Anupam Kumar Singh


Research Summary:

I have been working with Dr. Maneesh Thakur on a problem about reality properties of semisimle elements in the exceptional group of type $G_2$. Given a group of type $G_2$ over a field $k$, one can realize it as the automorphism group of an octonion algebra over $k$. One wants to study whether every semisimple element of $G_2(k)$ can be conjugated to its inverse in $G_2(k)$. One knows that this can be done in $G_2(\bar k)$.This property for any element of the group is called reality property and it has been studied for classical groups in literature. We are studying this question over an arbitrary field. Also we are exploring similar questions for other exceptional groups.

Preprints:

Reality properties of conjugacy classes in $G_2$, in preparation.

Conference/Workshops Attended:

  1. Workshop on Topological Methods in Group Theory (July 15 - 27, 2002) in IMSc, Chennai.

  2. Instructional workshop and International Conference on Geometric Group Theory (December 2 - 21, 2002) in IIT Guwahati.
Other Activities:
  1. I wrote lecture notes for a course ``Algebraic Number Theory `` given by Prof. D. Prasad in first semester of academic year 2002-03.
  2. I gave five introductry lectures on linear algebraic groups in group theory seminar organised by Prof. I.B.S. Passi.


© Harish-Chandra Research Institute