Current Course – Spring 2026

In the current semester, I am offering Differential Geometry at the Kerala School of Mathematics. This course studies the geometry of smooth manifolds through vector bundles, Riemannian metrics, connections, and curvature, with particular emphasis on the geometry of surfaces and global results such as the Gauss–Bonnet theorem.

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Teaching Approach

Teaching is an integral part of my work at the Kerala School of Mathematics. My approach focuses on helping students build a clear and intuitive understanding of mathematical ideas, encouraging critical thinking, and nurturing an appreciation for the subject. I strive to create an environment where learners feel confident exploring challenging concepts, asking questions, and developing their own problem-solving skills.

I aim to design courses that are both rigorous and supportive, linking abstract ideas to fundamental principles and practical applications whenever possible. My ongoing objective is to continually improve the learning experience and respond to the changing needs of students.

Courses Taught

At Kerala School of Mathematics

  • Analysis on Manifolds (Fall 2025, Fall 2024): Differentiable manifolds, integration theory, and applications to geometry and physics.
  • Bridge Course in Algebra (July–August 2025): Foundational algebra topics for incoming Integrated MSc-PhD students.
  • Algebraic Topology II (Spring 2024): Cohomology theory, duality theorems, and advanced topics.
  • Algebraic Topology I (Fall 2023): Homotopy, fundamental groups, and basic homology theory.
  • Differential Equations (Spring 2023): Techniques for solving ordinary and partial differential equations with applications.
  • Differential Geometry (Fall 2021 & Spring 2022): Geometry of curves and surfaces, curvature, and geodesics.
  • Complex Analysis (Spring 2021): Functions of a complex variable, integration, series, and residue theory.
  • Topology (Fall 2020): Topological spaces, continuity, compactness, and connectedness.

Online Courses via Swayam Central

  • Complex Analysis (Spring 2020): Accessible introduction to complex function theory. View lectures.
  • Linear Algebra (Fall 2020): Vector spaces, transformations, eigenvalues. View lectures.

At Chennai Mathematical Institute

  • Riemann Surfaces (Fall 2018): Theory of one-dimensional complex manifolds for advanced mathematics and physics.

At Indian Institute of Technology Madras

  • Linear Algebra and Numerical Analysis (Spring 2016 & 2017): Linear systems and numerical methods for scientific computing.