Raisa DSouza
Ph.D., IIT, MadrasRaisa DSouza
Ph.D., IIT, MadrasMy research interests lie in the areas of Algebraic Topology and some aspects Algebraic Combinatorics and Spectral Graph Theory.
More specifically,
- In algebraic topology, I have worked on the topology of real Bott manifolds and the generalized real Bott manifolds, characterizing when these manifolds have a spin structure.
- In Algebraic Combinatorics, I am interested in studying combinatorial structures associated with rings and their spectral properties.
- In spectral graph theory, I am interested in studying how the properties of a graph may be studied by looking at linear algebraic properties of the matrices associated with it.
Raisa is a mathematician and educator, with a research focus on algebraic topology and graph theory. As a research scholar at IIT Madras, she grew mathematically and strengthened her understanding of topology, analysis and algebra. Broadly, Raisa’s area of research was in Algebraic Topology, in particular the topology of real toric varieties and small covers. Algebraic Topology is the study of topological spaces (manifolds and varieties for example) through certain algebraic invariants associated with them. Her specific problem is the study of the topology of real Bott manifolds which are an interesting class of examples of real toric varieties. In her thesis titled “On the topology of real Bott manifolds”, supervised by Dr. V. Uma, they gave a criterion for the admittance of a spin structure on orientable real Bott manifolds as well as a graph theoretic interpretation of the same. Thus began her interest in graph theory. She is currently interested in graphs and studying the spectral properties of the matrices associated with them.
Before joining Chanakya University in 2025, Raisa was an Assistant Professor at St Joseph’s University in Bangalore (2018-2025) where she taught several Mathematics courses at the undergraduate and postgraduate levels. She shares a commitment to nurturing students’ understanding and appreciation of Mathematics.
- Ph.D., Department of Mathematics, 2018, Indian Institute of Technology, Madras
- M.Sc., (Mathematics), 2012, Mount Carmel College, Bangalore
- B.Sc., (Physics, Chemistry, Mathematics), 2010, Mount Carmel College, Bangalore
- P. Akhil and R. Dsouza, “On the Seidel spectrum of the total graphs of the rings of integers modulo n,” Mathematics Open, vol. 4, p. 2550014, 2025.
- V. B. Lama, B. N. Suhas, S. Mazumdar, and R. DSouza, “Extensions of i-reversible rings,” Journal of Algebra and Its Applications, vol. 23, no. 4, p. 2450081, 2024.
- R. Dsouza and V. Uma, “Results on the topology of generalized real Bott manifolds,” Osaka Journal of Mathematics, vol. 56, pp. 441–458, 2019.
- R. DSouza, “On the topology of real Bott manifolds,” Indian Journal of Pure and Applied Mathematics, vol. 49, pp. 743–763, 2018.
Researchgate – https://www.researchgate.net/profile/Raisa-Dsouza