Maneesh Thakur

Research Summary:

With Anupam Singh, I have completed our investigations of reality properties for conjugacy classes in groups of type G₂. We have used our results and techniques to compute centralisers of elements and their conjugacy classes in groups of type G₂ over arbitrary fields. We plan to carry out this for other exceptional groups as well. The project to describe rational subgroups of algebraic groups is in progress. There is a one to one correspondence between isomorphism classes of k-maximal tori in SU(V,h) and isomorphism classes of certain etale algebras of dimension n containing L, a quadratic extension of k. Here (V,h) is a hermitian space over L of dimension n. This has been effectively used to describe maximal tori in anisotropic groups of type G₂. With Dr. R. P. Shukla, have completed two articles on Coxeter Groups and Pseudo Reflection groups. These are to be published in the proceedings of the Geometric Group Theory workshop (GGT 2002), held at Guwahati.

Preprints:

1. Reality Properties of Conjugacy Classes in G₂ (with Anupam Singh), submitted.
2. Coxeter Groups, Preprint (with R. P. Shukla)
3. Some topics in Pseudo Reflection Groups, Preprint (with R. P. Shukla).
4. A note on Hermitian forms, Preprint.
5. Conjugacy Classes in G₂ (in progress).
6. Rational subgroups of G₂ and F₄ (work in progress)

1. Buildings and Polygons, University of Wurzburg, September 2003.
2. Joint AMS-India meeting, IISc. Bangalore (December 2003).
3. Algebraic Groups and Homogeneous Spaces, TIFR Bombay (January 2004).

Visits to other Institutes:

1. FernUniversitat, Hagen (Germany), July 2003.
2. ICTP, Trieste, August-October 2003.

1. Reality Prperties for Conjugacy Classes in G₂, 3 lectures at Hagen.
2. G₂ and Reality, in "Buildings and Polygons", at University of Wurzburg.
3. Some conjugacy results for G₂, ICTP.
4. Reality Properties for G₂, AMS-India meeting, IISc.
5. Algebras with Involutions and Classical Groups, 3 lectures at HRI.