## Return to Answer

1 [made Community Wiki]

Raman Parimala is an algebraist and algebraic geometer. She studies problems related to the existence of rational points on algebraic varieties over various fields (both "dimension one" : local and global, and "higher dimensional" fields, like function fields of curves over local fields, etc.), in particular varieties associated to algebraic groups : quadrics, Severi-Brauer varieties, varieties linked to algebras with involutions... The methods include Galois cohomology, K-theory, unramified cohomology on the one hand and the classical algebraic theory of quadratic forms on the other.

As a personal note, I would say this is the area of algebraic geometry which is most satisfying from the point of view of sophisticated cohomological/K-theoretic tools (including the whole machinery developped in the wake of Morel-Voevodesky's $\mathbb{A}^1$-homotopy theory) because one can make a lot of computations of otherwise intractable invariants.

A few collaborators : Bayer-Fluckiger, Colliot-Thélène, Gille, Quequiner, Srinivas, Suresh, Tignol...

A few of her important results (some with said collaborators):

• The first proof for classical groups of Serre's conjecture II on Galois cohomology of algebraic groups over fields of cohomological dimension 2

• Examples of zero cycles of degree 1 without rational points on projective homogeneous varieties

• Results on the u-invariant (i.e whether a quadratic forms in enough variables is automatically isotropic, like in Meyer's theorem for number fields) of function fields over p-adic fields

...

She gave a lecture in the Suslin birthday conference in Saint Petersburg in july : see the end of the following webpage, which hosts videos of all the talks :

http://www.pdmi.ras.ru/EIMI/2010/ag/program.html