# Steven Zucker

Steven Zucker
BornSeptember 12, 1949 (age 70)[1]
Nationality American
Alma materPrinceton University
Scientific career
FieldsMathematics
InstitutionsJohns Hopkins University

Steven Mark Zucker (born September 12, 1949) is an American mathematician who introduced the Zucker conjecture, proved in different ways by Eduard Looijenga (1988) and by Leslie Saper and Mark Stern (1990).

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Zucker completed his Ph.D. in 1974 at Princeton University under the supervision of Spencer Bloch. His work with David A. Cox led to an algorithm for determining if a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface ${\displaystyle E\to S}$, where ${\displaystyle S}$ is isomorphic to the projective line.

He is currently part of the mathematics faculty at the Johns Hopkins University. In 2012 he became a fellow of the American Mathematical Society.[2]

## References

• Cox, David A.; Zucker, Steven (1979), "Intersection numbers of sections of elliptic surfaces", Inventiones Mathematicae, 53 (1): 1–44, doi:10.1007/BF01403189, MR 0538682
• Looijenga, Eduard L2-cohomology of locally symmetric varieties. Compositio Mathematica 67 (1988), no. 1, 3–20. MR0949269
• Saper, Leslie; Stern, Mark L2-cohomology of arithmetic varieties, Annals of Mathematics (2) 132 (1990), no. 1, 1–69. MR1059935
• Zucker, Steven (1977), "The Hodge conjecture for cubic fourfolds", Compositio Mathematica, 34 (2): 199–209, MR 0453741
• Zucker, Steven, Théorie de Hodge à coefficients dégénérescents. Comptes Rendus Acad. Sci. 286 (1978), 1137–1140.
• Zucker, Steven, Hodge theory with degenerating coefficients: L2-cohomology in the Poincaré metric, Annals of Mathematics 109 (1979), 415–476.
• Zucker, Steven, L2-cohomology of warped products and arithmetic groups. Inventiones Mathematicae 70 (1982), 169–218.