FY2026

Principal Investigators

Camillo De Lellis, IBM von Neumann Professor, School of Mathematics
Edward Witten, Professor Emeritus, School of Natural Sciences

Project Summary

The rapid advances in artificial intelligence (AI) present both opportunities and challenges for mathematical research. We believe that we are at a historic moment for our discipline. Recent events raise urgent questions about how to support the long-term prospects for deep human understanding of mathematics.

The purpose of this group is to advise AI companies on their interactions with mathematical research and with the mathematical community, including the responsible presentation and release of mathematical results. We seek to work for the best interest of mathematics and the mathematical community, and to serve as one possible channel of communication between mathematicians and the AI industry.

Advisory Group Members

• François Charles (ENS-PSL)

• Camillo De Lellis (IAS, GSSI)

• Timothy Gowers (Collège de France, Cambridge)

• Martin Hairer (EPFL, Imperial College London)

• Nikhil Srivastava (Berkeley, Simons Institute)

• Ulrike Tillmann (Oxford, INI)

• Ravi Vakil (Stanford)

• Edward Witten (IAS)

• Melanie Matchett Wood (Harvard)

More details on this initiative are available at agmai.org

Principal Investigators

Wei Ho, Visiting Professor, School of Mathematics
Ishan Levy, Member, School of Mathematics

Duration

July 2026 - June 2028

Project Summary

The past few decades have witnessed a revolution in our understanding of the distributions of invariants of fundamental objects in number theory and arithmetic geometry. There have been major breakthroughs in long-standing problems regarding number fields, ideal class groups, and the ranks of elliptic curves. The burgeoning field of arithmetic statistics now integrates tools from a vast mathematical landscape—including algebraic topology, algebraic geometry, representation theory, dynamics, and combinatorics—to harness randomness in pursuit of precise asymptotic results. 

By uniting experts across diverse subfields, this five-day June 2027 IAS workshop will foster deep interdisciplinary collaboration to catalyze the next generation of progress in this important discipline. This convening and subsequent sessions will facilitate the exchange of recent discoveries and establish the foundation for collaborative breakthroughs.

Principal Investigator

Elon Lindenstrauss, Professor, School of Mathematics

Duration

July 2026 - June 2027

Project Summary

Mean dimension is a topological invariant used to measure the size or complexity of infinite-dimensional dynamical systems. It is related to bandwidth and rate distortion - two basic notions in information theory. Mean dimension is also connected to topical themes in the classification of C* algebras.

This activity will involve short-term and medium-term academic visits to IAS by distinguished scholars, who will engage with faculty and IAS members interested in the area. Research on mean dimension and its many uses will be conducted, with a focus on exploring new connections, including those related to information theory and analog coding. 
 

Principal Investigators

Jim Stone Professor, School of Natural Sciences 
Mor Rozner, University of Cambridge  

Duration

July 2026 - June 2028

Project Summary

Astrophysical dynamics is a vast and interdisciplinary field that spans multiple scales, systems, and environments, which, while they may look different, can be described using similar physical principles and techniques. From the motion of planets and stars to the behavior of galaxies and black holes, dynamical processes lie at the heart of our understanding of the universe. The broad nature of dynamics requires an interdisciplinary approach, combining analytical methods, numerical simulations, and interdisciplinary insights drawn from diverse fields such as mathematics, plasma physics, climate science, and fluid dynamics. The interplay between these disciplines highlights the need for a comprehensive approach to studying astrophysical dynamics.  

This workshop to be held at IAS in July 2027 seeks to bring together leading experts and early-career researchers to establish a common foundation of understanding and collaboratively explore cutting-edge research in dynamics. By fostering discussion, collaboration, and knowledge exchange, the event aims to bridge gaps between different areas of expertise.   

Principal Investigators

Nicola Di Cosmo, Luce Foundation Professor in East Asian Studies, School of Historical Studies
Dominic Sachsenmaier, Göttingen University

Duration

July 2026 - June 2031

Project Summary

Under the joint stimulus of intellectual curiosity and funding available for interdisciplinary projects, historians and scientists have been increasingly engaged in collaborative work, ranging from small clusters to large consortia. The same collaborations, however, have also revealed limits inherent in the encounter between entirely different approaches to knowledge, stifling progress. Much of the difficulties experienced in collaborative work are due to insufficient attention to key methodological aspects as well as poor understanding of epistemological differences in particular across the humanities–natural sciences divide. This project, which focuses on developing a “lexicon” of concepts seen as foundational to the expansion of approaches to the past, aims to elevate the level of dialogues across the humanities, social sciences, and natural sciences to reach a better understanding of the respective research premises, strategies, and methods.

This collaborative project has two overarching goals, both of which involve the exploration and comparison of conceptual lexica across disciplinary and geopolitical boundaries. The first is to identify, define, and compare key concepts widely used for the investigation, reconstruction, and interpretation of the human past across different intellectual traditions and academic disciplines. The second is to explore how the past, historical consciousness, and national narratives of history (often embedded in educational programs and propagated through various media) contribute to the formation of ideas of civilization and the mobilization of historical narratives for political purposes.

Principal Investigators

Irit Dveer Dinur, Betsey Lombard Overdeck Theory of Computing Professor, School of Mathematics
Amir Shpilka, Tel Aviv University

Duration

July 2026 - June 2028

Project Summary

This project will support a conference to commemorate Avi Wigderson’s 70th birthday and retirement, together with 30 years of the Computer Science and Discrete Mathematics program (CSDM) at IAS. The conference will honor both Avi’s extraordinary scientific legacy and his transformative role in shaping the intellectual community around theoretical computer science and discrete mathematics at IAS. By bringing together researchers from multiple generations—sharing common intellectual roots but pursuing diverse and rapidly advancing research areas—the conference seeks to foster new collaborations and identify emerging frontiers in the field.  

Avi Wigderson has made foundational contributions across an exceptional range of areas in theoretical computer science and mathematics. His work has had a profound impact on complexity theory broadly, and especially on cryptography, circuit and proof complexity, communication complexity, pseudorandomness, and expander graphs; in recent years, he has also opened deep and unexpected connections to invariant theory. These contributions have shaped major research directions and influenced generations of mathematicians and theoretical computer scientists.