*“Mathematics rightly viewed possesses not only truth but supreme beauty.”*

*- Bertrand Russell, British mathematician*

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Pure mathematics investigates fundamental theoretical and abstract concepts, exploring the boundaries of basic principles including analysis, algebra and geometry. Research in pure mathematics is not applied to real-world scenarios in the first instance; rather, it is usually shared amongst the mathematical community and academics. Pure mathematics is nevertheless fundamental to solving real-world problems as the mathematical techniques and theories at its core are utilised by applied mathematicians and underpin their work.

Dr Sugata Mondal’s research is based on the interplay between geometry and analysis. His main focus is on two dimensional objects such as the Euclidean plane and the two-dimensional sphere - the surface of a ball.

*“I love the clarity that mathematics can bring to a problem. Using some well-established mathematics, my research boils down to understanding the properties of some ‘functions’ defined by some differential equations and boundary conditions. This interplay between seemingly different areas of research excites me the most.”*

Sugata’s research contributes to two important problems: (1) small eigenvalues of surfaces; and (2) hot spots problem for Euclidean domains, and has had a significant impact for academics within the mathematical community.

*“Small eigenvalues have a connection with analytic number theory, differential geometry and graph theory. My research on ‘hot spots’ problems for Euclidean domains originated from a conjecture by J. Rauch who was motivated by a physical phenomenon.*

*“My most recent works on the ‘hot spots’ problem resolved an almost forty-five-year-old conjecture for the special case of triangular domains. This result renewed the interest in the truthfulness of the conjecture.”*

Mathematics students at Reading learn from Sugata’s expertise in analysis through the exploration of concepts such as inequalities, sequences and series, as well as functions and their fundamental properties. His teaching provides a rigorous foundation for further topics in analysis and its applications with emphasis on understanding concepts rather than mechanical computations.