Current Course — Fall 2026 KSM3E02

Algebraic Topology I — Fall 2026

In the current semester, I am teaching Algebraic Topology I at the Kerala School of Mathematics. This course develops algebraic invariants to study and classify topological spaces, with a focus on CW complexes, the fundamental group, the Seifert–van Kampen theorem, covering spaces, deck transformations, and introductory homology theory.

View Course Webpage & Notes

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

  • Algebraic Topology I (Fall 2026): Current course — covering CW complexes, fundamental groups, van Kampen's theorem, covering spaces, and introductory homology. Course page.
  • Differential Geometry (Spring 2026, Fall 2021 & Spring 2022): Smooth manifolds, vector bundles, Riemannian metrics, connections, and curvature.
  • Analysis on Manifolds (Fall 2025, Fall 2024): Differentiable manifolds, integration theory, and applications to geometry and physics. Fall 2025 page.
  • 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.
  • 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.