Steven Zucker

Steven Mark Zucker
Born	(1949-09-12)12 September 1949 New York City, New York
Died	13 September 2019(2019-09-13) (aged 70) Baltimore, Maryland
Alma mater	Princeton University
Known for	Zucker conjecture
Scientific career
Fields	Mathematics
Institutions	Johns Hopkins University
Doctoral advisor	Spencer Bloch

Steven Mark Zucker (12 September 1949 – 13 September 2019) was an American mathematician who introduced the Zucker conjecture, proved in different ways by Eduard Looijenga (1988) and by Leslie Saper and Mark Stern (1990).

Zucker completed his Ph.D. in 1974 at Princeton University under the supervision of Spencer Bloch. His work with David A. Cox led to the creation of the Cox–Zucker machine, 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 $E\to S$, where $S$ is isomorphic to the projective line.

He was part of the mathematics faculty at the Johns Hopkins University. In 2012, he became a fellow of the American Mathematical Society.

Bibliography

• Cox, David A.; Zucker, Steven (1979), "Intersection numbers of sections of elliptic surfaces", Inventiones Mathematicae, 53 (1): 1–44, Bibcode:1979InMat..53....1C, doi:10.1007/BF01403189, MR 0538682, S2CID 15130840
• Looijenga, Eduard (1988). "L²-cohomology of locally symmetric varieties". Compositio Mathematica. 67 (1): 3–20. MR 0949269.
• Saper, Leslie; Stern, Mark L₂-cohomology of arithmetic varieties, Annals of Mathematics (2) 132 (1990), no. 1, 1–69. MR 1059935
• Zucker, Steven (1977). "The Hodge conjecture for cubic fourfolds". Compositio Mathematica. 34 (2): 199–209. MR 0453741.
• Zucker, Steven (1978). "Théorie de Hodge à coefficients dégénérescents". Comptes rendus de l'Académie des Sciences. 286: 1137–1140.
• Zucker, Steven (1979). "Hodge theory with degenerating coefficients: L²-cohomology in the Poincaré metric". Annals of Mathematics. 109 (3): 415–476. doi:10.2307/1971221. JSTOR 1971221.
• Zucker, Steven (1982). "L²-cohomology of warped products and arithmetic groups". Inventiones Mathematicae. 70 (2): 169–218. Bibcode:1982InMat..70..169Z. doi:10.1007/BF01390727. S2CID 121348276.

External links

• Steven Zucker at the Mathematics Genealogy Project
• Steven Zucker at the Wayback Machine (archived 2020-02-03)