Facets 2019 : Schedule

Matrices are easy to understand, simple to manipulate and remain among the most useful tools in all of mathematics. Algebraic structures such as groups and rings are in general quite abstract, but can be better understood if one can find matrix "models" for them. In this talk, we will see numerous examples of such matrix representations and study some of their properties.

In this talk, I will attempt to prove that irreducible representations of a finite dimensional C*-algebra is finite in number. We will start with the most basic example of such C*-algebras which are n*n matrices.

The basic principle of perspective drawing is that parallel lines converge. Looking at examples, it is easy to see that pictures drawn "in perspective" correctly model our vision, while pictures that are not drawn "in perspective" fail to do so. But why is this the case? Namely, why is it that when we look at parallel lines in space, we actually observe them converging to a point? And why do different families of parallel lines seem to converge to different points? Rather than study points and lines in space, we will study the images of points and lines in our vision, in order to answer these questions.

In fact, using "homogeneous coordinates" we can make mathematically precise statements about the images we see. The mathematical laws these images obey are different from the usual "Euclidean" laws that we are used to studying, but nevertheless give rise to a rich geometric structure.

This talk describes how a one dimensional yarn magically transforms into a two dimensional fabric. We discuss the computational nature of this intricate and meditative craft with an activity. We explore some of the latent skills possessed by the 3 Million plus extant handloom weaver families in India and explore how these may be channelled into the 21st century.

Many problems in physics involve enumeration of different shapes. I will illustrate how elementary combinatorics help in doing so.

Sharing of resources is always difficult. As we see in the context of sharing river water, sharing is hard especially in times of distress. We want not only efflicient allocation of resources among the needy, we also want equitable, and fair allocation. Ideally the allocation should be by mutual consent rather than one dictated by an external authority. But are such requirements even consistent? Is there any mathematical way to approach such problems?

The talk is an invitation to think about such questions. The mathematics used is very simple, and yet leads to interesting research problems.

This talk will focus on the question of what is the role of student questioning in science and mathematics education. We will discuss the relation between teaching methods and educational goals, and also make some comparisons between the nature of science and mathematics. The claim is that questioning plays a central role in doing science and mathematics, and therefore it is strange that students hardly ask questions in classrooms where they are supposed to be learning how to do science and mathematics. It is surprising that researchers have not been asking more questions in order to investigate this problem.