Biography
Prof. Gurmeet K. Bakshi
Prof. Gurmeet K. Bakshi
Centre for Advanced Study in Mathematics, Panjab University, India
Title: Can we explicitly describe the structure of rational group algebras?
Abstract: 
It is a classical problem to determine the primitive central idem- potents (pcis) and the Wedderburn decomposition of a rational group algebra QG. This problem has relevence to other problems in group rings and coding theory. The classical method of computing pcis in- volves the knowledge of the character table of G and does not bring the subgroup structure of G into picture. It also does not give any insight into the structure of the corresponding simple components of QG. In 2004, Olivieri, del Rio and Simon introduced a powerful character free method and proved that these computations can be efficiently done for strongly monomial groups (in particular abelian by supersolvable groups). In this talk we will show that the method of Olivieri, del Rio and Simon can be extended for a very large class of monomial groups, which we call as generalized strongly monomial groups. We'll show that the class of generalized strongly monomial groups is vast, and rather so vast that it is difficult to construct an example of a monomial group which is not generalized strongly monomial.
Biography: 

Personal History:

I received PhD degree in Mathematics from Panjab University Chandigarh in 1996 and joined my alma mater as lecturer in Mathematics in Dec 1999. I got promoted as associate professor in 2010 and received full professorship in 2013. Since 2018, I am serving as the Chairperson, department of Mathematics, Panjab University. Before joining Panjab University, I have worked as lecturer in Mathematics at Guru Nanak Dev University, Amritsar (1994-96), Thapar University, Patiala (1997) and Govt college Mohali (1998-99).

 

Research Interests: Group Rings, Representation Theory, Coding Theory

Representation theory is a fundamental tool to study finite groups by means of linear algebra. Group Algebras occur naturally in the theory of representations of finite groups and play a major role in understanding them. The knowledge of the algebraic structure of semi simple group algebras can reveal good information about the representations. My recent research focuses on a modern approach to compute the precise algebraic structure of semi simple group algebras. I am also interested in its applications in coding theory.