Agata Smoktunowicz

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Agata Smoktunowicz (born October 12, 1973 ) is a Polish mathematician who works with algebra .

Smoktunowicz studied mathematics at the University of Warsaw from 1992 (diploma 1997) and did her doctorate in 2000 at the Institute of Mathematics of the Polish Academy of Sciences , where she completed her habilitation in 2007. From 2001 to 2003 she was Gibbs Lecturer at Yale University . Since 2000 she has been assistant professor at the Institute of Mathematics of the Polish Academy of Sciences in Warsaw and at the same time professor at Edinburgh University (lecturer from 2005). In 2004 she was a visiting scholar at the University of California, San Diego .

Smoktunowicz deals with non-commutative ring theory, applications of associative algebras in group theory, with Lie groups and in projective geometry, and with algebras (e.g. Golod-Schafarewitsch algebras and algebras with finite Gelfand-Kirillow dimensions, algebras with exponential growth). In doing so, she solved some assumptions, some of which were decades old.

She constructed simple Nile rings over any number of countable bodies and thus solved an old problem by Jakob Levitzki , Nathan Jacobson and Irving Kaplansky (the question of the existence of simple Nile rings was previously unsolved). She also showed that polynomial rings over Nile rings can be non-Nile over countable bodies (in contrast to the case of uncountable bodies examined by Shimshon Amitsur in 1956).

For graded algebras, it proved an old conjecture by Michael Artin and JT Stafford (Artin Stafford Gap Conjecture, gap conjecture by Artin and Stafford) that there are no graded integrity regions with Gelfand-Kirillow dimensions (which measures the growth of algebras) between 2 and 3 gives (the dimensions for curves or surfaces in non-commutative projective geometry). The theorem proved by it corresponds to the Bergman gap theorem in the non-graded case (which prohibits GK dimensions between 1 and 2 there).

In 1998 she received the Polish Academy of Sciences Prize and in 2001 the Bialkowski Prize. In 2006 she received the Whitehead Prize and the Waclaw Sierpinski Prize. In 2006 she was invited speaker at the ICM in Madrid (Some results in non commutative ring theory). She is a member of the London Mathematical Society and the Edinburgh Mathematical Society , whose Whittaker Prize she received in 2009. In 2006 she received an EPSRC Advanced Research Fellowship. In 2008 she received the EMS Prize (lecture: Graded algebras associated to algebraic algebras need not be algebraic ). She is a Fellow of the American Mathematical Society .

Web links

References

  1. ↑ in which each element nilpotently is
  2. ↑ Smoktunowicz, A simple Nil Ring exists , Communications in Algebra, Vol. 30, 2002, p. 27
  3. ↑ Smoktunowicz Polynomial rings over nil rings need not be nil , Journal of Algebra, Vol. 233, 2000, p. 427
  4. ↑ Smoktunowicz There are no graded domains with GK dimension strictly between 2 and 3 , Inventiones Mathematicae, Vol. 164, 2006, p. 635
  5. ^ Smoktunowicz The Artin-Stafford Gap Theorem , Proc. AMS Vol. 133, 2005, p. 1925
personal data
SURNAME Smoktunowicz, Agata
BRIEF DESCRIPTION Polish mathematician
DATE OF BIRTH October 12, 1973