Dr. Krishnendu Gongopadhyay

   Associate Professor (Mathematics)
   Knowledge city, Sector 81, SAS Nagar,
   Manauli PO 140306

   Email: krishnendu[at]
   Telefax: +91-172-2240266

Research Area: Hyperbolic spaces, discrete groups and geometric group theory

My research has been centered around the hyperbolic spaces and their isometries. We have obtained algebraic classifications of the isometries of the real, complex and quaternionic hyperbolic spaces, for eg. see [6]. We have also classified real or reversible isometries of the real and complex hyperbolic spaces, for eg. see [1]. We recall that an element in a group is called reversible if it is conjugate to its inverse. We asked the group theoretic question to classify conjugacy classes of centralizers or thez-classes in the isometry groups of the hyperbolic spaces. We have answerd this question in a series of papers, eg. see [2]. Currently, I am interested in understanding representations of surface groups in the isometry groups and also, many of the other directions related to the geometric structures modelled on the hyperbolic spaces.

In geometric group theory, we have studied palindromes and palindromic automorphisms of groups. An element in a group G is a palindrome if it reads same forward and backward. The palindromic width isthesupremumofallpalindromicwordlengthsina
group. Wehaveinvestigatedpalindromicwidthsinseveralclassesofgroups. Inparticular, we have obtained estimates for the palindromic widths in free nilpotent groups and have proved that the palindromic width is finite in certain solvable groups, see [3, 4]. A palindromic automorphism is a group automorphism that preserves palindromic words. We have obtained several algebraic results about palindromic automorphisms of free groups, see [5]. Recently, we are investigating palindromic automorphisms of free nilpotent groups and plan to study geometry of the outer automorphisms of free groups in the near future.

Selected Publications

  • K. Gongopadhyay. Conjugacy classes in Mobius groups, Geom. Dedicata, Volume 151, Number 1 (2011), 245-258.
  • K. Gongopadhyay, Thez-Classes of quaternionic hyperbolic isometries, J. Group Theory. Volume 16, Issue 6 (2013), 941-964.
  • K. Gongopadhyay and Valeriy G. Bardakov, Palindromic width of free nilpotent groups. J. Algebra 402 (2014), 379- 391.
  • K. Gongopadhyay and Valeriy G. Bardakov, Palindromic width of finitely generated solvable groups. Comm Algebra, Volume 43, issue 11 (2015), 4809-4824.
  • K. Gongopadhyay, Valeriy G. Bardakov and Mahender Singh, Palindromic automorphisms of free groups. J. Algebra, Volume 438 (2015), 260282.
  • K. Gongopadhyay, John R. Parker and ShivParsad, On the classification of unitary matrices. Osaka J. Math, Vol 52, no. 4, to appear.


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