NEWS Mathematics People The AMS Joan and Joseph Birman Fellowship for Women Melnick Awarded Scholars, established in 2017 with a generous gift from Joan and Joseph Birman, seeks to give exceptionally talented Birman Fellowship women extra research support during their mid-career Karin Melnick of the University of years. The first three Fellowships are also being supported by the Stephen and Margaret Gill Family Foundation, in Maryland, College Park, has been memory of Hilda Geiringer von Mises. The primary se- awarded the AMS Joan and Joseph lection criterion for the Birman Fellowship, which carries Birman Fellowship for Women Schol- a stipend of US$50,000, is the excellence of the candi- ars for the academic year 2020–2021. date’s research. Read an interview (www.ams.org/giving Melnick’s research is on differen- /honoring/the-line-newsletter-fall2017-PDF tial-geometric aspects of rigidity. This .pdf) with Joan Birman about her decision to create the work comprises global and local re- Fellowship with the goal of “helping more women math- sults relating the automorphisms of a ematicians to develop their creative voices.” Karin Melnick differential-geometric structure with The first two Birman Fellows were Margaret Beck (2018– the geometric and topological prop- 2019) and Lillian Pierce (2019–2020). For more informa- erties of the space. Melnick also works in smooth dynamics, tion about the Fellowship, see www.ams.org/profession in which an invariant differential-geometric structure plays /prizes-awards/Birman-Fellowship. an important role in the proof of rigidity theorems. Mel- nick is a leader in research on the Lorentzian Lichnerowicz —Elaine Kehoe conjecture, a statement about conformal transformations of compact Lorentzian manifolds. Together with collabo- rators, she has developed new techniques in the setting of Khayutin Awarded 2020– Cartan connections that have facilitated progress on this problem, as well as many results for other differential- 2021 Centennial Fellowship geometric structures and general parabolic Cartan geom- Ilya Khayutin of Northwestern Uni- etries. versity has been awarded the AMS Karin Melnick was born and raised in the San Francisco Centennial Fellowship for the aca- Bay area. She attended Reed College in Portland, Oregon, demic year 2020–2021. and completed her PhD at the University of Chicago in Khayutin tells the Notices: “I work 2006 under the direction of Benson Farb. With an NSF in homogeneous dynamics and num- Postdoctoral Research Fellowship, she went to Yale Uni- ber theory. The interface between versity as a Gibbs Assistant Professor. She received a Junior these fields is vast, so let me give a Research Fellowship from the Erwin Schrödinger Institute special example to demonstrate the in the spring of 2009 and began as an assistant professor Ilya Khayutin type of questions I have been study- at the University of Maryland in the fall of 2009. She has ing. Consider a degree n totally real been awarded an AMS Centennial Fellowship and an NSF irreducible integral polynomial P of discriminant D. We CAREER grant. She is currently associate professor at the are interested in solutions to P(X)=0 when X is an n × n University of Maryland. matrix. The space of these solutions is a nice algebraic Melnick lives between the United States and Germany variety VP. This variety carries an action of the group PGLn with her partner and their young child. She is very grateful by conjugation. The solutions in real matrices, V , are P(ℝ) for the flexibility provided by the Birman Fellowship and a homogeneous space for PGLn , simply because each the opportunities it provides to advance her research and semisimple real matrix with real(ℝ) eigenvalues can be diago- career goals. nalized over the reals. This observation allows us to identify 916 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 67, NUMBER 6 Mathematics People NEWS V , for any degree n polynomial P as above, with the in the “Mathematics Opportunities” section of an upcom- P(ℝ) coset space PGLn A, where A is the subgroup of diag- ing issue of the Notices. onal matrices. A classical(ℝ)/ question going back to Linnik is how do the solutions in integral matrices, V , distribute —Elaine Kehoe P(ℤ) in the space of real solutions PGLn A when one varies the polynomial P (the degree n is fixed).(ℝ)/ In many cases we 2020 Rolf Schock expect the distribution of the discrete points VP to be close to uniform when |D| is large enough. (ℤ) “For n=2 this question was partially answered by Prizes Awarded Skubenko in the 1950s using a method due to Linnik. The Nikolai G. Makarov of the California Institute of Tech- n=2 case was finally resolved by Duke in the 1980s. While nology has been awarded the 2020 Rolf Schock Prize in Linnik’s method relied on an intricate interplay between Mathematics “for his significant contributions to complex dynamics and arithmetic, Duke’s proof belongs to the analysis and its applications to mathematical physics.” Ac- theory of automorphic forms and builds upon Iwaniec’s cording to the prize citation, complex analysis “investigates amplification method. The case of higher n’s seems to be functions of complex variables. This field is vital to many much harder. The question was solved for n=3 by Einsiedler, branches of mathematics and has numerous applications Lindenstrauss, Michel, and Venkatesh after the turn of the in the natural sciences and engineering.” twenty-first century using a method inspired by Linnik’s The citation reads in part: “His most famous results work. The input they required both on the ergodic and the concern harmonic measure in two dimensions, stating that number theory sides is significantly more involved than the hitting probability distribution on the boundary for for n=2. The case of n>3 is still very much open, although Brownian motion in two-dimensional, simply connected some weak partial results are known. It would be pleasing domains (domains without holes) is one-dimensional. to see a solution of this problem in general. Brownian motion is the random movement of small par- “This is one flavor of questions I enjoy, some other prob- ticles floating in a fluid or gas, which was studied by Albert lems are related to the asymptotic behavior of automorphic Einstein in the early twentieth century. forms in various aspects. For example, how big can the “Nikolai Makarov has also made revolutionary contribu- sup-norm of a Hecke–Maass eigenform of large Laplace tions in the field of growth phenomena that describe crystal eigenvalue on the modular curve be when restricted to a growth in a two-dimensional space. In recent years, he has fixed compact set. The study of these problems has been also produced innovative results in conformal field theory pioneered by P. Sarnak, and important deep theorems in quantum mechanics, particularly its relationship to have been proven by many researchers. I find it especially complex analysis and probability theory.” Makarov received beautiful when we find a common thread between these his doctorate from the Steklov Mathematical Institute in spectral problems and the Diophantine problems above.” Leningrad in 1986. He is a past recipient of the Salem Prize Khayutin was born in the Soviet Union; his family immi- and was an invited speaker at the International Congress grated to Israel when he was five years old. He received his of Mathematicians in Berkeley in 1986. PhD in 2016 from Hebrew University under the direction of Dag Prawitz and Per Martin-Löf, both of Stockholm Elon Lindenstrauss. He was a Veblen Research Instructor at University, were awarded Rolf Schock Prizes in Logic and Princeton University and the Institute for Advanced Study Philosophy. They specialize in proof theory and construc- from 2016 to 2019. He says, “My parents played a formative tivist philosophy of mathematics. Prawitz was recognized role in my education and my interest in science, and I am for his work in “proof-theoretical normalization in natural very fortunate to have a wonderful family. Although I was deduction,” and Martin-Löf was honored “for the creation deeply interested in mathematics at an early age, it was of constructive type theory.” not till my late twenties when I have decided to pursue a The prize carries a cash award of 400,000 Swedish krona career in math. Since coming full circle to graduate studies (approximately US$39,000). The prizes are awarded in the in mathematics my passion about the subject continuously areas of mathematics, logic and philosophy, visual arts, grows.” and music. The Centennial Fellowship carries a stipend of US$93,000, a travel expense allowance of US$9,300, and —From a Schock Prize announcement a complimentary Society membership for one year. The award was made at the recommendation of the Centennial Fellows Selection Committee. The primary selection crite- rion is the excellence of the candidate’s research. Please note: Information about the competition for the 2021–2022 AMS Centennial Fellowship will be published JUNE/JULY 2020 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 917 Mathematics People NEWS Bandeira Awarded Bedrossian Awarded Smale Prize 2019 IMA Prize Afonso Bandeira of ETH Zurich has Jacob Bedrossian of the Center for been awarded the fourth Stephen Scientific Computation and Mathe- Smale Prize “for his pioneering work matical Modeling at the University on the foundations of computational of Maryland, College Park, has been mathematics.” The citation states: awarded the 2019 IMA Prize of the “Bandeira is an incredibly produc- Institute for Mathematics and Its tive and versatile researcher who has Applications (IMA) for his important successfully applied and combined contributions to the study of partial concepts and tools from optimiza- differential equations of fluid dy- Afonso Bandeira tion theory, probability theory, infor- Jacob Bedrossian namics and in particular to the area mation theory, statistics, theoretical of hydrodynamic stability.