FACETS 2026

July 3, 2026 9:30 - 17:00

Equivalence relations and building new worlds!
Subhankar Dey, IIT Palakkad

How do you like to play 'The Creator', the one who likes to build new worlds, but likes to play by the rules, with the rules being only from basic college-level mathematics? In this talk, we will discuss, conspire, and build new worlds. At the end, we might see some 3-dimensional worlds, and ask which is the exact world that we are living in!
Visualizing complex plane curves
Mohan Swaminathan, TIFR Mumbai

After recalling how to represent the algebra of complex numbers geometrically on the real 2D plane, we will discuss how to visualize the set of complex solutions to a polynomial equation P(x,y) = 0. For instance, we will see that the complex solutions to the equation x^4 + y^2 + 1 = 0 parametrize a torus (i.e., the surface of a medhu vadai) minus two points, even though this equation has no real solutions.
Can you build a manifold from a cube?
Raisa D'Souza, Azim Premji University, Bangalore

Can a cube contain enough information to describe a manifold? In this talk, we will explore how combinatorial data attached to simple polytopes can be used to construct topological spaces. Through examples and short activities, we will learn how local gluing rules determine global topological properties.