Mark Lee Green (1 October 1947,

Minneapolis Minneapolis is a city in Hennepin County, Minnesota, United States, and its county seat. With a population of 429,954 as of the 2020 United States census, 2020 census, it is the state's List of cities in Minnesota, most populous city. Locat ...

) 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 ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...

, 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 an algebraic curve, divisor on a Riemann surface ''C'' is a for ...

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 research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

and in 1972 his PhD from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

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 is a major developer in particular ...

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 university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

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, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...

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

Institute for Pure and Applied Mathematics An institute is an organizational body created for a certain purpose. They are often research organisations (research institutes) created to do research on specific topics, or can also be a professional body. In some countries, institutes ca ...

(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 a middle and senior-career master's degree program in general management and leadership offered at MIT, Stanford University, and London Business School (LBS). Initially supported by a grant from Alfred P. Sloan, fo ...

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

ICM ICM may refer to: Organizations * Irish Church Missions, an Anglican mission * Institut du Cerveau, the Paris Brain Institute, a research center * Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw * Interna ...

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

. 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. He was elected a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) 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 other ...

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