AMS News

Merritt Named CIO of NIH

Thu, 26 Dec 2024 00:00:00 EST

Dr. Adele Merritt is the new Chief Information Officer (CIO) of the National Institutes of Health (NIH).

Adele Merritt

Credit: Office of the Director of National Intelligence, via Wikimedia Commons

Merritt will lead NIH's information technology (IT) strategy, policy, security, and oversight, bringing over twenty years' experience in federal cybersecurity, IT management, and related policy. Her experience includes leadership positions at Department of Energy, Office of the Director of National Intelligence, and National Security Council Staff at the White House.

Dr. Merritt was a National Security Fellow at the John F. Kennedy School of Government, Harvard University. She earned her Ph.D. in mathematics from the University of Rhode Island.

Read the full NIH announcement.

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.

McDuff to Receive 2025 AMS Steele Prize for Lifetime Achievement

Thu, 19 Dec 2024 00:00:00 EST

Dusa McDuff, the Joan Lyttle Birman ’48 Professor of Mathematics at Barnard College, will receive the 2025 AMS Leroy P. Steele Prize for Lifetime Achievement. She is honored “for foundational and far-reaching contributions in C*-algebras and symplectic geometry and topology and for long-continued leadership and mentoring in mathematics,” according to the citation.

Dusa McDuff

Credit: Chelsea L. McCord

From the citation

The 2025 Steele Prize for Lifetime Achievement is awarded to Dusa McDuff for her outstanding and seminal contributions in von Neumann algebras, algebraic topology, and especially symplectic geometry and topology. Her many foundational papers and her two monographs with D. Salamon, “Introduction to symplectic topology” and “J-holomorphic curves and symplectic topology,” are essential references in symplectic geometry and topology.

McDuff’s numerous fundamental research contributions include the construction of many new and surprising examples of symplectic manifolds, symplectic packing and embedding, classification of symplectic rulings, geometry of Hamiltonian diffeomorphism groups, quantum homology, and foundational results on Kuranishi atlases for moduli of holomorphic curves. Her contributions have been enormously influential in the development of symplectic topology, which has been a major theme of research for the past 40 years.

In addition to her extensive service in lecturing about mathematics and training students, McDuff has been a distinguished role model for women in mathematics, providing essential leadership and outreach for 10 years as director of the Women in Mathematics program at the Institute for Advanced Study, and providing many other mentoring activities for women in mathematics.

McDuff is a Fellow of the American Mathematical Society and a member of the National Academy of Sciences.

Response of Dusa McDuff

I am delighted to have been awarded the 2025 Leroy P. Steele Prize for Lifetime Achievement and am honored by the generous citation.

When I was growing up it was generally considered very strange for a woman to set her sights on being a mathematician. Thus, first I must thank my mother, who always practiced her profession of architecture so that I felt free to pursue beauty where I found it. There are many other people to thank for making my career possible. First, my teachers — Miss Cobban for making high school math so absorbing, Israel Moiseevich Gelfand for opening my eyes to the beauty and unity of mathematics, Graeme Segal for helping me construct my first proofs in topology, André Haefliger, who first made me aware of symplectic geometry, and of course all my colleagues and collaborators in that rich and wonderful field.

Next, I wish to thank the people who took a chance by giving me my first jobs — John Williamson (in York), Cristopher Zeeman (in Warwick), and Irwin Kra (in Stony Brook).

Finally, I thank my husbands, David McDuff and John Milnor, for being (very different) sources of inspiration, and my children, Anna McDuff and Thomas Milnor, for enriching my life.

Biographical sketch of Dusa McDuff

Born in London in 1945, Dusa McDuff grew up in Edinburgh. After her first degree at the University of Edinburgh (1967), she did a PhD (1970) and a post doc at Cambridge University. Although her thesis was on von Neumann algebras, she radically changed direction after a visit to Moscow in 1969-70. She was a Lecturer at the Universities of York (1972-76) and Warwick (1976-78), and then moved to the USA to accept an assistant professorship at Stony Brook, working her way up to a Distinguished Professorship in 1998. Since 2007 she has worked at Barnard College, where she is now the Joan Lyttle Birman ’48 Professor of Mathematics. She is a Fellow of the Royal Society (1994), a member of the National Academy of Sciences (1999), and has several honorary degrees.

About the prize

Presented annually, the AMS Leroy P. Steele Prize for Lifetime Achievement is awarded for the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through PhD students. The Steele Prizes were established in 1970 in honor of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein and are endowed under the terms of a bequest from Leroy P. Steele. The current award is US$10,000.

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

Contact: AMS Communications

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Ndiaye Named 2025-26 AMS Claytor-Gilmer Fellow

Wed, 18 Dec 2024 00:00:00 EST

Cheikh Birahim Ndiaye, associate professor of mathematics, Howard University, has been named the 2025-2026 Claytor-Gilmer Fellow by the American Mathematical Society (AMS).

“I am honored to receive the 2025-2026 AMS Claytor-Gilmer Fellowship. This fellowship supports research excellence and highlights the value of diversity in mathematics,” Ndiaye said. “I look forward to contributing further to the field and its community through this opportunity.

“I would also like to thank my collaborators, mentors, and colleagues for their continued support and inspiration over the years,” he said.

Cheikh Birahim Ndiaye

Credit: BKImagery

At Howard, Ndiaye works in geometric analysis with a particular focus on non-compact geometric variational problems. “During this fellowship year, I will work on finding a Min-Max version of the Algebraic Topological argument of Bari-Coron and Lojaciewicz’s inequalities at infinity for Yamabe type problems,” he said.

Ndiaye earned his Master of Science in Applied Mathematics from the University of Gaston Berger in Senegal. He earned a Diploma in Pure Mathematics from the Abdus Salam International Centre for Theoretical Physics (ICTP) and his PhD in Mathematical Analysis from Scuola Internazionale Superiore di Studi Avanzati (SISSA).

Ndiaye served in research positions at Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) and Humboldt-Universitaet zu Berlin and as a postdoctoral researcher at the University of Tübingen, the University of Giessen, and the University of Basel. He was a visiting professor at Osaka University and was awarded research fellowships at Centro di Ricerca Matematica Ennio De Giorgi, Mathematisches Forschungsinstitut Oberwolfach, and Institut des Hautes Études Scientifiques (IHES).

In 2020, Ndiaye received the National Science Foundation Excellence in Research Award. In 2024, he received the Howard University (COAS) 2023-2024 Outstanding Research Award and a Research Membership at the Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI).

About the fellowship
The AMS Claytor-Gilmer Fellowship aims to further excellence in mathematics research and to help generate wider and sustained participation by Black mathematicians. It carries an award of $50,000 and is typically conferred on one individual per year. Awardees may use the fellowship in any way that most effectively enables their research—for instance, for release time, participation in research programs, travel support, or childcare. The most likely awardee is a mid-career Black mathematician based at a US institution whose achievements demonstrate significant potential for further contributions to mathematics. The fellowship is named for Dr. William Schieffelin Claytor, the first African American man to publish a research article in a peer-reviewed mathematics journal, and Dr. Gloria Ford Gilmer, the first African American woman to publish a research article in a peer-reviewed mathematics journal. Read more about Dr. Claytor and Dr. Ford Gilmer.

Contact: AMS Communications

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Gross, Hacking, Keel, Kontsevich to Receive 2025 AMS Moore Prize

Tue, 17 Dec 2024 00:00:00 EST

Mark Gross (University of Cambridge), Paul Hacking (University of Massachusetts Amherst), Seán Keel (University of Texas at Austin) and Maxim Kontsevich (Institut des Hautes Études Scientifiques) will receive the 2025 AMS E.H. Moore Research Article Prize. They are honored for the paper “Canonical Bases for Cluster Algebras,” published in the Journal of the American Mathematical Society, Volume 31, Number 2, April 2018, pp. 497–608.

(l-r) Mark Gross, Paul Hacking, Seán Keel, Maxim Kontsevich

Credit: photo of Gross by Mark Gross; photo of Kontsevich © IHES / Chris Peus

“This paper settled several important conjectures in the structural theory of cluster algebras and cluster varieties, including the Laurent positivity conjecture of Fomin and Zelevinsky and the duality conjecture of Fock and Goncharov,” according to the citation. “This was accomplished by introducing new concepts and techniques that proved highly influential for subsequent development of the field.”

From the citation

In this work, by introducing novel mirror symmetry techniques into the field, Gross, Hacking, Keel, and Kontsevich accomplished several breakthroughs on the main problems of general structure theory of cluster algebras and varieties. Among other things, they solved the Laurent positivity conjecture of Fomin and Zelevinsky and the duality conjecture of Fock and Goncharov.

This paper introduced new important constructions and techniques on cluster algebras. Using the combinatorics of Gross-Siebert scattering diagrams and broken lines, they defined the “theta series” associated with an arbitrary g-vector; this enabled them to produce, for the first time, an explicit construction of a “canonical” basis in a cluster algebra.

Response of Mark Gross

I am delighted and honored to receive the E.H. Moore Prize. I would especially like to thank my longtime collaborator, Bernd Siebert. This work would not have been possible without the many ideas developed together. I would also like to thank the cluster community, which was welcoming and very happy to give time and listen to an outsider to the field like myself!

Response of Paul Hacking

I'd like to thank the AMS for their kind recognition of our work. I'd also like to acknowledge the dependence of our work on prior work of the following researchers: Sergey Fomin and Andrei Zelevinsky, who developed the theory of cluster algebras around 2001; Vladimir Fock and Alexander Goncharov, who recast that theory in a more geometric form in 2003 and formulated an intriguing duality conjecture; Kontsevich-Soibelman and Gross-Siebert, who developed the notion of scattering diagrams in mirror symmetry (building on work of Fukaya) which plays a crucial role in our paper, allowing us to prove the Fock-Goncharov duality conjecture and construct canonical bases of cluster algebras as envisaged by Fomin-Zelevinsky. I'd like to thank the cluster algebra community for their openness to assimilating new ideas and kindness in patiently explaining existing theory to us. Thanks to IHES for hosting us during some of our work on this project. Finally, thanks to my family for their love and support.

Response of Maxim Kontsevich

I am honored that our paper with Mark Gross, Paul Hacking, and Sean Keel, Canonical Bases for Cluster Algebras, has been recognized by the Moore Prize of the American Mathematical Society.

This paper is special to me for several reasons. First, it refines and affirms a conjecture by my longtime friends Alexander Goncharov and Vladimir Fock. Sacha Goncharov, in particular, profoundly influenced my career, beginning when we met at Israel Gelfand’s seminar at Moscow State University. As an older student, Sacha often reexplained seminar material to younger students like me, becoming my first scientific mentor and a lifelong collaborator.

Second, the paper demonstrates how powerful methods inspired by physical theories—such as string theory and quantum field theory—can be in mathematics. In this paper in particular, we used techniques from mirror symmetry, including scattering diagrams and broken lines—concepts I have helped develop in close collaboration with my friend and colleague Yan Soibelman. I feel this award also recognizes the significance of our work.

Finally, the paper reminds me of my coauthors’ visits to IHES, where we shared many stimulating discussions. I really enjoy welcoming colleagues at the Institute, where I have benefited from outstanding working conditions for 30 years now.

Biographical sketch of Mark Gross

Mark Gross was born in Ithaca, NY, in 1965. He was an undergraduate at Cornell University and obtained his PhD from UC Berkeley in 1990 under the direction of Robin Hartshorne. He then held postdoctoral positions at University of Michigan, Université de Paris VI, and MSRI. Afterwards, he held positions at Cornell, University of Warwick, University of California San Diego, and since 2014, University of Cambridge, where he is also a Fellow of King's College. Jointly with Bernd Siebert, he won the Clay Research Award in 2016. He was elected Fellow of the Royal Society in 2017.

Biographical sketch of Paul Hacking

Paul Hacking was born in Lancashire, England, in 1974. He first became interested in mathematics through his teacher Clive Horsford at Lancaster Royal Grammar School and the British Mathematical Olympiad. He was an undergraduate student at Trinity College, Cambridge, where his directors of studies were algebraic geometers Pelham Wilson and Nick Shepherd-Barron. He stayed in Cambridge for his PhD in algebraic geometry supervised by Alessio Corti, graduating in 2001. He was subsequently a postdoc at University of Michigan, MSRI, and Yale University, and assistant professor at University of Washington, before joining UMass Amherst in 2009. He lives in Northampton, MA, with his partner, Naila (married 2007), and their son, Oliver (born 2020). He has advised graduate students Anna Kazanova, Huy Le, Feifei Xie, Jennifer Li, Angelica Simonetti, Cristian Rodriguez, and Ethan Zhou.

Biographical sketch of Seán Keel

Seán Keel is an algebraic geometer with a particular focus on birational geometry, moduli spaces, and mirror symmetry.

Biographical sketch of Maxim Kontsevich

Maxim Kontsevich is a mathematician specializing in algebraic geometry and mathematical physics. Born in 1964 in Khimki, Russia, he completed his undergraduate studies at Moscow State University (1980-1985), followed by work at the Institute for Information Transmission Problems (1985-1990). He earned his Ph.D. from Bonn University in 1992 and served as a Professor of Mathematics at UC Berkeley from 1994 to 1995. Since 1995, he has been a Permanent Professor at the Institut des Hautes Études Scientifiques (IHES) in Bures-sur-Yvette, France. Kontsevich was awarded the Fields Medal in 1998.

About the prize

The E.H. Moore Research Article Prize is awarded every three years for an outstanding research article that appeared in one of the AMS’s primary research journals (Journal of the AMS, Proceedings of the AMS, Transactions of the AMS, Memoirs of the AMS, Mathematics of Computation, Electronic Journal of Conformal Geometry and Dynamics, or Electronic Journal of Representation Theory) during the six calendar years ending a full year before the meeting at which the prize is awarded. The current prize amount is US$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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Ribet to Receive 2025 AMS Steele Prize for Seminal Research

Thu, 12 Dec 2024 00:00:00 EST

Kenneth A. Ribet of the University of California, Berkeley, will receive the 2025 AMS Leroy P. Steele Prize for Seminal Contribution to Research for his 1976 paper "A modular construction of unramified $p$-extensions of Q($\mu_p$)."

Kenneth A. Ribet

Credit: Xiyuan Tracy Zhang

From the citation

The 2025 Steele Prize for Seminal Contribution to Research is awarded to Kenneth A. Ribet for his 1976 Inventiones Mathematicae paper, "A modular construction of unramified $p$-extensions of Q($\mu_p$)." Ribet gave a striking converse to Bernoulli number divisibility properties that were discovered by Kummer and Herbrand, and along the way he provided a highly original construction of unramified extensions of Q($\mu_p$). The paper introduced modular forms and Eisenstein series decisively into the study of special values of zeta functions, and experts quickly recognized it as a "thunderbolt" with robust potential to be used widely. "Ribet's method," as it is called today, has since been applied repeatedly in major advances in Iwasawa theory, the Birch and Swinnerton-Dyer conjecture and Stark's conjectures. Its far-reaching impact continues to grow with time.

Response of Kenneth A. Ribet

It is a singular honor for me to be receiving the 2025 Steele Prize for Seminal Contribution to Research. This prize reflects the high quality of the literature in our subject and the value that we place in citing the work of our predecessors.

When I began the research that I published in 1976, I was under the incorrect impression that the unramified extensions in my paper were already known to exist. My intention was simply to connect well-known algebraic objects with the theory of modular forms. When I described my construction to colleagues, I was stunned to learn that the extensions in my article had never been constructed before. It is a further happy surprise that my method has been of enduring value.

My deep thanks go out to our colleagues who initiated and supported my prize nomination. Further, it is a pleasure for me to acknowledge the large number of generous mathematicians who mentored me around the time when I wrote my paper, a period when I was only two years past my PhD and needed plenty of guidance. Among them were my advisor, John Tate, and also the mathematicians who are thanked in my article: N. Katz, J. Coates, P. Deligne, B. Mazur, and J-P. Serre.

Biographical sketch of Kenneth A. Ribet

Kenneth Ribet studied at Brown University and Harvard University. He received his PhD in 1973 from Harvard, where his advisor was John Tate. After several years of teaching and research at Princeton University and in Paris, Ribet joined the Berkeley faculty in 1978. At Berkeley, he is Distinguished Professor Emeritus and a Senior Fellow in the Miller Institute for Basic Research in Science.

Ribet works in arithmetic geometry. He is best known for his proof that Fermat's Last Theorem would follow from the modularity conjecture, then a well-known unproved conjecture about elliptic curves. When Andrew Wiles obtained cases of this conjecture in 1995, Wiles obtained Fermat's Last Theorem as a corollary because of Ribet's prior work.

Ribet was elected to the American Academy of Arts and Sciences in 1997 and the US National Academy of Sciences in 2000. He shared the Fermat Prize in 1989 and was awarded an honorary doctorate by Brown University in 1998. He received the Brouwer medal from the Royal Dutch Mathematical Society in 2017. He served as AMS President, 2017-2018.

About the prize

The Leroy P. Steele Prize for Seminal Contribution to Research is awarded for a paper, whether recent or not, which has proved to be of fundamental or lasting importance in its field, or a model of important research. The current prize amount is US$5,000. The Steele Prize for Seminal Contribution to Research is awarded according to the following six-year rotation of subject areas:
•   Open
•   Analysis/Probability
•   Algebra/Number Theory
•   Applied Mathematics
•   Geometry/Topology
•   Discrete Mathematics/Logic

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

Contact: AMS Communications

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Milne to Receive 2025 AMS Steele Prize for Mathematical Exposition

Tue, 10 Dec 2024 00:00:00 EST

James S. Milne, professor emeritus of mathematics, University of Michigan, will receive the 2025 AMS Leroy P. Steele Prize for Mathematical Exposition for his “extensive corpus of excellent expository works” on his website. “These have educated a generation of arithmetic geometers,” according to the prize citation.

James S. Milne

James Milne

From the citation

The 2025 Steele Prize for Mathematical Exposition is awarded to James S. Milne for his extensive corpus of excellent expository works provided on his website. The website, which Milne has been developing since 1996, now contains over 2,000 pages of notes, as well as other expository articles, covering a wide range of topics within algebra and number theory, from basic group theory to class field theory to abelian varieties to Shimura varieties to Tannakian categories (with Deligne) and much more. Many of the documents began as course notes but have been expanded and polished over decades to become some of the most thorough and well-written accounts available of the topics they cover. The inclusion of ample historical remarks and guides to the literature adds value for both newcomers and experts. To make the expositions useful to as broad an audience as possible, Milne has taken care not to assume more prerequisites than are necessary for a reasonable treatment of the topic at hand. The expository works have educated a generation of arithmetic geometers and will continue to do so for as long as they are available.

Response of James S. Milne

It is an honor and a pleasure to receive this award, and I thank the committee for its generous citation. Once I began preparing my lectures on a computer, it seemed natural to put them on the web when this became available in the early 1990s. Initially, this was for the benefit of my own students, but the web was not so crowded then as it is now, and they were soon picked up by students at other universities. And not only universities --- one (very bright) high school student wrote to say that he was happy to find my notes as his school library was somewhat lacking in material on elliptic curves!

Once on the web, they were, of course, freely available wherever the web is available, which is essentially everywhere, and indeed they have been used as the basis of courses in places as distant as Nepal and Vietnam. Helping to spread the mathematics I find most beautiful and getting friendly responses from readers across the globe has been its own reward, but it is nice to have this recognition.

Biographical sketch of James S. Milne

James Milne was born in Invercargill, New Zealand, and received his undergraduate education at Otago University. He did his PhD (1964-1967) at Harvard University under the supervision of John Tate. After spending two years as a lecturer at University College London, he joined the faculty of the University of Michigan in 1969, where, except for visiting positions, he has remained since, currently as professor emeritus of mathematics. Apart from Tate, the greatest influence on his research has been the Grothendieck school, and especially Pierre Deligne. In his writing, his model has always been the great master of mathematical exposition, Jean-Pierre Serre.

About the prize

The AMS Leroy P. Steele Prize for Mathematical Exposition is awarded annually for a book or substantial survey or expository research paper. The current award amount is US$5,000. The Steele Prizes were established in 1970 in honor of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein and are endowed under the terms of a bequest from Leroy P. Steele.

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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McNerney Wins Seat in California State Senate

Tue, 10 Dec 2024 00:00:00 EST

Jerry McNerney, former US Congressman who holds a PhD in mathematics, won his election on November 5 and will begin his term as a California State Senator in January 2025.

Jerry McNerney

From 2007 to 2023, McNerney served in the US Congress, representing California’s House district 11 and following redistricting, district 9. He earned his PhD in mathematics from the University of New Mexico, focusing on differential geometry. After completing his PhD, he worked first at Sandia National Laboratories and then as an entrepreneur in the clean energy sector, developing wind energy technology in California.

In Congress, McNerney worked on science and energy issues and championed clean energy polices. Since leaving Congress, he has worked as a Fellow at Stanford University’s Institute for Human-Centered Artificial Intelligence and a Senior Policy Advisor at Pillsbury Winthrop Shaw Pittman LLP.

An AMS member, McNerney currently serves on the AMS Committee on Science Policy.

Contact: AMS Communications

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Stange Named 2025-26 AMS Birman Fellow

Wed, 04 Dec 2024 00:00:00 EST

Katherine E. Stange, professor of mathematics at the University of Colorado Boulder, has been named the 2025-26 AMS Joan and Joseph Birman Fellow.

Katherine Stange

Credit: Jonathan Wise

“I am both honored and humbled by this award,” Stange said. “As my career has unfolded, I've learned the incredible value of community in mathematics, and I feel a great debt of gratitude to my amazing collaborators, and the support of my mathematical community.

“Joan and Joseph Birman's vision, to support the careers of women reconciling the many aspects of work and life, goes beyond these individual awards; and so, I hope to support those around me, just as I have been privileged by the support of so many.”

Stange earned her Bachelor of Mathematics at the University of Waterloo. She received her PhD in 2008 at Brown University under the direction of Joseph H. Silverman. Stange held postdoctoral positions at Harvard University, Stanford University, and the Pacific Institute for Mathematical Sciences / Simon Fraser University. She was awarded the 2020 Ribenboim Prize (presented in 2024) for research in number theory. Stange is a Fellow of the Association for Women in Mathematics.

As a high-schooler, attending PROMYS in Boston ignited Stange’s passion for number theory, she said. “I've found myself drawn to problems in number theory that have a geometric flavor; my thesis work was in elliptic curves, and shortly after that I became enchanted by Apollonian circle packings.

“Somewhat serendipitously, I was also drawn into cryptography, where old problems are thrown under new light, something I first learned under the mentorship of Kristin Lauter. I'm also an active member of the Illustrating Mathematics community, which aims, among other things, to support the use of mathematical illustration, including computer visualization, as a research tool.”

About the Fellowship
The Joan and Joseph Birman Fellowship for Women Scholars is a mid-career research fellowship made possible by a generous gift from Joan and Joseph Birman.

The fellowship seeks to address the paucity of women at the highest levels of research in mathematics by giving exceptionally talented women extra research support during their mid-career years.

The most likely awardee will be a mid-career woman, based at a US institution, whose achievements demonstrate significant potential for further contributions to mathematics. A requirement of this fellowship is that the awardee must be a member of the AMS at the time of application.

Candidates must have a carefully thought-through research plan for the fellowship period. Special circumstances (such as time off for care of children or other family members) may be taken into consideration in making the award. Awardees may use the fellowship in any way that most effectively enables their research: for instance, for release time, participation in special research programs, travel support, or child care. The award is issued through the recipient's institution, and no part of it may be used for indirect costs. The award for the 2025-2026 academic year is US$50,000.

Contact: AMS Communications

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Hatcher to Receive Inaugural Stein Prize for Transformative Exposition

Tue, 03 Dec 2024 00:00:00 EST

Allen Hatcher, professor emeritus, Cornell University, will receive the inaugural Elias M. Stein Prize for Transformative Exposition for his book Algebraic Topology.

“Allen Hatcher’s Algebraic Topology has transformed the teaching of this topic with its lively mix of intuition, salient examples, and formal mathematics,” according to the prize citation. “Its careful approach and spirit of fun has attracted many newcomers to the field.”

Allen Hatcher

Credit: Allen Hatcher

From the citation

The 2025 Elias M. Stein Prize for Transformative Exposition is awarded to Allen Hatcher for his book Algebraic Topology. The book's combination of geometric intuition, algebraic formalism, and enlightening examples makes the subject readily accessible to a broad readership, ranging from beginning students with only a modest background in abstract algebra and point-set topology to professional mathematicians working in other areas. Each topic is introduced with an informal discussion of the key ideas, followed by careful definitions, precise statements of theorems with detailed proofs, and illuminating illustrative examples. Both the computations that are carried out in detail and the exercises for the reader are well chosen and enlightening. While many books on algebraic topology systematically develop the formalism of homological algebra before applying it to topology, Hatcher's treatment is firmly grounded in geometric intuition, introducing the more technical homological formalism only as needed.

Response of Allen Hatcher

My Algebraic Topology book had a long period of development since I had the ambitious goal of making it both readable and cover a lot of material. For readability I kept in mind the principle of not keeping secrets from the reader, so I wanted to include explanations that are sometimes left out. The inclusion of large numbers of examples and exercises was also intended to aid readability. I wanted the book to be easily accessible to readers everywhere, and by lucky coincidence the internet was emerging as the book was being written in the 1990s so preliminary versions could be made freely downloadable online, and this has continued after publication of the print version. This has led to valuable and much-appreciated feedback from many readers. I also wanted the book to look as nice as I could make it, so much thought and effort went into layout and typography. It is a great pleasure to have all the work recognized by the Elias M. Stein Prize for Transformative Exposition. I hope many other textbooks will follow the precepts I had in mind when writing this one.

Biographical sketch of Allen Hatcher

Allen Hatcher spent his early years in Indianapolis before obtaining bachelor's degrees in music and mathematics at Oberlin College. Opting to continue in mathematics, he received a PhD at Stanford advised by Hans Samelson, then held positions at Princeton and UCLA, finally settling at Cornell for the next three decades. He retired nine years ago to have more time for writing. As a topologist Hatcher initially studied high-dimensional manifolds, with a focus on their diffeomorphism groups following the lead of Jean Cerf, then he switched to low-dimensional topology, inspired by Bill Thurston, with whom he wrote two joint papers. After this, he applied low-dimensional topology to studying automorphism groups of free groups, including a series of seven papers with Karen Vogtmann. Overall, he has published some forty papers, with a total of fifteen coauthors. Besides his algebraic topology textbook, he has published an undergraduate textbook on number theory from a geometric perspective and has other drafts of textbooks available on his webpage.

About the prize

The Elias M. Stein Prize for Transformative Exposition is awarded for a written work, such as a book, survey, or exposition, in any area of mathematics that transforms the mathematical community's understanding of the subject or reshapes the way it is taught.

This prize of US$5,000 was endowed in 2022 by Stein’s students, colleagues, and friends to honor his remarkable legacy of writing monographs and textbooks, both singly and with collaborators. The prize will be presented at the 2025 Joint Mathematics Meetings in Seattle.

Contact: AMS Communications

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Green to Receive Inaugural I. Martin Isaacs Prize

Tue, 26 Nov 2024 00:00:00 EST

Ben Green, Waynflete Professor of Pure Mathematics, University of Oxford, will receive the inaugural I. Martin Isaacs Prize for Excellence in Mathematical Writing for his article “On Sárközy’s theorem for shifted primes,” published in Journal of the American Mathematical Society in 2024.

Ben Green

Credit: Liubov Yevenok

From the citation

The 2025 I. Martin Isaacs Prize for Excellence in Mathematical Writing is awarded to Ben Green for his article “On Sárközy’s theorem for shifted primes,” published in the Journal of the AMS in 2024.

… Green successfully balances serving different audiences. Experts can readily extract the key ideas from his paper, while beginners can appreciate the motivation and context for the techniques. Those who wish to check the details will find every detail made available to them, while those who are trying to understand the big picture will also find what they need. Green’s paper is a joy to read, and his effort and skill in writing are a model of how to communicate technically forbidding mathematics.

Response of Ben Green

I am very happy to be awarded this prize, as writing is something I have always taken quite seriously. I am particularly pleased that the prize is associated with I. Martin Isaacs, whose famous book on character theory I have owned and enjoyed looking at since I was an undergraduate. Although the cited paper is single-author, I have learned a great deal about how to write mathematics from several collaborators over many years. Let me mention in particular Terence Tao, with whom I have written over 30 joint papers and who taught me much about how to structure an argument; my first coauthor, Imre Ruzsa, who writes with exceptional clarity and elegance; and my PhD supervisor, Timothy Gowers, whose papers are always a pleasure to read.

Biographical sketch of Ben Green

Ben Green was born and grew up in Bristol, England, attending local schools there. His undergraduate and graduate education was at Trinity College, Cambridge, where he was awarded a PhD in 2003, supervised by Timothy Gowers. He was a Junior Research Fellow at Trinity, a Clay Research Fellow, and a PIMS Postdoctoral Fellow before returning to Cambridge as the first Herchel Smith Professor of Pure Mathematics in 2006. He moved to Oxford in 2013, where he is the Waynflete Professor of Pure Mathematics and a Fellow of Magdalen College. He is married and has two sons aged 8 and 6.

About the prize

The I. Martin Isaacs Prize is awarded annually for excellence in writing of a research article published in a primary journal of the AMS in the past two years.

The prize focuses on the attributes of excellent writing, including clarity, grace, and accessibility. The quality of the research is implied by the article’s publication in Communications of the AMS, Journal of the AMS, Mathematics of Computation, Memoirs, Proceedings of the AMS, or Transactions of the AMS, and is therefore not a prize selection criterion. The current prize amount is US$5,000.

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

Contact: AMS Communications

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