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Ana Caraiani, Royal Society University Research Fellow and professor of pure mathematics, Imperial College London, has been awarded the 2025 Ruth Lyttle Satter Prize in Mathematics by the American Mathematical Society (AMS). She has been honored for contributions to arithmetic geometry and number theory: in particular, the Langlands program.

From the citation

Ana Caraiani’s work is characterized by a combination of novel ideas and a fearlessness in the face of technical obstacles that would daunt almost any other researcher. This has enabled her to prove several fundamental theorems in the Langlands program.

In the joint paper with Scholze, titled “On the generic part of the cohomology of non-compact unitary Shimura varieties” (Annals of Math., 2024), Caraiani proved very general results about the torsion cohomology classes in non-compact Shimura varieties, strengthening the early results in their 2017 paper in the compact case. The proof is a tour de force, combining perfectoid spaces, a mastery of the trace formula, and a new theory of perverse sheaves in p-adic geometry. These results are of intrinsic interest (for example, they give the first indications of a characteristic p version of Arthur’s conjectures), but they also have many applications throughout the Langlands program. One spectacular application of these results is in her joint paper, “Potential automorphy over CM fields” (with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne, Annals of Math., 2023), which among other results proves the Ramanujan conjecture for Bianchi modular forms, a problem that had been thought of as being completely out of reach.

The Ramanujan conjecture is of analytic nature, asserting a bound on the eigenvalue of a certain differential operator, but the only way in which cases of it have been proved is via algebraic geometry. In particular, the original Ramanujan conjecture for modular forms was proved by Deligne in the 1970s, as a consequence of his proof of the Weil conjectures. However, in the case of Bianchi modular forms there is no direct relationship with algebraic geometry, and it seems to be impossible to make any direct deductions from the Weil conjectures. Langlands (also in the 1970s) suggested a strategy for proving the Ramanujan conjecture as a consequence of his functoriality conjecture. Caraiani and her coauthors’ proof of the Ramanujan conjecture for Bianchi modular forms proceeds via a variant of Langlands’ strategy, and in particular does not use the Weil conjectures.

Most recently with James Newton, in the paper “On the modularity of elliptic curves over imaginary quadratic fields” (arXiv: 2301.10509), Caraiani has improved upon these results and applied them to the modularity of elliptic curves over imaginary quadratic fields. They come close to completely solving it, with only a small number of exceptions (which constitute 0% of cases).

Response of Ana Caraiani

First, I would like to thank Joan Birman and the AMS for establishing an award that recognizes research contributions by women mathematicians. This is particularly meaningful to me because I looked to many of the previous recipients of the Satter Prize for inspiration at challenging moments in my career. It is a great honour to be selected as a recipient!

I am indebted to my many collaborators, mentors and colleagues who have generously shared their mathematical ideas with me over the years and supported me in different but crucial ways. Special thanks go to Peter Scholze for the wonderful opportunity to collaborate with him on understanding a part of the geometry and cohomology of Shimura varieties, to Richard Taylor for initiating the "ten author" collaboration, which was much more successful than we had originally expected, and to James Newton for our joyful exploration of elliptic curves over imaginary quadratic fields. I also particularly want to acknowledge Jessica Fintzen and Toby Gee for their longstanding friendship and moral support.

Finally, I want to thank my family, especially my husband, Steven, my mother, Zoe, and my daughter, Nadia.

Biographical sketch of Ana Caraiani

Ana Caraiani was born in Bucharest, Romania, in 1984. She received a bachelor's degree in mathematics from Princeton University in 2007 and completed her PhD at Harvard University in 2012. After temporary positions at the University of Chicago, Princeton and the Institute for Advanced Study (IAS), and the University of Bonn, she moved to Imperial College London in 2017, where she is currently a Royal Society University Research Fellow and Professor of Pure Mathematics. She is a Fellow of the AMS, a recipient of an EMS Prize and a New Horizons Prize in Mathematics and was an invited speaker at the 2022 ICM. 

About the prize

Awarded every two years, the Ruth Lyttle Satter Prize in Mathematics recognizes an outstanding contribution to mathematics research by a woman in the previous six years. The prize was established by Joan Birman in honor of her sister, Ruth. The 2025 prize will be recognized during the 2025 Joint Mathematics Meetings in January in Seattle.

Read more and see the list of past recipients.

Contact: AMS Communications

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The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through our publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

Kenta Suzuki of the Massachusetts Institute of Technology (MIT) is awarded the 2025 American Mathematical Society (AMS)-Mathematical Association of America (MAA)-Society for Industrial and Applied Mathematics (SIAM) Frank and Brennie Morgan Prize for his extraordinary research in the representation theory of $p$-adic groups. His papers, including two solo works, represent significant progress in different areas of the field.

From the citation

Suzuki worked on deep problems in representation theory, and he has authored and coauthored six research papers. In particular, he has made important contributions to the representation theory of $p$-adic groups. His results include asymptotics for the dimension of spaces fixed by a congruence subgroup in an admissible representation of $GL(n).$ His joint works include working out the local Langlands correspondence for several rank two $p$-adic groups, and the determination of canonical bases in the subregular quotient of the affine Hecke algebra and its antispherical module, along with their “coherent” categorifications.

Response of Kenta Suzuki

It is an honor for me to receive the Frank and Brennie Morgan Prize. I thank the Morgan family and the AMS, MAA, and SIAM for their generosity. I thank my mentors throughout the years, Toshihiko Nakazawa, Li Li, Michael Zieve, and Colin Hinde, for kindling my interest in mathematics. Toshihiko Nakazawa patiently explored mathematics with me from a young age and continues to inspire me with his insights. I thank Roman Bezrukavnikov, Wei Zhang, Zhiwei Yun, Ivan Losev, Vasily Krylov, and Calder Morton-Ferguson for further stimulating my interest in mathematics at MIT and introducing me to the many wonders of representation theory. Wei Zhang’s unwavering support has motivated me to explore many areas of mathematics. I leave every conversation with Roman Bezrukavnikov with new ideas, and he has helped me grow as a researcher by encouraging me to pursue even my most ambitious ideas. The mathematical community at MIT and Harvard have been supportive and taught me so much, both mathematical and nonmathematical. Finally, I thank my parents, particularly my mother, for supporting me throughout my journey in every possible way. She has been my role model and is one of the most intelligent and charismatic people I know.

Biographical sketch of Kenta Suzuki

Kenta Suzuki is a fourth-year undergraduate at MIT from Tokyo, Japan, and Plymouth, Michigan. Suzuki’s work focuses on the representation theory of $p$-adic groups and geometric representation theory. Suzuki is particularly interested in applying geometric methods to solve problems of representation theory. In his free time, he runs, reads, and is (slowly) learning how to cook.

About the prize

The AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student is awarded annually to an undergraduate (or students for joint work) for outstanding research in mathematics. The prize recipient's research can include more than one paper, however, the paper or papers to be considered for the prize must be completed while the student is an undergraduate. Publication of research is not required.

Established in 1995, the prize is entirely endowed by a gift from Mrs. Frank (Brennie) Morgan. The current prize amount is $1,200.

The prize will be presented at the 2025 Joint Mathematics Meetings in Seattle.

Learn more about the prize and previous recipients.

Contact: AMS Communications

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The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through our publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

Forty-six mathematical scientists have been named recipients of AMS-Simons Research Enhancement Grants for Primarily Undergraduate Institution (PUI) Faculty. Each awardee will receive $3,000 per year for three years. 

The grants foster and support research collaboration by full-time mid-career mathematicians at US institutions that do not offer a mathematics doctoral degree.

This year’s grant recipients hail from 42 institutions across 21 US states. The grants will support their research in several different areas, from number theory to applied mathematics.

This is the grant program’s second cohort, said Sarah Bryant, associate vice president of programs. “Over the first two years, we’ve worked with faculty from 75 different institutions, including 19 minority-serving institutions, which shows just how much this program is expanding and making an impact,” Bryant said. She noted that “in the first year, the grants supported 87 trips, helped produce 70 publications and preprints, and gave awardees the resources needed to collaborate and advance their work.”

The grant allows for any activities that will further the awardee’s research program. Expenses include but are not limited to conference participation, institute visits, collaboration travel (awardee or collaborator), computer equipment or software, family-care expenses, and teaching assistants.

Administration of the award by the grantee’s institution is required; annual discretionary funds for a grantee’s department and administrative funds for a grantee's institution will be available at the end of each grant year.

The grants are made possible through funding from the Simons Foundation and the American Mathematical Society (AMS), as well as Eve, Kirsten, Lenore, and Ada of the Menger family.

Applications for the next cohort are anticipated to open on MathPrograms.org on January 9, 2025. Visit the AMS website to view an informational PowerPoint or sign up to receive email updates about the program. Faculty who applied for but did not receive the 2023 or 2024 awards are encouraged to reapply if they are still eligible for the grant. 

Robert McCann, University of Toronto, will receive the 2025 American Mathematical Society (AMS) - Society for Industrial and Applied Mathematics (SIAM) Norbert Wiener Prize in Applied Mathematics “in recognition of his groundbreaking contributions to optimal transport theory, and for pioneering deep applications to economics and physics,” according to the citation. McCann holds a Canada Research Chair in Mathematics, Economics, and Physics.

From the citation

Robert McCann has made fundamental contributions to optimal transport theory, reflecting remarkable technical abilities and amazing conceptual creativity. His discovery of displacement convexity and his solution to Monge’s (1746-1818) problem for different transportation costs were early, foundational advances that preceded by nearly 30 years the current enormous attention bestowed on optimal transport theory and its applications. Beyond these, McCann produced many important, unexpected results, linking optimal transport to new areas of application within and outside mathematics: different notions of curvature, new and hidden convexities in the economics of information, and a non-smooth theory of gravity based on the interaction of entropy with the Einstein field equation.

Response of Robert McCann

I am honored and humbled to have my work on optimal transportation and its applications to economics and physics recognized by the AMS-SIAM 2025 Norbert Wiener Prize (endowed by MIT). I think the whole optimal transport community can join me in taking pride in this acknowledgement of the impact and success of our efforts and can view this award as an incentive to further achievements. After singling out my PhD advisor, Elliott Lieb, who first taught me about the mines and the factories, I'd like to thank the many other mentors, collaborators, colleagues, and students – too numerous to name – who shared in my mathematical, physical, and economic adventures (and those who wrote letters to document!). Our interactions inspire and sustain me on my scientific journey; I could not have achieved these results without you, and my life is enriched by your presence. I try to pass it forward by giving as good as I got, and I encourage you to do the same. I also thank my family for their love and support, and their willingness to share me by putting up with my long hours of distraction and frequent travels. I hope this recognition helps to reassure them that their sacrifices are not for nought.

Biographical sketch of Robert McCann

Robert McCann studied engineering and physics before graduating with a degree in mathematics from Queen's University at Kingston, Ontario, and a doctorate from Princeton University. Following a Tamarkin appointment at Brown University and a postdoctoral fellowship at Institut des Hautes Études Scientifiques (IHES), he became a professor of mathematics at the University of Toronto, where he now holds a Canada Research Chair in Mathematics, Economics, and Physics. He is an authority on optimal transportation and has played a pioneering role in its rapid development since the 1990s. In particular, the notion of displacement convexity introduced in his 1994 PhD thesis lies behind many of the area's myriad applications. He serves on the editorial board of various journals, and as editor-in-chief of the Canadian Journal of Mathematics since 2007 (with a hiatus from 2017-21). His research has been recognized by awards such as an invitation to lecture at the 2014 International Congress of Mathematicians in Seoul; election to the Royal Society of Canada in 2014; the 2017 Jeffery-Williams Prize of the Canadian Mathematical Society; and the 2023 W.T. and Idalia Reid Prize of the Society for Industrial and Applied Mathematics (SIAM).

About the prize

The AMS-SIAM Norbert Wiener Prize in Applied Mathematics is awarded every three years for an outstanding contribution to applied mathematics in the highest and broadest sense.The American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) award the prize jointly. Recipients must be a member of one of these societies. 

This prize was established in 1967 in honor of Professor Norbert Wiener and was endowed by a fund from the Department of Mathematics of the Massachusetts Institute of Technology. The endowment was supplemented further by a generous donor. The current award is $5,000.

The 2025 prize will be presented at the 2025 Joint Mathematics Meetings in Seattle.

Learn more about the prize and previous recipients.

Contact: AMS Communications

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The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through our publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

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