Facets 2020

Name: Facets 2020
Start: 2020-10-12T19:00
End: 2020-10-15T20:00
Location: Online

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.

Schedule

Time	Event
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.