Facets 2026
Facets is a mathematics outreach program organized by IMSc. It is aimed at students with a background in college level mathematics.
Who should apply?
#- Students in BSc and MSc mathematics programmes,
- Students in mathematical disciplines such as science and engineering who have a strong interest in mathematics.
What to expect in the programme?
#- There will be 3 lectures. The lectures will give you a glimpse of what lies beyond the mathematics you learn in college.
- The lectures will require you to be hands-on, working on mathematical problems and activities.
- After the lectures, we will have a panel discussion, where you can ask questions to mathematics professors.
- The day's activities are likely to get you excited about learning and exploring more mathematics!
Speakers
#- Subhankar Dey (IIT Palakkad)
- Mohan Swaminathan (TIFR Mumbai)
- Raisa D'Souza (Azim Premji University, Bangalore)
Schedule
#| 3 July | |
| 9:00 - 9:30 | Registration |
| 9:30 - 11:00 | Equivalence relations and building new worlds! Talk Slides PDF (1.5 MB) Subhankar Dey |
| Tea/Coffee | |
| 11:30 - 13:00 | Visualizing complex plane curves Mohan Swaminathan |
| Lunch Break | |
| 14:00 - 15:30 | Can you build a manifold from a cube? Raisa D'Souza |
| Tea/Coffee | |
| 16:00 - 17:00 | Panel Discussion S Viswanath, IMSc (Chair), Subhankar Dey, Mohan Swaminathan, Raisa D'Souza |
Talk Recordings
#
Abstracts
#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.