Maneesh Thakur

Research Summary:

During this academic year, I have worked mainly on three projects. In one, jointly with Anupam Kumar Singh, I have been investigating reality properties of conjugacy classes in algebraic groups over a field. We have proved that for groups of type over a field of characteristic not 2, under certain restrictions, every semisimple element is conjugate to its inverse (this is being written up). We are looking for similar results on the groups of type and trialitarian . In another work, I am working on a one to one correspondence between subalgebras of a given Albert algebra and connected reductive subgroups of its automorphism group (these groups are precisely the forms of ). I am working on an article on Coxeter groups in collaboration with Dr. Ravindra Shukla of Allahabad University.

Preprints:

1. The etale Tits Process of Jordan Algebras revisted (with Holger Petersson), to appear in Journal of Algebra.
2. Reality properties of conjugacy classes in , in preparation (with Anupam Kumar Singh).
3. On subgroups of type in groups of type (in preparation).
4. Coxeter Groups (with Ravindra Shukla), in preparation.

Conference/Workshops Attended:

1. Attended GGT-2002 at IIT Guwahati in December 2002.
2. Attended the workshop on Arithmetic algebraic geometry at HRI in January 2003.

Visits to other Institutes:

I visited ISI Bangalore in June 2002 for a month. During this visit I mainly interacted with Prof. N. S. N. Sastry and we started a collaboration on studying geometry of exceptional groups with Dr. Ravindra Shukla of Allahabad University.

Invited Lectures/Seminars:

1. Triality and , at ISI Bangalore.
2. Groups of type , at IISc. Bangalore.
3. Taught a course on Coxeter groups at Allahabad University.
4. Taught a course on Coxeter groups in GGT-2002 at IIT Guwahati.
5. Delivered 4 lectures on Dimensions and Products in the workshop on Arithmetic algebraic geometry at HRI.

Academic recognition/Awards:

Was elected Associate at ICTP (till 2007) .

Other Activities:

Taught a one semester course on Algebraic Topology. I took Anupam Kumar Singh as my Ph.D. student from August 2002. I taught a basic course on Topology in VSSP-2002.