Bishal Deb - Gonit Sora

Ramanujan Graphs and the Matrix Completion Problem

Prof. Mathukumalli Vidyasagar FRS, SERB National Science Chair and Distinguished Professor of the Indian Institute of Technology Hyderabad gave a talk on 20th March, 2021 on “Ramanujan Graphs and the Matrix Completion Problem.” The slides of the talk can be found here. The full video of the talk is available

Geometry

An Introduction to Minimal Surfaces

Prof. Rukmini Dey of the International Centre for Theoretical Sciences (ICTS), Bengaluru gave a talk on 13th March, 2021 on “An Introduction to Minimal Surfaces.” The slides of the talk can be found here. All images were taken from the internet which were publicly available. A list of all past

C.S. Seshadri

Classification Problems in Mathematics (in memory of Prof. C.S. Seshadri (1932-2020))

Prof. S. Ramanan of Chennai Mathematical Institute gave a talk in a webinar organized by Gonit Sora on Classification Problems in Mathematics. This talk was dedicated to the of Prof. C.S. Seshadri (1932-2020). The slides of the talk can be found here. The full video of the talk is

Alexander Grothendieck

An Introduction to Algebraic Geometry

Dr. Tarig Abdelgadir of Loughborough University, UK gave a talk in a webinar organized by Gonit Sora on An Introduction to Algebraic Geometry. The full video of the talk is available in our YouTube channel as well as below. A list of all past and future webinars are available at

$2018 Breakthrough Prize in Mathematics awarded to Christopher Hacon and James McKernan$

Breakthrough Prize

2018 Breakthrough Prize in Mathematics awarded to Christopher Hacon and James McKernan

The Breakthrough Prize in Mathematics is a prize that was announced in 2013 and is funded in parts by Yuri Miller and Mark Zuckerberg.The joint winners of the USD 3 million prize for 2018 are Christopher Hacon of the University of Utah and James McKernan of the University of

2016

Some Interesting Properties of the Number 2016

We look at some interesting properties of the number . We mention in passing that the year is a leap year. 1. The number factors as . 2. From the factorisation a lot of interesting observations can be made. Such as divides . The previous number where the number formed by its last

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra using Galois theory

In this article we shall prove that is algebraically closed. Here we consider as a splitting field of the polynomial . The proof uses very little analysis and most of it is Galois theory. The only facts from analysis which will be used in proof are : * Positive real numbers have square

characteristic polynomial

A Problem in Linear Algebra

In this article we shall show that the characteristic polynomial of both and are the same, where and are matrices over , a ring with unity. Let denote the characteristic polynomial of . Thus, we intend to show, . We first take and specialize in this ring. By multiplicity of the determinant function,

IMO

An Interview with Professor Po-Shen Loh

Po-Shen Loh is an associate professor of mathematics at the Carnegie Mellon University. He specializes in probabilistic and extremal combinatorics. He is the founder of Expii which “is a free interactive website, focused on math and science, where students, teachers, tutors, and enthusiasts are encouraged to add their voices and

automorphism

Automorphisms of the Upper Half Plane

In this article we see that the automorphism group of biholomorphic functions of the upper half plane and the open unit ball in the complex plane is isomorphic to the second projective special linear group over the field of real numbers. [pdf-embedder url=”/content/images/wordpress/2016/05/automorphisms-upper-half.pdf”

Alan Turing

What is a Turing Machine?

The movie The Imitation Game ends with the quote : “His machine was never perfected, though it generated a whole field of research into what became known as ‘Turing Machines‘. Today we call them ‘computers.’ ” The his here refers to the protagonist of the movie. Benedict Cumberbatch, who is the main

Berry

An Interview with Professor Sir Michael Berry (text)

Sir Michael Victor Berry is a professor of physics at the University of Bristol. He specializes in semi-classical optics (asymptotic physics and quantum chaos) applied to wave phenomena in quantum mechanics, and other areas such as optics. He is famous for the Berry phase, which is a geometric phase observed

Ars Magna

Solving The Cubic

People have been in an attempt to find roots of polynomials since a very long time. They may not have had a very concrete notion of a polynomial and may have been trying to solve some specific polynomials rather than solving some general polynomials. The quadratic equation was solved by

Berry

An Interview with Professor Sir Michael Berry

Professor Sir Michael Berry, eminent physicist, visited Chennai Mathematical Institute in April, early this year. I along with some of my friends had an opportunity to interview him. The text of the interview can be found here. Below is the interview from the CMI Youtube channel.

Equilateral Triangle

An Equilateral Triangle Inside a Square

This is an article on an olympiad problem. Here we present various solutions of the problem. We show the beauty of this problem by presenting different proofs to the same problem. The Problem Statement: – is a square. is a point inside the square such that . Show that is equilateral. A

Clocks

Some Commonly Occuring Clock Problems

Clock Problems are often seen in several aptitude test papers. The underlying principles are basic modular arithmetic although the questions may seem to be confusing at times. Some of the questions below keep coming in many different exams. We provide a list of basic facts needed to solve clock problems.

2015

2015 ICTP Ramanujan Prize goes to Amalendu Krishna

The ICTP Ramanujan Prize has been awarded since 2005 to mathematicians below the age of 45 from developing countries who have made a fundamental contribution to mathematics at an early age. It was originally instituted by ICTP, the Niels Henrik Abel Memorial Fund, and the International Mathematical Union (IMU). The

Sylow Theorems

Exceptional Embedding of S5 in S6

In this article we shall show a peculiar property of . We first note that there are several subgroups of isomorphic to . In fact there is one for each Let . All of the above subgroups have two orbits in . But for we show that there is a seventh embedding of which

A Short Note on Certain Vector Spaces Associated with Finite Groups

Throughout this article is a finite group. 1. Free vector space generated by : Given a field we take the set of all formal linear combinations of form where . We define addition on the set as and scalar multiplication as for all . We take to be the zero in the set.

norms

Norm Induced Topologies on Finite Dimensional Real Vector Spaces

In this article we show that the topology induced by a norm on a finite dimensional real vector space is an intrinsic topology irrespective of the norm. It is equivalent for all norms. Let V be a finite dimensional vector space over $$mathbb{R}$$ with dimension n. Let $$mathscr{B}

M. Satyanarayan

Morley's Theorem

INTRODUCTION: One of the most elementary theorems in elementary geometry was discovered about 1899 by F. Morley (whose son Cristopher wrote novels such as Thunder on the Left). He mentioned it to his friends, who spread it over the world in the form of mathematical gossip. At last, after ten