Dan Abramovich (; born March 12, 1963) is an Israeli-American mathematician working in the fields of
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
and
arithmetic geometry. As of 2019, he holds the title of L. Herbert Ballou University Professor at
Brown University, and he is an Elected Fellow of the
American Mathematical Society.
Education
Abramovich received a bachelor's degree at
Tel Aviv University
Tel Aviv University (TAU) is a Public university, public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv, the university is the center of teaching and ...
in 1987 and completed a doctorate at
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
in 1991 under
Joe Harris (''Subvarieties of abelian varieties and of Jacobians of curves''). From 1991 to 1994 he was
C. L. E. Moore instructor at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
. Thereafter he held faculty positions at
Boston University from 1994 to 1999 and since 2003 has been Professor at
Brown University.
Career
Among other topics, he has dealt with
birational geometry, the
resolution of singularities,
subvarieties of
abelian varieties, limits for the
torsion of
elliptic curves,
rational and
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
points on
algebraic varieties and
moduli spaces of
vector bundles on
curves. Together with
Felipe Voloch, in 1992 he succeeded in making progress toward proving the Mordell-Lang Conjecture in characteristic ''p'' (the full proof came later from
Ehud Hrushovski). He has been a guest scholar at, among other institutions, the
Hebrew University of Jerusalem
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...
, the
Max Planck Institute for Mathematics in Bonn, the
Mathematical Sciences Research Institute (MSRI), the
Pierre and Marie Curie University in Paris and at
IHES. He was an invited speaker at the 2018
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
("Resolution of singularities of complex algebraic varieties and their families").
Arxiv
/ref> From 1996 to 1998 he was a Sloan Fellow. He is a Fellow of the American Mathematical Society.
Publications
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*
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* with Voloch: ''Toward a proof of the Mordell-Lang conjecture in positive characteristic'', Intern. Math. Research Notices, Band 5, 1992, S. 103–115
References
External links
Homepage
{{DEFAULTSORT:Abramovich, Dan
1963 births
Living people
Massachusetts Institute of Technology School of Science faculty
20th-century American mathematicians
21st-century Israeli mathematicians
Tel Aviv University alumni
Harvard Graduate School of Arts and Sciences alumni
Brown University faculty
Scientists from Haifa
Sloan Research Fellows
Algebraic geometers
21st-century American mathematicians
Israeli emigrants to the United States