Gospels.

Principal Investigator:
 
^{Sabine Schmidtke, Professor, School of Historical Studies}

Co-Investigators:

^{Sofía Torallas Tovar, Distinguished Visiting Professor, School of Historical Studies}

^{George Kiraz, Research Associate, Nelson Center for Collaborative Research}

 

Vannevar Bush’s influential 1945 report “Science–The Endless Frontier” advocated for “pure science”—a model of government funding in exchange for scientific autonomy from political direction, with the expectation of broad social benefit. This became the dominant framework for American science policy. Seventy-five years later, this interdisciplinary project examines the historical evolution and contemporary crisis of research policy in the United States, with particular attention to the social contract between scientific institutions, democratic governance, and the public.

The project will establish an interdisciplinary research network bringing together researchers and practitioners with a broad range of disciplinary expertise, methodological approaches, and theoretical perspectives to develop scholarly frameworks for analyzing models of public science. This network will launch with two convenings: “Re-Envisioning Democratic Accountability and Science” (December 2025) and “Enacting Public Science” (Spring 2026). The first workshop will critically assess the documents that underwrite current U.S. science policy, particularly Bush’s “Science–The Endless Frontier.” The second will address questions vital to developing policy frameworks for a robust, publicly accountable research ecosystem.

Principal Investigator:

^{Alondra Nelson, Harold F. Linder Professor, School of Social Science}

Co-Investigator:

^{Jenny Reardon, University of California, Santa Cruz}

Mathematical structures known as expanders have played a crucial role in computer science, coding theory, and pure mathematics. While expander graphs are well understood, high dimensional expanders, which are generalizations of expander graphs to higher dimensions, remain mysterious. For instance, many important properties of expander graphs have been proven to exist using the random graph model, but high dimensional expanders are only known to exist via very sophisticated group theoretic constructions.

This project explores new approaches to understanding high-dimensional expanders through randomness—a method that has been immensely successful in graph theory but remains largely unexplored in higher dimensions. By bringing together expertise in high-dimensional expansion and random covers, this collaborative project has the potential to bridge different areas and open up new directions in mathematics. Given the wide-ranging applications of random structures such as graphs, having a theory of random covers for high dimensional expanders is expected to have a lasting impact.

Principal Investigator:

^{Irit Dveer Dinur, Betsey Lombard Overdeck Theory of Computing Professor, School of Mathematics}

Co-Investigator:

^{Doron Puder, Kovner Member, School of Mathematics}

Transmission of Magical Knowledge is a long-standing project, led by the University of Chicago, that brings an international group of scholars together to analyze, reedit, translate, and study the Greco-Egyptian magical handbooks that have been preserved on papyrus. In 2022, the team published The Greco-Egyptian Magical Formularies (GEMF) Volume 1, which contained new editions and translations of 54 magical handbooks or fragments of them, and the award-winning The Greco-Egyptian Magical Formularies: Libraries, Books and Individual Recipes, a volume of essays on the materiality and scribal features of the magic formularies. 

The project will continue this work over the next three years (2026–28) to publish the second volume of GEMF and then focus on the third volume of GEMF, which will complete the reedition, translation, and commentary of the 88 extant Greco-Egyptian magical formularies from Egypt. Other activities include organizing international conferences on the drawings in the magical handbooks and on voces magicae, the unintelligible “magical names” and ancient abracadabra words that proliferate in the magical handbooks.

Principal Investigator:

^{Sofía Torallas Tovar, Distinguished Visiting Professor, School of Historical Studies}

Co-Investigator:

^{Christopher Faraone, University of Chicago}

This three-day workshop aims to explore quantum aspects of black holes and spacetimes. Jointly supported by the Princeton Center for Theoretical Science, the Princeton Gravity Initiative, and IAS, the event will involve 175 participants from diverse fields. Specific topics will include quantum information applied to gravity, and quantum aspects of black holes and other interesting spacetimes such as de-Sitter.  

The workshop format, with structured talks from leading experts and open-ended dialogue, is intended to facilitate the deep, focused work needed to analyze this important topic in-depth, understand its associated problems, and move the research forward. More details on the event are available here. 

Principal Investigator:

^{Juan Maldacena, Carl P. Feinberg Professor, School of Natural Sciences}

Co-Investigators:

^{Netta Engelhardt, Massachusetts Institute of Technology  
Jonah Kudler-Flam, Marvin L. Goldberger Member, School of Natural Sciences 
Henry Lin, Princeton University 
Gautam Satishchandran, Princeton University 
Edward Witten, Professor Emeritus, School of Natural Sciences}

The al-Khanji Archive, documenting the influential role of the Syrian-Egyptian al-Khanji family in the Arabic manuscript trade and publishing in the early 20th century, is a unique resource for manuscript studies, print history, and intellectual networks. Acquired by the American University in Cairo through collaboration with five North American institutions, the archive contains thousands of documents, including letters, correspondence with prominent scholars, and business records detailing the family’s pivotal involvement in the translocation of Arabic manuscripts to major libraries in Europe and North America. This archive offers unprecedented insights into manuscript provenance, the publishing landscape, and the intellectual exchange between the Arab world and the West during this period.

The project will involve a series of activities, starting with a one-week workshop in Cairo in January 2025 to examine and digitize prioritized portions of the archive. Over the next year, an inventory of Khanji’s publications will be prepared, alongside an analysis of his editorial practices, culminating in a scholarly volume to be published by the American University in Cairo Press. Additionally, the project will create a digital portal to support future research, including a crowdsourced database of Khanji manuscripts. Collaborative conferences and workshops will engage scholars in advancing the study of this rich archive, contributing to a deeper understanding of the cultural and intellectual history of the Arab world in the early 20th century.

Principal Investigator:
 
^{Sabine Schmidtke, Professor, School of Historical Studies}

Co-Investigators:

^{Garrett Davidson, College of Charleston
Rana Mikati, College of Charleston}

This two-day workshop aims to explore the cognitive foundations of higher-level mathematics. Jointly supported by Princeton University and IAS, the event will involve 10–15 participants from diverse fields such as mathematics, philosophy, psychology, and education. The focus will be on understanding the psychological aspects of mathematical judgment, explanation, and concept development. Specific topics will include what makes a proof satisfying, how mathematical explanations relate to proofs, and what attributes make a mathematical concept valuable or useful. The workshop seeks to bridge these cognitive aspects with mathematical practice, offering deeper insights into how human cognition influences mathematical reasoning.

These issues are especially relevant as AI advances in automated reasoning for mathematical research. While machine-generated proofs can be produced, many are incomprehensible to humans. This workshop aims to address how to select proofs that best support human intuition and spark interdisciplinary discussions. The workshop format will focus on open-ended dialogue rather than structured talks, serving as a first step toward building a scholarly community dedicated to the cognitive science of mathematical understanding.

Principal Investigator:

^{Akshay Venkatesh, Robert & Luisa Fernholz Professor, School of Mathematics}

Co-Investigator:

^{Tania Lombrozo, Princeton University}

Computational methods are essential for addressing complex problems in astrophysics, but the diversity of high-performance computing systems and the complexity of astrophysical modeling pose significant challenges in research software development. This interdisciplinary task requires expertise in physics, applied mathematics, and computer science. Recently, the team secured federal funding over three years for the development of advanced astrophysical research software, with a portion dedicated to supporting postdoctoral researchers at IAS. Additionally, the team has been granted over 3 million node hours on exascale supercomputers.

The initiative offers non-stipendiary appointments at IAS for postdocs from collaborating institutions to facilitate frequent interactions. The team also proposes an annual research meeting at IAS, open to the IAS community, to discuss computational astrophysics and scientific software development. A one-week collaborative workshop will be held each year, and a small summer school on computational astrophysics for graduate students will be explored as a potential event at IAS.

Principal Investigator:

^{James Stone, Professor, School of Natural Sciences}

This collaborative research initiative examines artificial intelligence through three critical and interconnected lenses: applications, policy, and geopolitics. It brings together experts from the social sciences, sciences, and humanities; policymaking and government; and civil society and industry to bridge fragmentation in the AI research ecosystem and to examine the material foundations and theoretical frontiers presented by the expansion of AI development. Through research workshops, working groups, and cross-school seminars, the initiative will develop frameworks for understanding the societal impact of AI for democracy through the exploration of its intersection with quantum computing, its reliance on critical minerals, and its implications for policy, governance, and geopolitical competition.

The collaborations will result in a range of outputs, including research publications, policy recommendations, and strategic agendas that bridge traditional disciplinary and sectoral divides, challenge existing power dynamics in AI development, and propose new methodologies for understanding and governing global AI systems. Key activities include the AI Policy and Governance Working Group's research development and policy research, a quantum science and society seminar series coinciding with the UN's International Year of Quantum Science and Technology, and a research workshop examining critical mineral supply chains. This integrated approach aims to establish new paradigms for understanding and governing AI systems that account for their material and political prerequisites, their technological possibilities and limits, and their social and economic power.

Principal Investigator:

^{Alondra Nelson, Harold F. Linder Professor, School of Social Science}

This project establishes a research group focused on the recent history of mathematics. Mathematics has undergone multiple transformations in its nature, production, validation, and dissemination over the course of the 20th and 21st century. These transformations reflect not only the internal dynamics of the field, but also the evolution of institutions, technologies, and societies. We will therefore take a broad approach in examining those changes, bringing together mathematicians, philosophers, and historians to integrate cultural, intellectual, and social histories.

This initiative continues a tradition of engagement between mathematics and the humanistic disciplines at the Institute for Advanced Study, exemplified by Otto Neugebauer, André Weil, Hermann Weyl, and many others. The project will also engage with Princeton University’s strong community of historians of science and mathematics, rendering it well-positioned to become a global leader in the history of modern mathematics.

The project will commence with a pilot workshop in the spring of 2026 to raise awareness and inform future decisions.

Principal Investigators:

^{Helmut Hofer, Hermann Weyl Professor, School of Mathematics
Myles Jackson, Albers-Schönberg Professor in the History of Science, School of Historical Studies
Akshay Venkatesh, Robert & Luisa Fernholz Professor, School of Mathematics}

The IAS Gravitational Wave (GW) collaboration, founded in 2018, developed the first independent pipeline to analyze data from the LIGO observatory, from raw strain data to astrophysical interpretation. The group's work has been influential, with several innovations adopted by the broader scientific community, including the LIGO scientific collaboration. Despite many Members moving to other institutions, the collaboration continues to be recognized as the "IAS group." It has contributed over 20 publications, accumulated more than 1,500 citations, and earned numerous awards, including two Sloan fellowships and multiple NSF and BSF grants. Ongoing contributions from IAS include computational resources and continued support for the collaboration’s members, which helps attract new talent.

This project aims to elevate the IAS GW collaboration by fostering broader interactions and exploring new topics in gravitational wave astronomy. As the group has expanded and its researchers have become more geographically dispersed, the virtual center will provide tools to enhance collaboration and generate new transformative ideas. The center will also broaden its scope to include emerging areas, such as pulsar timing arrays and the Laser Interferometer Space Antenna (LISA) mission. Activities will include regular online talks and hackathons, focused collaboration support for small projects, an annual in-person meeting, and joint postdoctoral positions between IAS and partner institutions like University of California, Santa Barbara and the Weizmann Institute. These initiatives will strengthen connections within the gravitational wave community and encourage future collaborations with leading groups at Johns Hopkins University and the Center for Computational Astrophysics in New York.

Principal Investigator:

^{Matias Zaldarriaga, Richard Black Professor, School of Natural Sciences}

Co-Investigators:

^{Tejaswi Venumadhav Nerella, University of California Santa Barbara
Hang Yu, Montana State University
Barak Zackay, Weizmann Institute of Science}

The project, “Interactions of Topology and Geometry,” aims to advance research on fundamental open questions at the intersection of these two mathematical fields. The project brings together a group of established collaborators with a strong track record in topology and geometry, focusing on conjectures and problems that link geometric constraints with topological properties. Key areas of investigation include the sectional and Ricci curvature, singularities of nonlinear harmonic and holomorphic maps, and extensions of classical theorems in metric geometry. The research efforts will contribute both to theoretical advancements and to the development of educational resources for graduate students.

Specific project activities include work with Elia Bruè (Università Bocconi) and Daniele Semola, which explores the relationship between nonnegative sectional and Ricci curvature and fundamental group structure. Collaboration with Daniele Valtorta (Università degli Studi di Milano-Bicocca) focuses on understanding the dimension of singular sets in nonlinear harmonic and holomorphic maps, which play a crucial role in defining moduli spaces and their topological implications. Joint efforts with Bennett Chow (University of California, San Diego) and Wenshuai Jiang (Zhejiang University) will produce books on Ricci curvature and nonlinear harmonic maps, serving as foundational texts for graduate students. Additionally, work with Jeffrey D. Streets (University of California, Irvine) and Ruobing Zhang (University of Wisconsin–Madison) will seek to extend known rigidities in bounded curvature to the context of torsion. Through these collaborations, the project aims to make significant contributions to the mathematical understanding of topology and geometry.

Principal Investigator:

^{Aaron Naber, Professor, School of Mathematics}

Since 2021, IAS Faculty and Staff have established strong relationships with various Lunaape (Lenape or Delaware) Nations, working alongside Princeton University on a series of annual events aimed at preserving and revitalizing Lunaape language and history. These include the Munsee Language and History Symposium, the Munsee Story Evening, the Lunaape Language Camp, and the recent inaugural Unami Symposium. Collaborations have expanded through the Mellon Foundation-funded Hidden Stories project, focusing on research involving museums holding Native American artifacts across the U.S., Germany, and the U.K. Building on these initiatives, Suzanne Conklin Akbari, Professor in the School of Historical Studies, is launching a three-year project, “Knowledge on Lunaape Land,” to deepen and integrate Indigenous knowledge with academic research in fields beyond historical studies, including social sciences and natural sciences. 

This project acknowledges the evolving place of Indigenous studies within academia, a field that bridges multiple disciplines but often faces challenges in securing research-oriented positions, especially in the sciences. At IAS, the focus will be on facilitating pure research that respects and centers traditional Indigenous knowledge. The initiative will see Lunaape researchers collaborating with academic specialists, featuring in-residence researchers from Munsee- and Unami-speaking Nations. The project aims to create sustainable research models that extend beyond curriculum-based collaborations, with a final workshop to shape future funding requests for long-term impact and growth.

Principal Investigator:

^{Suzanne Conklin Akbari, Professor, School of Historical Studies}

Lyttos, a prominent city of ancient Crete, flourished during the Classical and Hellenistic periods but was destroyed by the Knossians in 221/20 B.C.E. and later rebuilt. Under Roman rule, the city thrived, particularly due to the export of its wine, which was highly sought after, as evidenced by amphoras found in Pompeii marked as containing "Lyttian wine." The city's aqueduct is one of the best-preserved ancient constructions on the island, while its large Roman theater was documented by Onorio Belli in the 16th century. Excavations at the site were initially limited but have been renewed since 2021 under the Athens Archaeological Society’s auspices. Significant findings include a fully excavated bouleuterion (town hall), a shrine dedicated to the emperor, and a variety of sculptures, pottery, and marble fragments, which are currently stored for further study.

The ongoing excavation project involves an international team of experts in archaeology, history, epigraphy, and related fields, and has been supported by various external sponsors. However, current support only covers excavation costs, not the subsequent study and publication of the findings. For the study phase, from July 2025 to June 2026, archaeologists will study architectural fragments, pottery, and small finds, in conjunction with a photographer, project administrator, and equipment for pottery analysis. Additionally, restoration of a Trajan statue will be a component of the research project and publication of the site’s discoveries.

Principal Investigator:

^{Angelos Chaniotis, Professor, School of Historical Studies}

This initiative aims to establish a groundbreaking interdisciplinary research hub, uniting experts in mathematics, particle physics, and cosmology to develop a novel framework for understanding the universe at all scales. Building on the vision of the ERC Synergy Grant UNIVERSE+, the MPC will foster collaboration between leading institutions. By bringing together world-class researchers, postdoctoral scholars, and students, the Center will create an environment conducive to deep theoretical breakthroughs, bridging gaps between fundamental physics and advanced mathematics. Key activities will include postdoctoral hires, focused workshops, summer schools, and international collaboration visits, ensuring a dynamic exchange of ideas across disciplines and geographic boundaries.

In addition to advancing scientific discovery, the Center will play a vital role in fostering young talent by offering a dedicated Ph.D. program to train the next generation of researchers fluent in this emerging interdisciplinary field. The project will provide a critical platform for cross-disciplinary research that is essential for addressing some of the most profound questions in cosmology and particle physics. Through its commitment to excellence and collaboration, the project will serve as a catalyst for transformative scientific advancements and intellectual synergy.

Principal Investigators:

^{Nima Arkani-Hamed, Gopal Prasad Professor, School of Natural Sciences
Matias Zaldarriaga, Richard Black Professor, School of Natural Sciences}

Co-Investigators:

^{Daniel Baumann, National Taiwan University and University of Amsterdam
Johannes Henn, Max Planck Institute for Physics}

This project aims to address the fundamental challenge of modeling multi-scale physics in both astrophysics and climate science, where structures and dynamics span vastly different length and time scales. In astrophysics, processes such as star formation and black hole-driven outflows influence structures across ten orders of magnitude, while in climate science, phenomena like cloud formation and ocean-atmosphere interactions must be modeled at scales far smaller than global atmospheric dynamics. Currently, sub-grid models—used to approximate unresolved physics—are developed independently within each discipline. However, given the overlap in underlying physics, cross-disciplinary collaboration could lead to significant advances in both fields. This initiative seeks to bring together experts from astrophysics and climate science to exchange methodologies, refine existing modeling approaches, and develop more effective sub-grid models applicable to both domains.

To facilitate this collaboration, a one-week workshop will be hosted at the Institute for Advanced Study during the 2025–26 academic year, leveraging the strong presence of astrophysics and climate science researchers at IAS and Princeton University. The Nelson Center will serve as a hub for local discussions, while international experts from institutions such as MIT and Caltech will be invited to participate. The workshop will serve as an initial exploratory effort. While the project is planned as a one-year initiative, its outcomes will inform the development of a more extensive research collaboration in the future, aiming to bridge the gap between these two disciplines and accelerate progress in multi-scale modeling.

Principal Investigators:

^{James Stone, Professor, School of Natural Sciences
Matias Zaldarriaga, Richard Black Professor, School of Natural Sciences}