Mark Lee Green (1 October 1947,

Minneapolis Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. Minneapolis has its origins ...

) is an American mathematician, who does research in

commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...

, algebraic geometry, Hodge theory, differential geometry, and the theory of several complex variables. He is known for

Green's Conjecture In mathematics, Clifford's theorem on special divisors is a result of on algebraic curves, showing the constraints on special linear systems on a curve ''C''. Statement A divisor on a Riemann surface ''C'' is a formal sum \textstyle D = \sum_P ...

on syzygies of canonical curves. Mark green

Green received in 1968 his bachelor's degree from

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the mo ...

and in 1972 his PhD from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

under

Phillip Griffiths Phillip Augustus Griffiths IV (born October 18, 1938) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particul ...

with thesis ''Some Picard Theorems for Holomorphic Maps to Algebraic Varieties''. In 1970/71 Green was a Procter Fellow in Princeton. He was an instructor from 1972 to 1974 at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

and for the academic year 1974/75 at MIT. He became in 1975 an assistant professor and in 1982 a full professor at

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

. He was a co-founder and the director of the

Institute for Pure and Applied Mathematics The Institute for Pure and Applied Mathematics (IPAM) is an American mathematics institute funded by the National Science Foundation. The initial funding for the institute was approved in May 1999 and it was inaugurated in August, 2000. IPAM i ...

(IPAM) for 7 years, starting in 2001. From 1968 to 1972 he was a Woodrow Wilson Fellow and from 1976 to 1980 a

Sloan Fellow The Sloan Fellows program is the world's first mid-career and senior career master's degree in general management and leadership. It was initially supported by a grant from Alfred P. Sloan, the late CEO of General Motors, to his alma mater, MIT ...

. In 1998 he was an Invited Speaker with talk ''Higher Abel-Jacobi Maps'' at the ICM in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

. He is a member of ''The Mathematical Sciences 2025'' committee of the National Academies of the USA and the committee's vice-chair with the chair Caltech's president

Thomas Everhart Thomas Eugene Everhart FREng (born February 15, 1932, Kansas City, Missouri) is an American educator and physicist. His area of expertise is the physics of electron beams. Together with Richard F. M. Thornley he designed the Everhart–Thornley ...

. He was elected a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 2010 and a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2012.

Selected publications

Articles

*"Holomorphic maps into complex projective space omitting hyperplanes." Transactions of the American Mathematical Society 169 (1972): 89–103. *"Some Picard theorems for holomorphic maps to algebraic varieties." American Journal of Mathematics (1975): 43–75. *"Holomorphic maps to complex tori." American Journal of Mathematics 100, no. 3 (1978): 615–620. *"Secant functions, the Reiss relation and its converse." Transactions of the American Mathematical Society 280, no. 2 (1983): 499–507. *"Infinitesimal methods in Hodge theory." In ''Algebraic cycles and Hodge theory'', pp. 1–92. Springer, Berlin, Heidelberg, 1994. *"Generic initial ideals." In ''Six lectures on commutative algebra'', pp. 119–186. Birkhäuser, Basel, 1998.

Books

* with P. Griffiths: ''On the tangent space to the space of algebraic cycles on a smooth algebraic variety'', Princeton University Press 2005. * with P. Griffiths and Matt Kerr: ''Hodge theory, complex geometry, and representation theory'', American Mathematical Society 2013 * with P. Griffiths and Matt Kerr: ''Mumford-Tate groups and domains : their geometry and arithmetic'', Princeton University Press 2012

References

{{DEFAULTSORT:Green, Mark Lee Massachusetts Institute of Technology alumni Princeton University alumni University of California, Los Angeles faculty Fellows of the American Academy of Arts and Sciences Fellows of the American Mathematical Society 1947 births Living people