Dan Abramovich
Dan Abramovich | |
|---|---|
| Born | March 12, 1963 Haifa, Israel |
| Occupation | Mathematician |
| Years active | 1991–present |
| Known for | Algebraic geometry, arithmetic geometry, Mordell-Lang Conjecture progress |
| Notable work | Lectures on Arakelov Geometry |
Dan Abramovich (; born March 12, 1963) is a mathematician of Israeli-American descent who focuses on algebraic geometry and arithmetic geometry. Since 2019, he has held the position of L. Herbert Ballou University Professor at Brown University and is recognized as an Elected Fellow of the American Mathematical Society.
Education
Abramovich obtained his undergraduate degree from Tel Aviv University in 1987. He then pursued doctoral studies at Harvard University, completing his Ph.D. in 1991 under the supervision of Joe Harris, with a dissertation titled Subvarieties of abelian varieties and of Jacobians of curves. Between 1991 and 1994, he served as a C. L. E. Moore instructor at the Massachusetts Institute of Technology. Subsequently, he joined Boston University as faculty from 1994 until 1999, and has been a professor at Brown University since 2003.
Career
His scholarly work encompasses topics such as birational geometry, the resolution of singularities, subvarieties within abelian varieties, torsion constraints on elliptic curves, rational and integral points on algebraic varieties, along with moduli spaces related to vector bundles on curves. In collaboration with Felipe Voloch in 1992, Abramovich made significant progress toward establishing the Mordell-Lang Conjecture in characteristic p, a result later completed by Ehud Hrushovski. He has held visiting appointments at various prestigious institutions including the Hebrew University of Jerusalem, Max Planck Institute for Mathematics, Mathematical Sciences Research Institute, Pierre and Marie Curie University, and the Institut des hautes études scientifiques. At the 2018 International Congress of Mathematicians, he was an invited speaker presenting on "Resolution of singularities of complex algebraic varieties and their families." Additionally, he was awarded a Sloan Research Fellowship from 1996 to 1998.
Publications
- Lectures on Arakelov Geometry, Cambridge University Press, 1992
- Abramovich, Dan, et al., "Torification and factorization of birational maps," Journal of the American Mathematical Society, 2002
- Abramovich, Dan, et al., "A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension," Tohoku Mathematical Journal, 1999
- Abramovich, Dan and Frans Oort, "Alterations and Resolution of Singularities," in Resolution of Singularities, Birkhäuser Basel, 2000
- Abramovich, D. and K. Karu, "Weak semistable reduction in characteristic 0," Inventiones Mathematicae, 2000
- With Voloch: "Toward a proof of the Mordell-Lang conjecture in positive characteristic," International Math. Research Notices, 1992
External links
- 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