Facets 2020

Mathematics lecture series

Organized by The Institute of Mathematical Sciences, Chennai

Venue: Online
Dates: 12--15 October 2020
Time: 1900--2000 IST

This is the 2020 edition of the institute's outreach program for advanced undergraduate (BSc third year) and postgraduate (MSc) students of mathematics.

However, students in other scientific or engineering disciplines with a background in college level mathematics can also attend.

The videos of the program are now available here.

The lectures:

12th October
1900--2000 IST
The cycle structure of permutations
Amritanshu Prasad, IMSc

A permutation of n objects is simply a rearrangement, such as the shuffling of a deck of cards. By tracking through the positions of each object upon repeated application of this rearrangement, we can visualize a permutation as a union of cycles. In this session we shall explore combinatorial and statistical properties of cycles in permutations.

13th October
1900--2000 IST
Codes, Computations and Constraints in Cosmology
Dhiraj Kumar Hazra, IMSc

The observable Universe has been expanding since the Big Bang. Based on several independent observations and certain theoretical assumptions, we are able to reconstruct this evolution of our Universe. Starting with a basic theory and simple codes, I will present a coherent picture to describe the process of constraining this evolution.

14th October
1900--2000 IST
Primes via probability
Anirban Mukhopadhyay, IMSc

In 1936, Harald Cramer proposed a simple probabilistic model for primes which makes various predictions about distribution of primes. In this talk we would discuss this probabilistic model and some of its consequences. Although several of these predictions have been proved or strongly believed to be true, there are known results that violate the predictive regular behavior, hinting at deeper mysteries.

15th October
1900--2000 IST
Determining if two bit strings are identical
Meena Mahajan, IMSc

Two people need to decide whether the files they have are identical. They are at distant locations, and communication between them is extremely expensive. How many bits do they really need to communicate? What if they are willing to settle for a randomised correct-with-high-probability decision? Communication complexity provides some surprising answers.

Links to upcoming and past outreach events (including videos, slides and notes) may be found here.

For any other queries, email us: outreach@imsc.res.in