Ramanujan Auditorium,  IMSc,  Chennai

Monday 01st July 2013

0830 -- 0915 	Registration

0915 -- 0930	Inauguration,  opening remarks
		R Balasubramanian,  Director, IMSc
		N Mukunda, for the Science Academies
		K N Raghavan,  Convener of the programme

0930 -- 1030	S Kesavan "On the spectrum of the Laplacian" 	projector + chalk
		chair: N Mukunda

		Abstract: We will discuss various properties of the eigenvalues and 
		eigenfuctions of the Laplacian and open problems connected to them.
	
1030 -- 1130	M. D. Srinivas "The cakravala method for solving quadratic indeterminate equations"  projector + chalk
		chair: N Mukunda

		Abstract: We shall present an outline of the cakravala method as discussed
		by Bhaskara.  We shall also summarise the analysis by Krishnaswamy Ayyangar,
		who has recast the method in a simpler form that can perhaps be taught
		to students even at the high school level.

1130 -- 1200 	Tea, Coffee, biscuits

1200 -- 1300	Mahan Mj  "Shapes and geometry of surfaces"	projector
		chair: Parameswaran Sankaran

		Abstract: Almost all shapes that we see around in space are examples
		of surfaces. We shall describe a method dating back to the 19th century
		of understanding these. We shall begin by trying to answer the following
		question: What is the domain of applicability of calculus?
		Time-permitting, we shall describe more sophisticated geometric
		structures on surfaces.
		
1300 -- 1400	Lunch

1400 -- 1500	Manoj Kummini "From linear algebra to robotic arm design via Groebner bases"  chalk 
		chair: Jugal Verma 

		Abstract: We will give a brief introduction to Groebner bases, with an
		application to automatic geometric theorem proving and to robotics.

1500 -- 1530	Tea, coffee

1530 -- 1730	Panel discussion:  Prospects in Mathematics
		Rajeeva Karandikar,  R. Ramanujam (anchor),  Jugal Verma 

1730 -- 1800	High tea (tea, coffee, sweet, savoury)

1800 -- 1900	Documetary film:  the genius of Srinivasa Ramanujan
		anchor:  A. Raghuram 	director: Nandan Kudhyadi
		co-produced by Vigyan Prasar and IISER-Pune

Tuesday 02nd July 2013

0930 -- 1030	Ronojoy Adhikari "Nuclear safety and the mathematical quantification of risk" 	projector
		chair: Krishna Maddaly

		Abstract : In our personal and public lives we are daily faced with choices which carry both
		rewards and penalties. We are guided in making such choices by an intuitive notion of risk,
		preferring choices which carry lower risks. I will demonstrate how this intuitive notion of risk
		is made quantitative by using Bayesian probability and the concept of utility. I will then
		show how this mathematical notion of risk is used in estimating the safety of technology
		such as aircrafts and nuclear reactors, whose safe operation brings great reward but
		whose failure brings, equally, great penalties. 

1030 -- 1130	Purusottam Rath "Analysis, transcendence, and arithmetic"   chalk
		chair: D S Nagaraj

		Abstract: We shall indicate the relevance of complex analysis in elliptic transcendence theory.
		Time permitting, we shall try to indicate how these seemingly transcendental techniques
		apply to arithmetic questions.

1130 -- 1200	Tea, coffee, biscuits

1200 -- 1300	Partha Mukhopadhyay "Determinant and Permanent" 	chalk
		chair: Meena Mahajan

		Abstract: Two polynomials are of fundamental interest in theoretical computer science:
		Determinant and Permanent. While Determinant is a very well-understood polynomial in mathematics,
		very little is known about Permanent. A long standing conjecture of Valiant says that
		Permanent can not be computed by determinant of small-size matrices. We will discuss
		one of the most important and recent results towards settling the conjecture.  

1300 -- 1400	Lunch

1400 -- 1500	T E Venkata Balaji "Imagine a sky filled with stars most of whom you cannot see"  chalk
		chair: G Youvaraj

		Abstract: Though transcendental numbers like e and pi (like stars) almost fill up the real line
		(likened to the sky), we can't list most of them explicitly in a satisfactory manner.
		Even the question whether a given real number is transcendental is not answered
		for many naturally arising numbers, like Euler's constant and the value of Riemann's
		zeta function at 3. The talk is aimed to indicate a few proofs of transcendentality
		to show how many areas of Mathematics are beautifully involved in such questions,
		and also to show how little we know about these numbers, thereby driving the point of
		view that their study has been and remains one of the most fundamental frontiers of Mathematics
		beyond which teem a myriad of unanswered mysteries.

1500 -- 1530	Tea, coffee

1530 -- 1700	Amrithanshu Prasad "Using online resources to learn Mathematics" 	projector 
		chair: Meena Mahajan

		Abstract: I will discuss various online resources for learning mathematics:
		MOOC's, video-sharing sites, stackexchange, wikipedia and so on.
		Participants can also share their favorite online mathematics resources with others.

1715		Tea, coffee, snack