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Evra Receives SASTRA Ramanujan Prize NEWS Mathematics People Lubotzky in 2016 by showing that 2-dimensional skeleta of Evra Receives 3-dimensional Ramanujan complexes have the topological overlap property, but it was unclear how to carry this over SASTRA Ramanujan Prize to higher dimensions. Very recently, Shai joined forces with Shai Evra of Princeton University Tali Kaufmann and spectacularly solved this problem by and the Hebrew University of Jerusa- showing that d-dimensional skeleta of (d + 1)-dimensional lem has been selected the recipient of Ramanujan complexes have the topological overlap prop- the 2020 SASTRA Ramanujan Prize, erty, and thus resolved Gromov’s problem in all dimen- awarded for outstanding contribu- sions. This seminal paper, which makes use of the work of tions by individuals not exceeding Lafforgue on the Generalized Ramanujan Conjectures, is the age of thirty-two in areas of math- to appear in the Journal of the AMS. It is expected that the ematics influenced by Ramanujan. ideas developed in this paper will find many other import- The prize citation reads: “Shai Evra ant applications. Higher dimensional expansion is related to questions in the broader field of quantitative geometry Shai Evra is an extraordinarily gifted mathe- matician whose research concerns and topology, as well as in coding theory and theoretical locally symmetric spaces of arithmetic groups and their computer science (quantum error correcting codes). combinatoric, geometric, and topological structure. He “Another major work of Evra (jointly with Ori Par- employs deep results from representation theory and zanchevski) concerns construction of ‘Golden Gates’ for number theory pertaining to the Ramanujan and Langlands three-dimensional unitary groups. The classic work of conjectures to establish expander-like properties. Lubotzky, Phillips, and Sarnak (1987, 1988), provides “Expander graphs are remarkable objects with connec- topological generators for the orthogonal group SO(3) tions to many parts of mathematics and computer science. such that for each , the set of -wise products of gener- Expanders are graphs which are highly connected; to sep- ators is distributed in an almost optimal manner on the arate them into disconnected pieces, one must remove a two-dimensional and three-dimensional spheres. Among large number of edges. In the last decade, mathematicians other things, their proof makes use of the full strength of have formulated the notion of expansion to higher dimen- the Ramanujan Conjecture for GL(2) as proved by Deligne. sional complexes. 2009 Abel Laureate Mikhail Gromov had Recently this problem has received renewed interest due to introduced the notion of ‘geometric expansion’ in terms of its importance and relevance for quantum computing. The an affine overlapping property for simplicial complexes. 3-sphere is isomorphic to SU(2), with the group of logical He showed that complete complexes are such expanders gates acting on a single qubit. Considered as elements of and that a much stronger topological overlap property SU(2), the generators provided by Lubotzky–Phillips–Sar- holds for them. He constructed several examples of higher nak were given the name ‘Golden Gates’ because the circuits dimensional expanders with unbounded degree and raised constructed from these gates approximate any gate in an the question in a very influential 2010 paper in GAFA, optimal manner. Ori Parzanchevski and Sarnak found whether bounded degree higher dimensional expanders Golden Gates for PU(2), but whether one could achieve exist. In a fundamental paper, ‘Finite Quotients of Bru- such miracles for higher dimensions was far from clear. In hat–Tits Buildings’ that appeared in the Journal of Topology a recent impressive paper, Evra and Parzanchevski show and Analysis in 2015, Evra extended both the combinatorics that this is possible for PU(3) with some striking exam- and automorphic form theory (specifically the Generalized ples, but this is demonstrated with very delicate analysis. Ramanujan Conjectures) and generalized the construction They employ deep results of Ragowski and James Arthur of Gromov to other Bruhat–Tits buildings. However, the (which had important consequences on the Generalized bounded degree problem of Gromov still remained un- Ramanujan Conjectures) to show that the optimal cov- resolved. In the case of dimension 2, Gromov’s question ering features are still valid. The Golden Gates for PU(2) was answered in the affirmative by Kaufman, Kazhdan, and and PU(3) are basic building blocks for the construction JANUARY 2021 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 127 Mathematics People NEWS of universal gate sets in quantum computation (much like applications, in particular obtain- ‘not’ and ‘and’ are universal one-bit and two-bit gates for ing a characterization of projective building the classical logical circuits). It is to be noted that spaces and hyperquadrics; for her the Ramanujan Conjectures and their generalizations are work in the study and classifica- a central piece of the outstanding work of Evra.” tion of Fano varieties; and her study Shai Evra was born in Be’er Yaakov, Israel. He received of algebraic foliations. Araujo has his PhD from the Hebrew University of Jerusalem in 2019 also played a key role in promoting under Alexander Lubotzky. He has been a postdoctoral women in mathematics and in the researcher at the Institute for Advanced Study (2018–2020) organization of important mathe- and is an instructor at Princeton University for 2020–2021. Carolina Araujo matical activities.” He will take up a permanent position at Hebrew University Araujo specializes in algebraic ge- in 2021. His recognitions include the 2015 Perlman Prize ometry, including birational geometry and foliations. She and the 2020 Nessyahu Prize. obtained her PhD from Princeton University in 2004 under The 2020 SASTRA Ramanujan Prize Committee con- the supervision of János Kollár. She has been a Simons sisted of Krishnaswami Alladi, Chair, University of Florida; Associate with ICTP since 2015 and is the vice president of William Duke, University of California, Los Angeles; Kevin the Committee for Women in Mathematics at the Interna- Ford, University of Illinois, Urbana-Champaign; Anne tional Mathematical Union. She was both an organizer and Schilling, University of California, Davis; Robert Tijdeman, an invited speaker at the 2018 International Congress of Leiden University; Maryna Viazovska, École Polytechnique, Mathematicians. Araujo tells the Notices: “I am mother of Lausanne; and Shouwu Zhang, Princeton University. four-year-old Iago, we love being in nature, and alternate The previous recipients of the SASTRA Ramanujan Prize between our residence in Rio de Janeiro and our cottage are: in the countryside, where we have spent most of our time • Manjul Bhargava and Kannan Soundararajan (two during the COVID-19 pandemic, enjoying the company of full prizes), 2005 our pets, growing bananas and vegetables.” • Terence Tao, 2006 The selection committee consisted of Alicia Dickenstein • Ben Green, 2007 (University of Buenos Aires), Lothar Goettsche (ICTP, • Akshay Venkatesh, 2008 chair), Kapil Hari Paranjape (Indian Institute of Science • Kathrin Bringmann, 2009 Education and Research [IISER], Mohali), Philibert Nang • Wei Zhang, 2010 (Ecole Normale Supérieure Libreville, Gabon), and Van • Roman Holowinsky, 2011 Vu (Yale University). The prize is awarded to a researcher • Zhiwei Yun, 2012 from a developing country who is under forty-five years of • Peter Scholze, 2013 age on December 31 of the year of the award and who has • James Maynard, 2014 conducted outstanding research in a developing country. It • Jacob Tsimerman, 2015 is administered by the Abdus Salam International Center • Kaisa Matomaki and Maksym Radziwill (shared), for Theoretical Physics (ICTP), the Department of Science 2016 and Technology (DST, Government of India), and the In- • Maryna Viazovska, 2017 ternational Mathematical Union (IMU). • Yifeng Lui and Jack Thorne, 2018 • Adam Harper, 2019 —From an ICTP-IMU announcement —Krishnaswami Alladi, University of Florida Rojo Receives SACNAS Award Araujo Awarded Javier Rojo of Oregon State Univer- sity has been honored with the 2020 ICTP-IMU Ramanujan Prize SACNAS Distinguished Scientist Award from the Society for Advance- Carolina Araujo of the Institute for Pure and Applied Math- ment of Chicanos/Hispanics and Na- ematics (IMPA) in Rio de Janeiro, Brazil, has been awarded tive Americans in Science (SACNAS). the 2020 ICTP-IMU Ramanujan Prize for Young Mathe- His work involves survival analysis, maticians from Developing Countries. She was awarded partial orders of distribution func- the prize “in recognition of her outstanding work in alge- tions and related inference problems, braic geometry, in particular in birational geometry and Javier Rojo extreme value theory and tail-heavi- the theory of extremal rays, of which she gave important ness of distributions, nonparametric 128 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 68, NUMBER 1 Mathematics People NEWS function estimation, statistical decision theory, random matrices, and dimension reduction techniques. Packard Fellowships Rojo is currently the Korvis Professor of Statistics at OSU. He received his PhD in statistics from the Univer- Awarded sity of California, Berkeley, under the direction of Erich The David and Lucile Packard Foundation has announced L. Lehmann. He previously progressed from assistant to its class of Fellows in Science and Engineering for 2020. full professor (1990–2000)
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