FACETS 2018 : Schedule

We shall see how group theory is used to understand the symmetries of geometric objects. Can different-looking geometries have the same groups of symmetries? We will play with some three dimensional solids and find out.

Working with Lagrangian formulation of classical mechanics and electromagnetism we will discuss the role of symmetries. We will aim to understand the conformal symmetry of field theories and how it relates to holography. (Slides)

The Riemann sphere is the complex plane with a point at infinity. Möbius transformations are isomorphisms of the Riemann spheres that preserve angles. What do these transformations look like? What is the the group of Möbius transformations? In this talk, we will explore these questions via examples and pictures.

The purpose of this session is to look at different ways in which mathematics is engaged with in different cultures through numbers, stories, puzzles and games In this session we look at different numeration systems both written and oral and both historical and contemporary. We will also solve puzzles based in folk stories and play folk games.

Does the order in which we add numbers matter? In certain cases, yes! We will begin by trying to understand how to add infinitely many numbers and this will lead us to explore the convergence of sequences. We will then proceed to discuss the rearrangement theorem of Riemann which states that, for certain lists of numbers, if we are allowed freedom in the order in which we add them, then we can get any answer we want!

In this talk I will explore the possibilities afforded through Machine Learning through examples of recent advances made by academia, industry and some of our work at Adobe. I will also attempt to look through the corners on what we can expect in the future and discuss some challenges. I will demonstrate some of the work we are doing in our research team in order to illustrate how areas of mathematics like topology and algebraic geometry can help in solving or shedding light on some practical problems.

Many things of interest can be regarded as sequences of symbols, from language to music to biomolecules like DNA. How do we describe such sequences? Starting from the basics of probability theory and the simplest random sequence (a run of coin tosses), we go on to discuss more sophisticated models applicable to language and biology. (Slides)

1. Aaloka Kanhere (HBCSE)
2. R. Sivaguru (Mathematics, TIFR CAM)
3. Balaji Krishnamurthy (Adobe Systems)
4. Ganesh Ramachandran (Physics, IMSc)