“János Kollár”的意思、由来-开放百科全书

János Kollár (born June 7, 1956) is a Hungarian mathematician, specializing in algebraic geometry.

Professional career

Kollár began his studies at the Eötvös University in Budapest and later received his PhD at Brandeis University in 1984 under the direction of Teruhisa Matsusaka with a thesis on canonical threefolds. He was Junior Fellow at Harvard University from 1984 to 1987 and Professor at the University of Utah from 1987 until 1999. Currently, he is professor at Princeton University.^[1]

Contributions

Kollár is known for his contributions to the minimal model program for threefolds and hence the compactification of moduli of algebraic surfaces, for pioneering the notion of rational connectedness (i.e. extending the theory of rationally connected varieties for varieties over the complex field to varieties over local fields), and finding counterexamples to a conjecture of John Nash. (In 1952 Nash conjectured a converse to a famous theorem he proved,^[2] and Kollár was able to provide many 3-dimensional counterexamples from an important new structure theory for a class of 3-dimensional algebraic varieties.) ^[3]

Kollár also gave the first algebraic proof of effective Nullstellensatz: let

be polynomials of degree at most

variables; if they have no common zero, then the equation

has a solution such that each polynomial

has degree at most

Awards and honors

Kollár is a member of the National Academy of Sciences since 2005 and received the Cole Prize in 2006.^[4] He is an external member of the Hungarian Academy of Sciences since 1995.^[5] In 2012 he became a fellow of the American Mathematical Society.^[6] In 2016 he became a fellow of the American Academy of Arts and Sciences.^[7] In 2017 he received the Shaw Prize in Mathematical Sciences.^[8]

In 1990 he was an invited speaker at the International Congress of Mathematicians (ICM) in Kyōto. In 1996 he gave one of the plenary addresses at the European Mathematical Congress in Budapest (Low degree polynomial equations: arithmetic, geometry and topology). He was also selected as a plenary speaker at the ICM held in 2014 in Seoul.

As a high school student, Kollár represented Hungary and won Gold medals at both the 1973 and 1974 International Mathematical Olympiads.

Works

References

1. ^{{cite web|url=http://www.math.princeton.edu/directory/|title=Mathematics Department Directory|publisher=Princeton University|accessdate=23 January 2010}}
2. ^{{cite journal | title = Real algebraic manifolds | journal = Annals of Mathematics | year = 1952 | pages = 405–21 | volume = 56 | doi=10.2307/1969649}}, {{MathSciNet|id=0050928}}. See {{cite journal | title = Proc. Internat. Congr. Math | publisher = AMS | year = 1952 | pages = 516–17}}
3. ^{{cite journal|author=Kollár, János|title=The Nash conjecture for threefolds|journal=Electron. Res. Announc. Amer. Math. Soc.|volume=4|year=1998|pages=63–73 (electronic)|mr=1641168|doi=10.1090/s1079-6762-98-00049-3}}
4. ^Notices AMS on Winner of the Cole Prize 2006, pdf-data file (67 kB)
5. ^{{cite web|url=http://www.mta.hu/index.php?id=members&LANG=e&TID=388&cHash=f8d2b29101|title=HAS: Members of HAS|publisher=Hungarian Academy of Sciences|accessdate=23 January 2010}}
6. ^List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
7. ^{{citation|url=https://www.amacad.org/content/members/newFellows.aspx?s=c|title=Newly Elected Members|date=April 2016|publisher=American Academy of Arts and Sciences|accessdate=2016-04-20}}
8. ^Shaw Prize 2017
9. ^{{cite journal|author=Reid, Miles|authorlink=Miles Reid|title=Review: Rational curves on algebraic varieties, by János Kollár|journal=Bull. Amer. Math. Soc. (N.S.)|year=2000|volume=38|issue=1|pages=109–115|url=http://www.ams.org/journals/bull/2001-38-01/S0273-0979-00-00889-2/S0273-0979-00-00889-2.pdf|doi=10.1090/s0273-0979-00-00889-2}}
10. ^{{cite journal|author=Kawamata, Yujiro|authorlink=Yujiro Kawamata|title=Review: Birational geometry of algebraic varieties, by János Kollár and Shigefumi Mori|journal=Bull. Amer. Math. Soc. (N.S.)|year=2001|volume=38|issue=2|pages=267–272|url=http://www.ams.org/journals/bull/2001-38-02/S0273-0979-01-00910-7/S0273-0979-01-00910-7.pdf|doi=10.1090/s0273-0979-01-00910-7}}
11. ^{{cite journal|author=Abramovich, Dan|title=Review: Resolution of singularities by Steven Dale Cutkovsky and Lectures on resolution of singularities by János Kollár|journal=Bull. Amer. Math. Soc. (N.S.)|volume=48|issue=1|pages=115–122|url=http://www.ams.org/journals/bull/2011-48-01/S0273-0979-10-01301-7/S0273-0979-10-01301-7.pdf|doi=10.1090/s0273-0979-10-01301-7}}

External links