Abstract:
We see all sorts of shapes around us — some rectangles tall, others wide; some triangles sharp, others squat. Just as any place on Earth can be described by two numbers, its latitude and longitude, the “shape” of a rectangle or triangle can be captured by one or two numbers. We can then imagine a single map on which every possible rectangle, or every possible triangle, is marked as a point. Such “spaces of shapes” — what mathematicians call moduli spaces — turn out to be surprisingly rich. In this talk we will build them up from the simplest examples all the way to flat tori — the vada-shaped surfaces whose moduli space has a beautiful geometry of its own. We will see how this part of mathematics connects to robotics, medical imaging, and even understanding the universe we live in. The talk will feature pictures, animations, and interactive demonstrations throughout — no mathematical background is needed.
About the Speaker:
Subhojoy Gupta received his Ph.D. in Mathematics from Yale University in 2012. He is an Associate Professor of Mathematics at the Indian Institute of Science in Bangalore, India, where he has taught since 2015. His research lies in low-dimensional geometry, and often involves Riemann surfaces and their moduli spaces, drawing on tools from complex analysis and hyperbolic geometry.
Supported by Arista Networks India Pvt. Ltd