2007 Satter Prize

The 2007 Ruth Lyttle Satter Prize in Mathematics for her deep contributions to was awarded at the 113th Annual Meeting of the algebraic geometry, and in par- AMSinNewOrleansinJanuary2007. ticular for her recent solutions The Satter Prize is awarded every two years to to two long-standing open prob- recognize an outstanding contribution to mathe- lems. Voisin solved the Kodaira matics research by a woman in the previous five probleminher paper“Onthe ho- years. Established in 1990 with funds donated by motopy types of compact Kähler Joan S. Birman, the prize honors the memory of and complex projective mani- Birman’s sister, Ruth Lyttle Satter. Satter earned a folds” , Invent. Math. 157 (2004), bachelor’s degree in mathematics and then joined no. 2, 329–343. There she shows the research staff at AT&T Bell Laboratories during that in every dimension greater World War II. After raising a family she received a than three, there exist compact Ph.D. in botany at the age of forty-three from the Kähler manifolds not homotopy equivalent to any smooth pro- University of Connecticut at Storrs, where she later became a faculty member. Her research on the bio- jective variety. This problem has logicalclocksinplantsearnedherrecognitioninthe been open since the 1950s when Kodaira proved U.S. and abroad. Birman requested that the prize thatevery compactKähler surface is diffeomorphic be established to honor her sister’s commitment to to (and hence homotopy equivalent to) some pro- researchandtoencouraging womeninscience. The jective algebraic variety. Her idea is to start with prizecarriesacashawardofUS$5,000. the fact that certain endomorphisms can prevent The Satter Prize is awarded by the AMS Council a complex torus from being realized as a projec- acting on the recommendation of a selection com- tive variety, and then to construct Kähler manifolds mittee. For the 2007 prize, the members of the se- whose Albanese tori must carry such endomor- lection committee were: BenedictH. Gross, KarenE. phisms for homological reasons. In a completely different direction, Voisin also solves Green’s Con- Smith,andChuu-LianTerng(chair). jecture in her papers “Green’s canonical syzygy Previous recipients of the Satter Prize are: Dusa conjecture for generic curves of odd genus”, Com- McDuff (1991), Lai-Sang Young (1993), Sun-Yung pos. Math. 141 (2005), no. 5, 1163–1190, and Alice Chang (1995), (1997), “Green’s generic syzygy conjecture for curves of Bernadette Perrin-Riou (1999), Karen E. Smith evengenuslyingonaK3surface”, J. Eur. Math. Soc. (2001), (2001), Abigail Thompson (2003), 4 (2002), no. 4, 363–404. andSvetlanaJitomirskaya(2005). A century ago, Hilbert saw that syzygies (rela- The 2007 Satter Prize was awarded to Claire tions among relations) were important invariants Voisin. The text that follows presents the selection of varieties in projective space, and in the early committee’s citation, a brief biographical sketch, 1980s, Mark Green conjectured that the syzygies and the awardee’s response upon receiving the of a general curve canonically embedded in pro- prize. jective space should be as simple as possible. This conjecture attracted a huge amount of effort by al- Citation gebraic geometers over twenty years before finally The Ruth Lyttle Satter Prize is awarded to Claire being settled by Voisin. Her idea is to work with Voisin of the Institut de Mathématiques de Jussieu curves on asuitable K3 surface,where she executes

April 2007 Notices of the AMS 523 deep calculations with vector bundles (at least in even genus) that lead to the required vanishing the- orems.

Biographical Sketch Claire Voisin defended her thesis in 1986 under the supervisionofArnaudBeauville.Shebeganemploy- ment in the Centre National de la Recherche Scien- tifique as chargée de recherche in 1986 and since then pursued her career in this institution. She oc- casionallytaughtgraduatecoursesbutmainlydoes research and advises students. Her honors include theEuropeanMathematicalSocietyPrize(1992),the Servant Prize (1996) and the Sophie Germain Prize (2003) of the Académie des Sciences de Paris, and the silver medal of the CNRS (2006). She was an in- vitedspeakerattheInternationalCongressofMath- ematicians in 1994 in Zurich.

Response I amdeeply honoredto have beenchosento receive the 2007 Ruth Lyttle Satter Prize. I feel of course very encouraged by this recognition of my work. I would like to thank the members of the prize com- mitteeforselectingme.Iamalsoverygratefultomy institution, the CNRS, whichmade itpossible for me todo researchin thebestconditions.

524 Notices of the AMS Volume 54, Number 4