The congruence subgroup problem

This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.Comment: 10 page

A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]

On the congruence subgroup problem

This article does not have an abstract

Kaun Banega Crorepati - a million dollars for a mathematician. 2. Poincaré conjecture

I will now embark on explaining as best as I can to the non-mathematician what the Poincaré conjecture is all about

On the congruence subgroup problem, II

This article does not have an abstract

A note on generators for arithmetic subgroups of algebraic groups

In this paper we construct systems of generators for arithmetic subgroups of algebraic groups

Tackling India’s deepening gender inequality during COVID-19

As India slowly re-opens its economy following its emergency national measures to contain the spread of the novel coronavirus, Kalyani Raghunathan (International Food Policy Research Institute (IFPRI), New Delhi) and M Niaz Asadullah (University of Malaya, Malaysia) explain how India’s already high levels of gender inequality will deepen thanks to the pandemic