Steven Zucker

Short description: American mathematician (1949–2019)

Steven Zucker

Born| (1949-09-12)12 September 1949[1]

New York City , New York

Died| 13 September 2019(2019-09-13) (aged 70)[2]

Baltimore, Maryland

Nationality| United States
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->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.[3]

## Bibliography

* Cox, David A.; Zucker, Steven (1979), "Intersection numbers of sections of elliptic surfaces", Inventiones Mathematicae 53 (1): 1–44, doi:10.1007/BF01403189, Bibcode: 1979InMat..53....1C
* Looijenga, Eduard (1988). "L2-cohomology of locally symmetric varieties". Compositio Mathematica 67 (1): 3–20.
* 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. http://www.numdam.org/item?id=CM_1977__34_2_199_0.
* 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.
* Zucker, Steven (1982). "L2-cohomology of warped products and arithmetic groups". Inventiones Mathematicae 70 (2): 169–218. doi:10.1007/BF01390727. Bibcode: 1982InMat..70..169Z.

## References

1. ↑ "Remembering Steve Zucker". Notices of the American Mathematical Society (August 2021, Volume 68 Number 7). https://www.ams.org/journals/notices/202107/rnoti-p1156.pdf.
2. ↑ Wallach, Rachel (19 September 2019). "Influential Johns Hopkins math professor Steven Zucker dies at 70". Johns Hopkins University. https://hub.jhu.edu/2019/09/19/stephen-zucker-mathematics-obituary/.
3. ↑ "List of Fellows of the American Mathematical Society". http://www.ams.org/profession/fellows-list.

## External links

* Steven Zucker at the Mathematics Genealogy Project
* "Official home page". http://www.math.jhu.edu/~sz/.

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