Raman Parimala

Raman Parimala (* 1948 ) is an Indian mathematician who studies algebra and algebraic geometry .

Life

Parimala went to school in Chennai and studied at Stella Maris College, University of Madras (bachelor's degree in 1968, master's degree in 1970) and at the University of Mumbai , where she completed her PhD in 1976 with R. Sridharan from the Tata Institute of Fundamental Research . After that she was a professor at the Tata Institute for many years. She has been an Asa Griggs Candler Professor at Emory University in Atlanta since 2005 . She was visiting scholar at the ETH Zurich , the University of Lausanne , the University of California, Berkeley , the University of Chicago , the Ohio State University and the University of Paris in Orsay . In 2006 she was an Emmy Noether visiting professor at the University of Göttingen .

Parimala deals with algebraic groups, quadratic forms, and Galois cohomology . In 1983 she gave the first example of a nontrivial square space above the affine plane. With Max-Albert Knus , Manuel Ojanguren, and Sridharan, she then investigated low-rank quadratic spaces in algebraic geometry that were used to solve (with Knus, Sridharan) a problem by Abraham Adrian Albert from the 1930s about conditions for the decomposability of involutions into central ones Division algebras led. They introduced a new invariant (Pfaff's discriminant of the involution) and proved the decomposability if this invariant vanishes.

Parimala also solved or promoted some other partially long open conjectures. In 2007 she and V. Suresh proved that the μ-invariant (the maximum dimension of an anisotropic square shape over the body) of the rational field of functions of an algebraic curve over the p-adic numbers is less than or equal to 10. That this invariant is finite and equal to 8 was already suspected in the 1950s. In 1995, together with Eva Bayer-Fluckiger , she proved a conjecture by Serre ( Conjecture 2 ) from 1962 on the Galois cohomology of algebraic groups for some classical groups.

She was invited speaker at the ICM 1994 in Zurich ( Study of quadratic forms — some connections with geometry ) and was invited to a plenary lecture for the ICM 2010 in Hyderabad ( Arithmetic of linear algebraic groups over two dimensional fields ). She is a Fellow of the Indian Academy of Sciences and the Indian National Science Academy. In 1987 she received the Shanti Swarup Bhatnagar Prize and in 2003 the Srinivasan Ramanujan Birth Centenary Award. In 1999 she received an honorary doctorate from the University of Lausanne . In 2005 she received the Mathematics Prize of the Academy of Sciences of the Developing World for her work on the "quadratic analogue of the Serre conjecture, the triviality of homogeneous spaces of classical groups over fields of cohomological dimension 2 and the μ-invariant of p-adic function fields" . In 2013 she gave the Noether Lecture . She is a Fellow of the American Mathematical Society .

Sujatha Ramdorai is one of her PhD students .

Fonts

with V. Suresh: The -invariant of the function fields of -adic curves. ${\ displaystyle u}$ ${\ displaystyle p}$ In: Annals of Mathematics . Series 2, Volume 172, No. 2, 2010, pp. 1391-1405, JSTOR 29764641 .
with Eva Bayer-Fluckiger : Classical groups and the Hasse principle. In: Annals of Mathematics. Series 2, Volume 147, No. 3, 1998, pp. 651-693, doi : 10.2307 / 120961 .
with Eva Bayer-Fluckiger: Galois cohomology of the classical groups over fields of cohomological dimension 2. ${\ displaystyle \ leqq}$ In: Inventiones Mathematicae . Vol. 122, 1995, pp. 195-229 .
Quadratic spaces over polynomial extensions of regular rings of dimension 2. In: Mathematische Annalen . Volume 261, No. 3, 1982, pp. 287-292, doi : 10.1007 / BF01455449 .
Failure of a quadratic analogue of Serre's conjecture. In: Bulletin of the American Mathematical Society . Volume 82, No. 6, 1976, pp. 962-964, doi : 10.1090 / S0002-9904-1976-14234-6 .

Web links

Individual evidence

↑ Vector space over a body with a square shape defined in this space.
↑ In the original of the laudation it says literally: “... for her work on the quadratic analogue of Serre's conjecture, the triviality of principal homogeneous spaces of classical groups over fields of cohomological dimensions 2 and the μ-invariant of p-adic function fields ".

personal data
SURNAME	Parimala, Raman
BRIEF DESCRIPTION	Indian mathematician
DATE OF BIRTH	1948

[1] Vector space over a body with a square shape defined in this space.

[2] In the original of the laudation it says literally: “... for her work on the quadratic analogue of Serre's conjecture, the triviality of principal homogeneous spaces of classical groups over fields of cohomological dimensions 2 and the μ-invariant of p-adic function fields ".