Alexandru Buium

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Alexandru Buium (* 1955 in Bucharest ) is a Romanian - American mathematician who studies algebraic geometry and number theory (arithmetic algebraic geometry).

Buium studied at the University of Bucharest , where he received his diploma in 1980 and his doctorate in 1983 with Nicolae Radu . He then did research at the National Institute for Scientific and Technical Research in Bucharest and from 1990 at the Institute for Mathematics of the Romanian Academy of Scientists . In 1995 he became Associate Professor and 1997 Professor at the University of New Mexico in Albuquerque . There he stayed until 1998 to 1999 as a professor at the University of Illinois at Urbana-Champaign .

He was a visiting scientist at the Max Planck Institute for Mathematics in Bonn (1993, 1994/95, 2010, 2012), at IHES (2011), at the University of Paris-Süd (2009), at the Institute for Advanced Study (1993/94 ) and the University of Essen (1992 as recipient of the Humboldt Research Award ). In 1991 he was visiting professor at Columbia University . In 2016 he became a Fellow of the American Mathematical Society .

Buium deals with arithmetic geometry and in the 1990s developed an arithmetic analogy to differential calculus in which functions are replaced by natural numbers and the derivation by the Fermat quotient operator (p prime number). The geometric Lie-Cartan theory of differential equations corresponds to arithmetic differential equations (with integer points on algebraic varieties as a solution instead of continuous functions) and the differential invariants of the Lie-Cartan theory correspond to arithmetic differential invariants of correspondences between algebraic varieties. He pursued applications of this theory of modular forms and number theory and extended the analogy to the case of partial differential equations (and other areas of analysis such as Fourier analysis).

In 1992 he made progress in the Mordell-Lang conjecture about function fields with the characteristic p, later proven by Ehud Hrushovski using model theory.

Buium received the award from the Romanian Academy of Sciences.

He is a US citizen.

Fonts

  • Differential Algebra and Diophantine Geometry, Hermann 1994
  • Differential Characters of Abelian Varieties over p-adic fields, Inventiones Mathematicae, Volume 122, 1995, pp. 309-340
  • Arithmetic Differential Equations, American Mathematical Society, Mathematical Surveys and Monographs 118, 2005
  • Differential Function Fields and Moduli of Algebraic Varieties, Lecture Notes in Mathematics 1226, Springer Verlag 1986
  • Differential Algebraic Groups of Finite Dimension, Lecture Notes in Mathematics, Volume 1506, Springer Verlag 1992
  • Intersections in jet spaces and a conjecture of S. Lang , Annals of Mathematics, Volume 136, 1992, pp. 583-593
  • Differential Modular Forms, J. Reine Angew. Math., Vol. 520, 2000, pp. 95-167

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Following the analogy of function fields and number fields has a long tradition in number theory and algebraic geometry
  3. ↑ Buium Differential Calculus and Integers , in: Differential equations and Galois theory, IHES 2011, pdf
personal data
SURNAME Buium, Alexandru
BRIEF DESCRIPTION Romanian-American mathematician
DATE OF BIRTH 1955
PLACE OF BIRTH Bucharest