Prof. Rajendra Bhatia, ISI Delhi & Ashoka University, Haryana.

Date and Time: 15/1/2018 (Monday) at 3:00 PM

Venue: MZ 194, Seminar Room, Department of Mathematics

Title: Diagonals of matrices

Abstract: Everyone knows that the trace of a matrix is the sum of its diagonal entries as well as the sum of its eigenvalues. A lot more can be said, and leads to much interesting mathematics., some of which will be discussed in the talk.

Prof. Ajay Kumar, Department of Mathematics, University of Delhi Date and Time: 24/1/2018 (Wednesday) at 4:00 PM

Venue: MZ 194, Seminar Room, Department of Mathematics

Title: Uncertainty Principles on locally compact groups

Abstract: We discuss uncertainty principles like Hardy’s theorem, Qualitative uncertainty principle, Beurling‘s theorem and Heisenberg inequality for locally compact groups such as R^n, abelian groups, Heisenberg group, nilpotent Lie groups and several other classes of non-abelian groups.

Prof. Apala Majumdar (Reader in Applied Mathematics, Universityof Bath, United Kingdom)
Date and Time: 31/1/2018 (Wednesday) at 4:00 PM
Venue: MZ 195, Committee Room, Department of Mathematics
Title:  Multistability for Liquid Crystal Systems

Abstract: Nematic liquid crystals are classical examples of mesophases intermediate between solids and liquids, with anisotropic or direction-dependent optical and electro-magnetic properties. We review two popular continuum theories for nematic liquid crystals: the Oseen-Frank and the Landau-de Gennes theories. We illustrate how these theories can be applied to liquid crystal devices, with the Planar  Bistable Nematic device as a case study. We model the Planar Bistable  Nematic Device in terms of problems in the calculus of variations and  theory of elliptic partial differential equations. We use tools from  singular perturbation theory, topology, functional analysis and numerical methods to study the multiple solution branches as a function  of the geometry, boundary conditions, temperature and material properties. We provide a semi-analytic description of a previously  unreported Well Order Reconstruction solution in this planar device.  This is joint work with a number of co-authors: Giacomo Canevari, Amy  Spicer, Martin Robinson,Radek Erban, Samo Kralj, Patrick Farrell and  Chong 


Prof. Ved Prakash Gupta, Jawaharlal Nehru University, New Delhi
Date and Time: 15/2/2018 (Thursday) at 4:00 PM
Venue: MZ 195, Committee Room, Department of Mathematics

Abstract: Every associative algebra inherits a canonical Lie algebra structure and there exists a deep relationship between ideals and Lie ideals of such algebras. This relationship extends to the category of normed algebras as well. After providing a quick overview of objects of interest, we will discuss some recent developments made in this direction. Some part of this talk will be based on joint works with Ranjana Jain and Bharat Talwar.

Prof. Krishnan Rajkumar, Jawaharlal Nehru University, New Delhi
Date and Time: 15/3/2018 (Thursday) at 4:00 PM
Venue: MZ 195, Committee Room, Department of Mathematics

Title:  Generalized factorials in several variables
Abstract: The discovery by M. Bhargava (1997), of generalized factorials in Dedekind domains, unified past work as well as answered questions in the fields of integer valued polynomials, polynomial mappings over finite abelian groups and fixed divisors of polynomials. The first part of the talk will be a historical account of these developments. In the second part, we will focus on attempts by M. Bhargava (2000) and S. Evrard (2012) to define the notion of generalized factorials in several variables. We will then outline a joint work with D. Prasad and A. S. Reddy, where this notion is further developed.