Facets 2015

A two-day mathematics program

Poster PDF (621 KB)

Abstracts PDF (55 KB)

This programme was targeted mainly at advanced undergraduate (BSc third year) and postgraduate (MSc) students of mathematics. However, anybody with an interest and background in college level mathematics (from student to senior professor) was welcome to apply to participate. In particular, summer interns, research scholars, and postdocs in any scientific or engineering discipline (with some liking and aptitude for mathematics) were encouraged to apply.

The programme featured six talks, a video screening, and a panel discussion.

• Videos (of the lectures and the panel discussion)

• Pictures: Day 1 and day 2

Talks:

Some Algorithmic questions in Finite Group Theory

V Arvind (IMSc)

A theorem of Jordan tells us that any transitive subgroup of the symmetric group has a fixed point free element. How efficiently can we find such an element if the subgroup is given by a generating set? We discuss algorithms for this and related questions.

The talk is primarily aimed at BSc/MSc students, and is meant as an invitation to algorithms concerning finite groups.

• Tuesday 30th June, 11:30am to 12:45pm
• Chair: Meena Mahajan

Slides PDF (430 KB)

Power and Limitations of Opinion Polls

Rajeeva Karandikar (CMI)

How can obtaining opinions of say 30,000 voters be sufficient to predict the outcome of an election in a country with over 60 crore voters? Can opinion polls conducted say a month before the election accurately predict what is to happen on voting day?

We will address such questions and show that simple mathematics and statistics, lots of common sense and a good understanding of the ground reality or domain knowledge together can yield very good forecast or predictions of the outcome of elections based on opinion polls and exit polls. I will share my own experiences with such polls over the last 15 years.

• Tuesday 30th June, 02:00pm to 03:15pm
• Chair: S Kesavan

Slides PDF (212 KB)

Knotted or not?

Vijay Kodiyalam (IMSc)

What is a knot? When are two knots "the same"? How do we determine whether two knots are the same or different? In this talk we will explore such questions with particular emphasis on the Jones polynomial—a Laurent polynomial invariant of knots or links—introduced about 30 years ago, which created a revolution in the field of knot theory.

• Monday 29th June, 11:30am to 12:45pm
• Chair: V S Sunder

Contagion: Modelling Infectious Diseases

Gautam Menon (IMSc)

Mathematical models play a crucial role in understanding how infectious diseases, such as Ebola, flu, measles, tuberculosis and AIDS, spread within a population. They also help decide the strategies that public health officials and governments must use in response to outbreaks. I will motivate the general study of models of infectious diseases from a historical perspective, describe some of these models very simply and then explain how they have been used and continue to be used in real-life situations. Studies of such models lie at the interface of applied mathematics, data science, bio-statistics and public policy, providing an interesting example of how, in some cases, improved mathematical methods can really make the difference between life and death.

• Monday 29th June, 03:45pm tp 05:00pm
• Chair: Krishna Maddaly

Slides PDF (27 MB)

Mathematics, Measurement and Information Technology

M Ram Murty (Queen's University)

• Monday 29th June, 09:45am to 11:00am
• Chair: R Balasubramanian

In this talk, we will highlight the importance of measurement, discuss what can and cannot be measured. Focusing on the measurement of position, importance, and shape, we illustrate by dicussing the mathematics behind GPS, Google and laser surgery. The talk will be accessible to a wide audience.

Slides PDF (2.9 MB)

Shapes and Connectivity

Harish Seshadri (IISc)

• Tuesday 30th June, 09:45am to 11:00am
• Chair: Parameswaran Sankaran

Abstract: I'll try to describe some elementary aspects of differential geometry (which deals with shapes of spaces) and topology (which is concerned with connectivity of spaces). More specifically, I'll discuss the fundamental notion of curvature of curves and surfaces and how it influences the connectivity of the underlying space.

Video from IMSc archives of a talk given by Joseph Oesterle (Paris VI) at the golden jubilee celebrations of IMSc.

Title: Some simple open problems in Mathematics (click for video)

Panel discussion on Prospects in Mathematics.

Panelists: Ronojoy Adhikari (IMSc), Rajeeva Karandikar (CMI), and S Kesavan (IMSc).

• Tuesday 30th June, 345–500pm
• Chair: R Ramanujam

Slides PDF (663 KB) of the presentation by Ronojoy Adhikari on "Applications of Mathematics"

Slides PDF (78 KB) of the presentation by Rajeeva Karandikar on "Opportunities for Mathematicians in the Real World"

The programme was free. No fee of any kind was charged. Free lunch and snacks were provided.

Participation was by online registration. There were also some "spot" registrations (which were allowed because there was room). The number of participants was 182 on the first day, 135 on the second. Participants had to make their own arrangements for travel to Chennai and for their stay. No reimbursement or even help towards stay was offered by the organizers.

Schedule

Monday, 29th June 2015

Tuesday, 30th June 2015