GRAPH THEORY

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.

COMPLEX ANALYSIS

Complex analysis traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.

SOLID STATE LUMINESCENCE

Lanthanide-based luminescence nanomaterials have attracted considerable attention over the last few decades because of the unique optical properties of lanthanides. Given their 4f electronic configuration, these nanomaterials exhibit unique emission spectra, including tunable emissions spanning the ultraviolet (UV) to near-infrared (NIR) regions, long excited-state lifetime, high resistance to optical photobleaching, no optical blinking, superior photostability, as well as large Stoke or anti-Stoke shifts. This set of outstanding features makes the study of lanthanide-based luminescence nanomaterials a subject of fundamental and technological importance. This has driven our research group forward to understand the underlying mechanisms of luminescence and explore the manifold possible applications.

English Language Teaching (ELT)

English Language Teaching (ELT) includes various approaches, techniques and methods that are involved in teaching English, to people with English as their medium of instruction and also those who use it as a second and a foreign language. Some common techniques and strategies used in English language instruction include communicative language teaching, task- based learning, and content and language integrated learning. These approaches prioritize student engagement and practical language use in a variety of contexts.